वर्गमूल सर्पिल में यदि पिछले कर्ण की लंबाई \(\sqrt{80}\) है और नई लंब (1) इकाई है, तो नया कर्ण किस सटीक मान पर स्थित होगा?
In a square root spiral, if the previous hypotenuse is \(\sqrt{80}\) and the new perpendicular is (1) unit, at what exact value will the new hypotenuse lie?
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A \(\sqrt{81}=9\)
B \(\sqrt{79}\)
C \(\sqrt{160}\)
D \(\sqrt{82}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{81}=9\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{80+1}=\sqrt{81}\) होगा। \(\sqrt{81}=9\), इसलिए पूर्ण वर्ग पर सटीक मान लिखें। / The new hypotenuse is \(\sqrt{80+1}=\sqrt{81}\). Since \(\sqrt{81}=9\), write the exact value at a perfect square.
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वर्गमूल सर्पिल में \(\sqrt{48}\) और \(\sqrt{50}\) की संख्या-रेखा स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the number-line positions of \(\sqrt{48}\) and \(\sqrt{50}\) in a square root spiral is correct?
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A \(\sqrt{48}\) और \(\sqrt{50}\) दोनों (6) और (7) के बीच हैं / Both \(\sqrt{48}\) and \(\sqrt{50}\) lie between (6) and (7)
B \(\sqrt{48}\) (6) और (7) के बीच है, \(\sqrt{50}\) (7) और (8) के बीच है / \(\sqrt{48}\) lies between (6) and (7), \(\sqrt{50}\) lies between (7) and (8)
C \(\sqrt{48}=7\) और \(\sqrt{50}\) अपरिमेय है / \(\sqrt{48}=7\) and \(\sqrt{50}\) is irrational
D दोनों ठीक (7) पर हैं / Both are exactly at (7)
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Correct Answer
B. \(\sqrt{48}\) (6) और (7) के बीच है, \(\sqrt{50}\) (7) और (8) के बीच है / \(\sqrt{48}\) lies between (6) and (7), \(\sqrt{50}\) lies between (7) and (8)
Explanation
Simple Explanation
क्योंकि \(6^2<48<7^2\) और \(7^2<50<8^2\) है। अंतराल तय करते समय निकटतम पूर्ण वर्ग देखें। / Because \(6^2<48<7^2\) and \(7^2<50<8^2\). Check nearest perfect squares while deciding intervals.
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यदि किसी विद्यार्थी ने \(\sqrt{12}\) से अगला कर्ण निकालते समय \(\sqrt{12}+1=\sqrt{13}\) लिखा, तो सही सुधार क्या होगा?
If a student writes \(\sqrt{12}+1=\sqrt{13}\) while finding the next hypotenuse from \(\sqrt{12}\), what is the correct correction?
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A \(\sqrt{12}+1=\sqrt{24}\) लिखना चाहिए / We should write \(\sqrt{12}+1=\sqrt{24}\)
B \(\sqrt{12}-1=\sqrt{13}\) लिखना चाहिए / We should write \(\sqrt{12}-1=\sqrt{13}\)
C (\sqrt{\(\sqrt{12}\)2 +12 }=\sqrt{13}) लिखना चाहिए / We should write (\sqrt{\(\sqrt{12}\)2 +12 }=\sqrt{13})
D \(\sqrt{12^2+1^2}=\sqrt{13}\) लिखना चाहिए / We should write \(\sqrt{12^2+1^2}=\sqrt{13}\)
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Correct Answer
C. (\sqrt{\(\sqrt{12}\)2 +12 }=\sqrt{13}) लिखना चाहिए / We should write (\sqrt{\(\sqrt{12}\)2 +12 }=\sqrt{13})
Explanation
Simple Explanation
वर्गमूल सर्पिल में सीधे लंबाइयाँ नहीं जोड़ी जातीं। सही विधि पाइथागोरस प्रमेय से वर्गों का योग लेना है। / Lengths are not added directly in a square root spiral. The correct method is to add squares using Pythagoras theorem.
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वर्गमूल सर्पिल में \(\sqrt{143}\) पर (1) इकाई लंब बनाने से कौन-सा कर्ण बनेगा और उसका मान कहाँ होगा?
In a square root spiral, drawing a (1) unit perpendicular on \(\sqrt{143}\) forms which hypotenuse and where will its value lie?
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A \(\sqrt{142}\), (11) और (12) के बीच / \(\sqrt{142}\), between (11) and (12)
B \(\sqrt{144}\), (11) और (12) के बीच / \(\sqrt{144}\), between (11) and (12)
C \(\sqrt{286}\), (16) और (17) के बीच / \(\sqrt{286}\), between (16) and (17)
D \(\sqrt{144}\), ठीक (12) पर / \(\sqrt{144}\), exactly at (12)
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Correct Answer
D. \(\sqrt{144}\), ठीक (12) पर / \(\sqrt{144}\), exactly at (12)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{144}\) है। क्योंकि \(\sqrt{144}=12\), यह किसी अंतराल में नहीं बल्कि ठीक (12) पर है। / The new hypotenuse is \(\sqrt{144}\). Since \(\sqrt{144}=12\), it is not in an interval but exactly at (12).
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वर्गमूल सर्पिल में \(\sqrt{35}\) बनाने के लिए कौन-सा पिछला कर्ण और नई लंब भुजा सही है?
To construct \(\sqrt{35}\) in a square root spiral, which previous hypotenuse and new perpendicular side are correct?
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#construction
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A \(\sqrt{34}\) और (1) / \(\sqrt{34}\) and (1)
B \(\sqrt{33}\) और (2) / \(\sqrt{33}\) and (2)
C \(\sqrt{35}\) और (1) / \(\sqrt{35}\) and (1)
D \(\sqrt{36}\) और (1) / \(\sqrt{36}\) and (1)
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Correct Answer
A. \(\sqrt{34}\) और (1) / \(\sqrt{34}\) and (1)
Explanation
Simple Explanation
(\(\sqrt{34}\)2 +12 =35) होता है। इसलिए \(\sqrt{35}\) के लिए पिछला कर्ण \(\sqrt{34}\) होगा। / Since (\(\sqrt{34}\)2 +12 =35). Therefore the previous hypotenuse for \(\sqrt{35}\) is \(\sqrt{34}\).
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वर्गमूल सर्पिल में \(\sqrt{98}\) और \(\sqrt{100}\) के बीच \(\sqrt{99}\) का स्थान समझने के लिए कौन-सा कथन सही है?
Which statement is correct for understanding the position of \(\sqrt{99}\) between \(\sqrt{98}\) and \(\sqrt{100}\) in a square root spiral?
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A \(\sqrt{99}=10\)
B \(\sqrt{99}\) (9) और (10) के बीच है / \(\sqrt{99}\) lies between (9) and (10)
C \(\sqrt{99}\) (10) और (11) के बीच है / \(\sqrt{99}\) lies between (10) and (11)
D \(\sqrt{99}\) पूर्ण संख्या है / \(\sqrt{99}\) is a whole number
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Correct Answer
B. \(\sqrt{99}\) (9) और (10) के बीच है / \(\sqrt{99}\) lies between (9) and (10)
Explanation
Simple Explanation
क्योंकि \(9^2<99<10^2\) है। \(\sqrt{100}=10\) है, इसलिए \(\sqrt{99}\) उससे थोड़ा कम है। / Because \(9^2<99<10^2\). Since \(\sqrt{100}=10\), \(\sqrt{99}\) is slightly less than it.
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यदि वर्गमूल सर्पिल में नई लंब (1) इकाई की जगह (5) इकाई ले ली जाए, तो \(\sqrt{n}\) से बनने वाला कर्ण किस रूप का होगा?
If the new perpendicular is taken as (5) units instead of (1) unit in a square root spiral, what form will the hypotenuse from \(\sqrt{n}\) have?
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A \(\sqrt{n+1}\)
B \(\sqrt{n+5}\)
C \(\sqrt{n+25}\)
D \(\sqrt{5n}\)
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Correct Answer
C. \(\sqrt{n+25}\)
Explanation
Simple Explanation
पाइथागोरस से (\(\sqrt{n}\)2 +52 =n+25) होगा। इसलिए सामान्य \(\sqrt{n+1}\) क्रम टूट जाएगा। / By Pythagoras, (\(\sqrt{n}\)2 +52 =n+25). So the usual \(\sqrt{n+1}\) sequence will break.
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वर्गमूल सर्पिल में यदि नया कर्ण \(\sqrt{226}\) है, तो उससे ठीक पहले कौन-सा कर्ण था और नया मान किस अंतराल में है?
If the new hypotenuse in a square root spiral is \(\sqrt{226}\), what was the immediately previous hypotenuse and in which interval does the new value lie?
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A \(\sqrt{224}\), (14) और (15) के बीच / \(\sqrt{224}\), between (14) and (15)
B \(\sqrt{225}\), (15) और (16) के बीच / \(\sqrt{225}\), between (15) and (16)
C \(\sqrt{226}\), (15) और (16) के बीच / \(\sqrt{226}\), between (15) and (16)
D \(\sqrt{227}\), (16) और (17) के बीच / \(\sqrt{227}\), between (16) and (17)
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Correct Answer
B. \(\sqrt{225}\), (15) और (16) के बीच / \(\sqrt{225}\), between (15) and (16)
Explanation
Simple Explanation
\(\sqrt{226}\) से पहले \(\sqrt{225}\) था। क्योंकि \(15^2<226<16^2\), नया मान (15) और (16) के बीच है। / Before \(\sqrt{226}\), the previous hypotenuse was \(\sqrt{225}\). Since \(15^2<226<16^2\), the new value lies between (15) and (16).
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वर्गमूल सर्पिल में \(\sqrt{3}\) से \(\sqrt{4}\) बनाते समय किस कथन में तर्क की गलती है?
While forming \(\sqrt{4}\) from \(\sqrt{3}\) in a square root spiral, which statement contains a logical error?
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A (\(\sqrt{3}\)2 +12 =4)
B \(\sqrt{3}\) और (1) समकोण भुजाएँ हैं / \(\sqrt{3}\) and (1) are right-angle sides
C \(\sqrt{3}+1=\sqrt{4}\)
D नया कर्ण \(\sqrt{4}\) है / The new hypotenuse is \(\sqrt{4}\)
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Correct Answer
C. \(\sqrt{3}+1=\sqrt{4}\)
Explanation
Simple Explanation
नया कर्ण सीधे \(\sqrt{3}+1\) से नहीं मिलता। सही आधार भुजाओं के वर्गों का योग है। / The new hypotenuse is not obtained directly from \(\sqrt{3}+1\). The correct basis is the sum of squares of sides.
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वर्गमूल सर्पिल में \(\sqrt{168}\) के बाद अगला कर्ण किस विशेष कारण से सरल हो जाता है?
In a square root spiral, why does the next hypotenuse after \(\sqrt{168}\) simplify specially?
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A \(\sqrt{169}\) बनता है और (169) पूर्ण वर्ग है / \(\sqrt{169}\) is formed and (169) is a perfect square
B \(\sqrt{167}\) बनता है और (167) पूर्ण वर्ग है / \(\sqrt{167}\) is formed and (167) is a perfect square
C \(\sqrt{336}\) बनता है और (336) पूर्ण वर्ग है / \(\sqrt{336}\) is formed and (336) is a perfect square
D \(\sqrt{168}\) ही रहता है / It remains \(\sqrt{168}\)
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Correct Answer
A. \(\sqrt{169}\) बनता है और (169) पूर्ण वर्ग है / \(\sqrt{169}\) is formed and (169) is a perfect square
Explanation
Simple Explanation
\(\sqrt{168}\) के बाद \(\sqrt{169}\) बनता है। \(169=13^2\) होने से कर्ण का मान (13) है। / After \(\sqrt{168}\), \(\sqrt{169}\) is formed. Since \(169=13^2\), the hypotenuse value is (13).
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वर्गमूल सर्पिल में \(\sqrt{242}\) और \(\sqrt{256}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{242}\) and \(\sqrt{256}\) in a square root spiral?
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A \(\sqrt{242}\) (14) और (15) के बीच है, \(\sqrt{256}=16\) है / \(\sqrt{242}\) is between (14) and (15), \(\sqrt{256}=16\)
B \(\sqrt{242}\) (15) और (16) के बीच है, \(\sqrt{256}=16\) है / \(\sqrt{242}\) is between (15) and (16), \(\sqrt{256}=16\)
C \(\sqrt{242}=16\), \(\sqrt{256}\) अपरिमेय है / \(\sqrt{242}=16\), \(\sqrt{256}\) is irrational
D दोनों (16) से बड़े हैं / Both are greater than (16)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{242}\) (15) और (16) के बीच है, \(\sqrt{256}=16\) है / \(\sqrt{242}\) is between (15) and (16), \(\sqrt{256}=16\)
Explanation
Simple Explanation
क्योंकि \(15^2<242<16^2\) और \(256=16^2\) है। इसलिए \(\sqrt{242}\) (16) से कम है। / Because \(15^2<242<16^2\) and \(256=16^2\). Therefore \(\sqrt{242}\) is less than (16).
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वर्गमूल सर्पिल में \(\sqrt{15}\) कर्ण पर (1) इकाई लंब बनाने से नया कर्ण बनने पर कौन-सा निष्कर्ष सही है?
In a square root spiral, after drawing a (1) unit perpendicular on hypotenuse \(\sqrt{15}\), which conclusion about the new hypotenuse is correct?
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A नया कर्ण \(\sqrt{30}\) है और अपरिमेय है / The new hypotenuse is \(\sqrt{30}\) and irrational
B नया कर्ण \(\sqrt{14}\) है और अपरिमेय है / The new hypotenuse is \(\sqrt{14}\) and irrational
C नया कर्ण \(\sqrt{16}\) है और (4) के बराबर है / The new hypotenuse is \(\sqrt{16}\) and equals (4)
D नया कर्ण \(\sqrt{15}+1\) है / The new hypotenuse is \(\sqrt{15}+1\)
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Correct Answer
C. नया कर्ण \(\sqrt{16}\) है और (4) के बराबर है / The new hypotenuse is \(\sqrt{16}\) and equals (4)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{15+1}=\sqrt{16}\) होगा। \(\sqrt{16}=4\), इसलिए यह पूर्ण संख्या है। / The new hypotenuse is \(\sqrt{15+1}=\sqrt{16}\). Since \(\sqrt{16}=4\), it is a whole number.
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वर्गमूल सर्पिल में \(\sqrt{125}\) की स्थिति पहचानने के लिए कौन-सी असमानता सही है?
Which inequality is correct to identify the position of \(\sqrt{125}\) in a square root spiral?
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A \(,10^2<125<11^2,\)
B \(,11^2<125<12^2,\)
C \(,12^2<125<13^2,\)
D \(,13^2<125<14^2,\)
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Correct Answer
B. \(,11^2<125<12^2,\)
Explanation
Simple Explanation
(121<125<144) है। इसलिए \(\sqrt{125}\) (11) और (12) के बीच होगा। / Since (121<125<144). Therefore \(\sqrt{125}\) lies between (11) and (12).
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वर्गमूल सर्पिल में यदि \(\sqrt{n}\) के बाद बना कर्ण पूर्ण संख्या (20) है, तो (n) का मान क्या था?
In a square root spiral, if the hypotenuse formed after \(\sqrt{n}\) is the whole number (20), what was the value of (n)?
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A (399)
B (400)
C (401)
D (20)
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Explanation
Simple Explanation
नया कर्ण \(20=\sqrt{400}\) है। इसलिए (n+1=400), अतः (n=399)। / The new hypotenuse is \(20=\sqrt{400}\). Therefore (n+1=400), so (n=399).
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वर्गमूल सर्पिल में \(\sqrt{8}\) को \(\sqrt{7}\) और (1) से बनाने का सही कारण कौन-सा है?
What is the correct reason for constructing \(\sqrt{8}\) from \(\sqrt{7}\) and (1) in a square root spiral?
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#hard
#pythagoras
#construction
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A (\(\sqrt{7}\)2 +12 =8)
B \(\sqrt{7}+1=\sqrt{8}\)
C (\(\sqrt{7}\)2 +22 =8)
D \(\sqrt{7}\times1=\sqrt{8}\)
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Correct Answer
A. (\(\sqrt{7}\)2 +12 =8)
Explanation
Simple Explanation
पाइथागोरस प्रमेय से भुजाओं के वर्ग जुड़ते हैं। इसलिए \(\sqrt{7}\) और (1) से कर्ण \(\sqrt{8}\) बनता है। / By Pythagoras theorem, the squares of sides are added. Therefore \(\sqrt{7}\) and (1) form hypotenuse \(\sqrt{8}\).
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वर्गमूल सर्पिल में \(\sqrt{63}\) के बाद बने कर्ण और \(\sqrt{65}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the hypotenuse formed after \(\sqrt{63}\) and \(\sqrt{65}\) in a square root spiral?
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#comparison
#perfect-square
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A अगला कर्ण \(\sqrt{64}=8\) है और \(\sqrt{65}\) (8) और (9) के बीच है / The next hypotenuse is \(\sqrt{64}=8\), and \(\sqrt{65}\) is between (8) and (9)
B अगला कर्ण \(\sqrt{64}\) है और \(\sqrt{65}=8\) है / The next hypotenuse is \(\sqrt{64}\), and \(\sqrt{65}=8\)
C दोनों ठीक (8) पर हैं / Both are exactly at (8)
D दोनों (7) और (8) के बीच हैं / Both lie between (7) and (8)
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Correct Answer
A. अगला कर्ण \(\sqrt{64}=8\) है और \(\sqrt{65}\) (8) और (9) के बीच है / The next hypotenuse is \(\sqrt{64}=8\), and \(\sqrt{65}\) is between (8) and (9)
Explanation
Simple Explanation
\(\sqrt{63}\) के बाद \(\sqrt{64}=8\) बनता है। \(8^2<65<9^2\), इसलिए \(\sqrt{65}\) (8) और (9) के बीच है। / After \(\sqrt{63}\), \(\sqrt{64}=8\) is formed. Since \(8^2<65<9^2\), \(\sqrt{65}\) lies between (8) and (9).
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वर्गमूल सर्पिल में किसी चरण पर कर्ण \(\sqrt{m}\) है। यदि (m) पूर्ण वर्ग से ठीक (1) कम है, तो अगला कर्ण कैसा होगा?
At a step in a square root spiral, the hypotenuse is \(\sqrt{m}\). If (m) is exactly (1) less than a perfect square, what will the next hypotenuse be like?
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A हमेशा अपरिमेय / Always irrational
B हमेशा पूर्ण संख्या / Always a whole number
C हमेशा शून्य / Always zero
D हमेशा \(\sqrt{m}\) ही / Always \(\sqrt{m}\) itself
Explanation opens after your attempt
Correct Answer
B. हमेशा पूर्ण संख्या / Always a whole number
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{m+1}\) होगा। यदि (m+1) पूर्ण वर्ग है, तो उसका वर्गमूल पूर्ण संख्या होगा। / The next hypotenuse is \(\sqrt{m+1}\). If (m+1) is a perfect square, its square root is a whole number.
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वर्गमूल सर्पिल में \(\sqrt{288}\) का सही स्थान कौन-सा है?
What is the correct position of \(\sqrt{288}\) in a square root spiral?
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#number-line
#interval
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A \(15<\sqrt{288}<16\)
B \(16<\sqrt{288}<17\)
C \(17<\sqrt{288}<18\)
D \(18<\sqrt{288}<19\)
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Correct Answer
B. \(16<\sqrt{288}<17\)
Explanation
Simple Explanation
क्योंकि \(16^2=256\) और \(17^2=289\) हैं। (288) इनके बीच है, इसलिए \(\sqrt{288}\) (16) और (17) के बीच है। / Because \(16^2=256\) and \(17^2=289\). The number (288) lies between them, so \(\sqrt{288}\) lies between (16) and (17).
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वर्गमूल सर्पिल में \(\sqrt{48}\) बनाने के लिए \(\sqrt{46}\) और (2) इकाई लंब का प्रयोग सामान्य नियम में क्यों गलत है?
Why is using \(\sqrt{46}\) and a (2) unit perpendicular wrong for constructing \(\sqrt{48}\) by the usual rule of square root spiral?
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#construction
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A क्योंकि सामान्य नियम में नई लंब (1) इकाई होती है और पिछला कर्ण \(\sqrt{47}\) होना चाहिए / Because in the usual rule the new perpendicular is (1) unit and the previous hypotenuse should be \(\sqrt{47}\)
B क्योंकि \(\sqrt{46}\) बन ही नहीं सकता / Because \(\sqrt{46}\) cannot be constructed
C क्योंकि (2) इकाई लंब से समकोण नहीं बनता / Because a (2) unit perpendicular cannot make a right angle
D क्योंकि \(\sqrt{48}\) पूर्ण संख्या है / Because \(\sqrt{48}\) is a whole number
Explanation opens after your attempt
Correct Answer
A. क्योंकि सामान्य नियम में नई लंब (1) इकाई होती है और पिछला कर्ण \(\sqrt{47}\) होना चाहिए / Because in the usual rule the new perpendicular is (1) unit and the previous hypotenuse should be \(\sqrt{47}\)
Explanation
Simple Explanation
सामान्य वर्गमूल सर्पिल में हर बार (1) इकाई लंब जोड़ी जाती है। \(\sqrt{48}\) के लिए पिछला कर्ण \(\sqrt{47}\) होता है। / In the usual square root spiral, a (1) unit perpendicular is added every time. For \(\sqrt{48}\), the previous hypotenuse is \(\sqrt{47}\).
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वर्गमूल सर्पिल में \(\sqrt{300}\) और \(\sqrt{324}\) की स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the positions of \(\sqrt{300}\) and \(\sqrt{324}\) in a square root spiral is correct?
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A \(\sqrt{300}\) (16) और (17) के बीच है, \(\sqrt{324}=18\) है / \(\sqrt{300}\) is between (16) and (17), \(\sqrt{324}=18\)
B \(\sqrt{300}\) (17) और (18) के बीच है, \(\sqrt{324}=18\) है / \(\sqrt{300}\) is between (17) and (18), \(\sqrt{324}=18\)
C \(\sqrt{300}=18\) और \(\sqrt{324}\) अपरिमेय है / \(\sqrt{300}=18\) and \(\sqrt{324}\) is irrational
D दोनों (17) और (18) के बीच हैं / Both lie between (17) and (18)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{300}\) (17) और (18) के बीच है, \(\sqrt{324}=18\) है / \(\sqrt{300}\) is between (17) and (18), \(\sqrt{324}=18\)
Explanation
Simple Explanation
क्योंकि \(17^2<300<18^2\) और \(324=18^2\) है। इसलिए \(\sqrt{324}\) ठीक (18) है। / Because \(17^2<300<18^2\) and \(324=18^2\). Therefore \(\sqrt{324}\) is exactly (18).
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वर्गमूल सर्पिल में यदि नया कर्ण \(\sqrt{n+1}\) है और यह पूर्ण संख्या (12) है, तो पिछला कर्ण कौन-सा था?
In a square root spiral, if the new hypotenuse is \(\sqrt{n+1}\) and it is the whole number (12), what was the previous hypotenuse?
#square-root-spiral
#hard
#reverse-rule
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A \(\sqrt{142}\)
B \(\sqrt{143}\)
C \(\sqrt{144}\)
D \(\sqrt{145}\)
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Correct Answer
B. \(\sqrt{143}\)
Explanation
Simple Explanation
नया कर्ण \(12=\sqrt{144}\) है, इसलिए (n+1=144)। अतः पिछला कर्ण \(\sqrt{143}\) था। / The new hypotenuse is \(12=\sqrt{144}\), so (n+1=144). Therefore the previous hypotenuse was \(\sqrt{143}\).
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वर्गमूल सर्पिल में \(\sqrt{10}\) बनाने के लिए निम्न में से कौन-सा क्रम सबसे सही है?
Which of the following sequences is most correct for constructing \(\sqrt{10}\) in a square root spiral?
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#sequence
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A \(\sqrt{8}\rightarrow\sqrt{9}\rightarrow\sqrt{10}\)
B \(\sqrt{7}\rightarrow\sqrt{9}\rightarrow\sqrt{10}\)
C \(\sqrt{9}\rightarrow\sqrt{11}\rightarrow\sqrt{10}\)
D \(\sqrt{10}\rightarrow\sqrt{9}\rightarrow\sqrt{8}\)
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Correct Answer
A. \(\sqrt{8}\rightarrow\sqrt{9}\rightarrow\sqrt{10}\)
Explanation
Simple Explanation
सर्पिल में कर्ण क्रम से बढ़ते हैं। \(\sqrt{10}\) से ठीक पहले \(\sqrt{9}\) और उससे पहले \(\sqrt{8}\) आता है। / The hypotenuses increase in order in the spiral. Just before \(\sqrt{10}\) comes \(\sqrt{9}\), and before that \(\sqrt{8}\).
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वर्गमूल सर्पिल में \(\sqrt{195}\) का अंतराल पहचानते समय कौन-सी गलती सबसे अधिक संभव है?
While identifying the interval of \(\sqrt{195}\) in a square root spiral, which mistake is most likely?
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A \(\sqrt{195}\) को (13) और (14) के बीच रखने की गलती / Mistakenly placing \(\sqrt{195}\) between (13) and (14)
B \(\sqrt{195}\) को (14) और (15) के बीच रखने की गलती / Mistakenly placing \(\sqrt{195}\) between (14) and (15)
C \(\sqrt{195}\) को (15) और (16) के बीच रखने की गलती / Mistakenly placing \(\sqrt{195}\) between (15) and (16)
D \(\sqrt{195}\) को (12) और (13) के बीच रखने की गलती / Mistakenly placing \(\sqrt{195}\) between (12) and (13)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{195}\) को (14) और (15) के बीच रखने की गलती / Mistakenly placing \(\sqrt{195}\) between (14) and (15)
Explanation
Simple Explanation
वास्तव में \(13^2=169\) और \(14^2=196\) हैं। इसलिए \(\sqrt{195}\) (13) और (14) के बीच है, (14) से कम। / Actually \(13^2=169\) and \(14^2=196\). Therefore \(\sqrt{195}\) lies between (13) and (14), less than (14).
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वर्गमूल सर्पिल में कर्ण \(\sqrt{n}\) पर (1) इकाई लंब जोड़ने से नया कर्ण \(\sqrt{n+1}\) क्यों है?
Why does adding a (1) unit perpendicular to hypotenuse \(\sqrt{n}\) in a square root spiral give new hypotenuse \(\sqrt{n+1}\)?
#square-root-spiral
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A क्योंकि \(\sqrt{n}+1=\sqrt{n+1}\) / Because \(\sqrt{n}+1=\sqrt{n+1}\)
B क्योंकि (n+1) हमेशा पूर्ण वर्ग है / Because (n+1) is always a perfect square
C क्योंकि (\(\sqrt{n}\)2 +12 =n+1) / Because (\(\sqrt{n}\)2 +12 =n+1)
D क्योंकि \(n^2+1=n+1\) / Because \(n^2+1=n+1\)
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Correct Answer
C. क्योंकि (\(\sqrt{n}\)2 +12 =n+1) / Because (\(\sqrt{n}\)2 +12 =n+1)
Explanation
Simple Explanation
पाइथागोरस प्रमेय में कर्ण का वर्ग भुजाओं के वर्गों के योग के बराबर होता है। यही सामान्य नियम है। / In Pythagoras theorem, the square of the hypotenuse equals the sum of squares of the sides. This is the general rule.
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वर्गमूल सर्पिल में \(\sqrt{255}\) के बाद बनने वाला कर्ण किस सटीक मान पर आएगा?
In a square root spiral, the hypotenuse formed after \(\sqrt{255}\) will come at what exact value?
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A \(\sqrt{254}\)
B \(\sqrt{256}=16\)
C \(\sqrt{510}\)
D \(\sqrt{257}\)
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Correct Answer
B. \(\sqrt{256}=16\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{255+1}=\sqrt{256}\) है। \(\sqrt{256}=16\), इसलिए यह ठीक (16) पर है। / The next hypotenuse is \(\sqrt{255+1}=\sqrt{256}\). Since \(\sqrt{256}=16\), it lies exactly at (16).
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वर्गमूल सर्पिल में \(\sqrt{50}\) और \(\sqrt{63}\) की स्थिति की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the positions of \(\sqrt{50}\) and \(\sqrt{63}\) in a square root spiral?
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A \(\sqrt{50}\) (6) और (7) के बीच है, \(\sqrt{63}\) (7) और (8) के बीच है / \(\sqrt{50}\) lies between (6) and (7), \(\sqrt{63}\) lies between (7) and (8)
B \(\sqrt{50}\) (7) और (8) के बीच है, \(\sqrt{63}\) (7) और (8) के बीच है / \(\sqrt{50}\) lies between (7) and (8), \(\sqrt{63}\) lies between (7) and (8)
C \(\sqrt{50}\) (7) और (8) के बीच है, \(\sqrt{63}\) (8) और (9) के बीच है / \(\sqrt{50}\) lies between (7) and (8), \(\sqrt{63}\) lies between (8) and (9)
D दोनों ठीक (8) पर हैं / Both are exactly at (8)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{50}\) (7) और (8) के बीच है, \(\sqrt{63}\) (7) और (8) के बीच है / \(\sqrt{50}\) lies between (7) and (8), \(\sqrt{63}\) lies between (7) and (8)
Explanation
Simple Explanation
क्योंकि \(7^2<50<8^2\) और \(7^2<63<8^2\) है। दोनों (7) और (8) के बीच हैं। / Because \(7^2<50<8^2\) and \(7^2<63<8^2\). Both lie between (7) and (8).
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वर्गमूल सर्पिल में \(\sqrt{120}\) पर (1) इकाई लंब जोड़ने से जो कर्ण बनता है, वह किस कारण विशेष है?
In a square root spiral, why is the hypotenuse formed by adding a (1) unit perpendicular to \(\sqrt{120}\) special?
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A वह \(\sqrt{121}=11\) है / It is \(\sqrt{121}=11\)
B वह \(\sqrt{119}\) है / It is \(\sqrt{119}\)
C वह \(\sqrt{240}\) है / It is \(\sqrt{240}\)
D वह अपरिभाषित है / It is undefined
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Correct Answer
A. वह \(\sqrt{121}=11\) है / It is \(\sqrt{121}=11\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{121}\) है। \(121=11^2\), इसलिए कर्ण का सटीक मान (11) है। / The next hypotenuse is \(\sqrt{121}\). Since \(121=11^2\), the exact value of the hypotenuse is (11).
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वर्गमूल सर्पिल में \(\sqrt{224}\) बनाने के लिए सही पिछला कर्ण कौन-सा है और बनने वाला कर्ण किस अंतराल में होगा?
To construct \(\sqrt{224}\) in a square root spiral, what is the correct previous hypotenuse and in which interval will the formed hypotenuse lie?
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#interval
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A \(\sqrt{222}\), (14) और (15) के बीच / \(\sqrt{222}\), between (14) and (15)
B \(\sqrt{223}\), (14) और (15) के बीच / \(\sqrt{223}\), between (14) and (15)
C \(\sqrt{223}\), (15) और (16) के बीच / \(\sqrt{223}\), between (15) and (16)
D \(\sqrt{225}\), ठीक (15) पर / \(\sqrt{225}\), exactly at (15)
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Correct Answer
B. \(\sqrt{223}\), (14) और (15) के बीच / \(\sqrt{223}\), between (14) and (15)
Explanation
Simple Explanation
\(\sqrt{223}\) से \(\sqrt{224}\) बनता है। क्योंकि \(14^2<224<15^2\), यह (14) और (15) के बीच होगा। / \(\sqrt{224}\) is formed from \(\sqrt{223}\). Since \(14^2<224<15^2\), it lies between (14) and (15).
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वर्गमूल सर्पिल में यदि किसी चरण पर कर्ण \(\sqrt{399}\) है, तो अगला कर्ण किस विशेष मान पर होगा?
In a square root spiral, if the hypotenuse at a step is \(\sqrt{399}\), at which special value will the next hypotenuse be?
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A \(\sqrt{400}=20\)
B \(\sqrt{398}\)
C \(\sqrt{798}\)
D \(\sqrt{401}\)
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Correct Answer
A. \(\sqrt{400}=20\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{399+1}=\sqrt{400}\) है। \(\sqrt{400}=20\), इसलिए यह पूर्ण संख्या है। / The next hypotenuse is \(\sqrt{399+1}=\sqrt{400}\). Since \(\sqrt{400}=20\), it is a whole number.
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वर्गमूल सर्पिल में \(\sqrt{2}\) को संख्या रेखा पर अंकित करने में कौन-सा चरण सबसे सटीक है?
Which step is most precise while marking \(\sqrt{2}\) on the number line using a square root spiral?
#square-root-spiral
#hard
#number-line
#compass
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A कंपास में (2) इकाई लेकर चाप खींचना / Take (2) units in compass and draw an arc
B कंपास में \(\sqrt{2}\) कर्ण की लंबाई लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{2}\) hypotenuse length in compass and draw an arc from the origin
C किसी भी बिंदु से कोई भी चाप खींचना / Draw any arc from any point
D कर्ण को आधा करके अंकित करना / Mark half of the hypotenuse
Explanation opens after your attempt
Correct Answer
B. कंपास में \(\sqrt{2}\) कर्ण की लंबाई लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{2}\) hypotenuse length in compass and draw an arc from the origin
Explanation
Simple Explanation
कंपास में वही लंबाई ली जाती है जिसे संख्या रेखा पर अंकित करना है। मूल बिंदु से चाप खींचना सही स्थान देता है। / The same length to be marked is taken in the compass. Drawing an arc from the origin gives the correct position.
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वर्गमूल सर्पिल में \(\sqrt{150}\) और \(\sqrt{169}\) के बारे में कौन-सा कथन सही है?
Which statement about \(\sqrt{150}\) and \(\sqrt{169}\) in a square root spiral is correct?
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A \(\sqrt{150}\) (11) और (12) के बीच है, \(\sqrt{169}=13\) है / \(\sqrt{150}\) lies between (11) and (12), \(\sqrt{169}=13\)
B \(\sqrt{150}\) (12) और (13) के बीच है, \(\sqrt{169}=13\) है / \(\sqrt{150}\) lies between (12) and (13), \(\sqrt{169}=13\)
C \(\sqrt{150}=13\), \(\sqrt{169}\) अपरिमेय है / \(\sqrt{150}=13\), \(\sqrt{169}\) is irrational
D दोनों (13) हैं / Both are (13)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{150}\) (12) और (13) के बीच है, \(\sqrt{169}=13\) है / \(\sqrt{150}\) lies between (12) and (13), \(\sqrt{169}=13\)
Explanation
Simple Explanation
क्योंकि \(12^2<150<13^2\) और \(169=13^2\) है। इसलिए \(\sqrt{150}\) (13) से कम है। / Because \(12^2<150<13^2\) and \(169=13^2\). Therefore \(\sqrt{150}\) is less than (13).
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वर्गमूल सर्पिल में \(\sqrt{5}\) बनाने के लिए \(\sqrt{4}\) और (1) क्यों सही भुजाएँ हैं?
Why are \(\sqrt{4}\) and (1) correct sides for constructing \(\sqrt{5}\) in a square root spiral?
#square-root-spiral
#hard
#construction
#pythagoras
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A क्योंकि (\(\sqrt{4}\)2 +12 =5) / Because (\(\sqrt{4}\)2 +12 =5)
B क्योंकि \(\sqrt{4}+1=\sqrt{5}\) / Because \(\sqrt{4}+1=\sqrt{5}\)
C क्योंकि \(4+1=\sqrt{5}\) / Because \(4+1=\sqrt{5}\)
D क्योंकि (\(\sqrt{4}\)2 -12 =5) / Because (\(\sqrt{4}\)2 -12 =5)
Explanation opens after your attempt
Correct Answer
A. क्योंकि (\(\sqrt{4}\)2 +12 =5) / Because (\(\sqrt{4}\)2 +12 =5)
Explanation
Simple Explanation
\(\sqrt{4}\) पिछले कर्ण की लंबाई है और (1) नई लंब है। पाइथागोरस से नया कर्ण \(\sqrt{5}\) मिलता है। / \(\sqrt{4}\) is the previous hypotenuse and (1) is the new perpendicular. Pythagoras gives the new hypotenuse \(\sqrt{5}\).
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वर्गमूल सर्पिल में \(\sqrt{440}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही है?
Before placing \(\sqrt{440}\) on the number line using a square root spiral, which interval is correct?
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A \(19<\sqrt{440}<20\)
B \(20<\sqrt{440}<21\)
C \(21<\sqrt{440}<22\)
D \(22<\sqrt{440}<23\)
Explanation opens after your attempt
Correct Answer
B. \(20<\sqrt{440}<21\)
Explanation
Simple Explanation
क्योंकि \(20^2<440<21^2\) है। इसलिए \(\sqrt{440}\) (20) और (21) के बीच होगा। / Because \(20^2<440<21^2\). Therefore \(\sqrt{440}\) lies between (20) and (21).
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वर्गमूल सर्पिल में यदि (k)वाँ कर्ण \(\sqrt{k}\) माना जाए, तो \(\sqrt{25}\) कौन-सा कर्ण होगा और उसका मान क्या होगा?
If the (k)-th hypotenuse in a square root spiral is considered as \(\sqrt{k}\), which hypotenuse is \(\sqrt{25}\), and what is its value?
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#sequence
#perfect-square
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A (24)वाँ, (5) / (24)-th, (5)
B (25)वाँ, (5) / (25)-th, (5)
C (26)वाँ, (5) / (26)-th, (5)
D (25)वाँ, (25) / (25)-th, (25)
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Correct Answer
B. (25)वाँ, (5) / (25)-th, (5)
Explanation
Simple Explanation
यदि (k)वाँ कर्ण \(\sqrt{k}\) है, तो \(\sqrt{25}\) (25)वाँ कर्ण है। \(\sqrt{25}=5\) होता है। / If the (k)-th hypotenuse is \(\sqrt{k}\), then \(\sqrt{25}\) is the (25)-th hypotenuse. Also, \(\sqrt{25}=5\).
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वर्गमूल सर्पिल में \(\sqrt{35}\) के बाद बनने वाले कर्ण के बारे में कौन-सा कथन सही है?
Which statement about the hypotenuse formed after \(\sqrt{35}\) in a square root spiral is correct?
#square-root-spiral
#hard
#next-root
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A वह \(\sqrt{36}=6\) है / It is \(\sqrt{36}=6\)
B वह \(\sqrt{34}\) है / It is \(\sqrt{34}\)
C वह \(\sqrt{70}\) है / It is \(\sqrt{70}\)
D वह \(\sqrt{37}\) है / It is \(\sqrt{37}\)
Explanation opens after your attempt
Correct Answer
A. वह \(\sqrt{36}=6\) है / It is \(\sqrt{36}=6\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{35+1}=\sqrt{36}\) है। \(\sqrt{36}=6\), इसलिए सटीक मान (6) है। / The next hypotenuse is \(\sqrt{35+1}=\sqrt{36}\). Since \(\sqrt{36}=6\), the exact value is (6).
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वर्गमूल सर्पिल में कौन-सा कथन निर्माण की दृष्टि से सबसे सटीक है?
Which statement is most precise from the construction point of view in a square root spiral?
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A हर नया कर्ण पिछले कर्ण में (1) जोड़कर बनता है / Each new hypotenuse is formed by adding (1) to the previous hypotenuse
B हर नया त्रिभुज पिछले कर्ण और (1) इकाई लंब से बनने वाला समकोण त्रिभुज है / Each new triangle is a right triangle made from the previous hypotenuse and a (1) unit perpendicular
C हर नया कर्ण पिछले कर्ण का दुगुना होता है / Each new hypotenuse is double the previous hypotenuse
D हर नया त्रिभुज समबाहु होता है / Each new triangle is equilateral
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Correct Answer
B. हर नया त्रिभुज पिछले कर्ण और (1) इकाई लंब से बनने वाला समकोण त्रिभुज है / Each new triangle is a right triangle made from the previous hypotenuse and a (1) unit perpendicular
Explanation
Simple Explanation
वर्गमूल सर्पिल का सही आधार समकोण त्रिभुज और पाइथागोरस प्रमेय है। सीधे लंबाइयों को जोड़ना गलत तरीका है। / The correct basis of a square root spiral is a right triangle and Pythagoras theorem. Directly adding lengths is wrong.
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वर्गमूल सर्पिल में \(\sqrt{27}\) और \(\sqrt{32}\) की स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the positions of \(\sqrt{27}\) and \(\sqrt{32}\) in a square root spiral is correct?
#square-root-spiral
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#comparison
#interval
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A दोनों (5) और (6) के बीच हैं / Both lie between (5) and (6)
B \(\sqrt{27}\) (5) और (6) के बीच है, \(\sqrt{32}\) (5) और (6) के बीच है / \(\sqrt{27}\) lies between (5) and (6), \(\sqrt{32}\) lies between (5) and (6)
C \(\sqrt{27}\) (4) और (5) के बीच है, \(\sqrt{32}\) (5) और (6) के बीच है / \(\sqrt{27}\) lies between (4) and (5), \(\sqrt{32}\) lies between (5) and (6)
D \(\sqrt{27}\) (5) और (6) के बीच है, \(\sqrt{32}\) (6) और (7) के बीच है / \(\sqrt{27}\) lies between (5) and (6), \(\sqrt{32}\) lies between (6) and (7)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{27}\) (5) और (6) के बीच है, \(\sqrt{32}\) (5) और (6) के बीच है / \(\sqrt{27}\) lies between (5) and (6), \(\sqrt{32}\) lies between (5) and (6)
Explanation
Simple Explanation
\(5^2<27<6^2\) और \(5^2<32<6^2\) दोनों सही हैं। इसलिए दोनों (5) और (6) के बीच हैं। / Both \(5^2<27<6^2\) and \(5^2<32<6^2\) are true. Therefore both lie between (5) and (6).
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वर्गमूल सर्पिल में \(\sqrt{624}\) का सही अंतराल कौन-सा है?
What is the correct interval for \(\sqrt{624}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(23<\sqrt{624}<24\)
B \(24<\sqrt{624}<25\)
C \(25<\sqrt{624}<26\)
D \(26<\sqrt{624}<27\)
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Correct Answer
B. \(24<\sqrt{624}<25\)
Explanation
Simple Explanation
क्योंकि \(24^2=576\) और \(25^2=625\) हैं। (624) इनके बीच है, इसलिए \(\sqrt{624}\) (24) और (25) के बीच है। / Because \(24^2=576\) and \(25^2=625\). The number (624) lies between them, so \(\sqrt{624}\) lies between (24) and (25).
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वर्गमूल सर्पिल में यदि \(\sqrt{n}\) के बाद बनने वाला कर्ण \(\sqrt{n+1}\) अपरिमेय है, तो कौन-सी बात निश्चित हो सकती है?
In a square root spiral, if the hypotenuse \(\sqrt{n+1}\) formed after \(\sqrt{n}\) is irrational, what can be definitely true?
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#concept
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A (n+1) पूर्ण वर्ग नहीं है / (n+1) is not a perfect square
B (n+1) हमेशा सम है / (n+1) is always even
C (n+1) हमेशा अभाज्य है / (n+1) is always prime
D (n=0) है / (n=0)
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Correct Answer
A. (n+1) पूर्ण वर्ग नहीं है / (n+1) is not a perfect square
Explanation
Simple Explanation
किसी धनात्मक पूर्णांक का वर्गमूल पूर्ण संख्या तभी होता है जब वह पूर्ण वर्ग हो। पूर्ण वर्ग न हो तो वर्गमूल अपरिमेय होता है। / The square root of a positive integer is a whole number only when it is a perfect square. If it is not a perfect square, the square root is irrational.
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वर्गमूल सर्पिल में \(\sqrt{21}\) बनाने के लिए \(\sqrt{20}\) पर (1) इकाई लंब क्यों पर्याप्त है?
Why is a (1) unit perpendicular on \(\sqrt{20}\) sufficient to construct \(\sqrt{21}\) in a square root spiral?
#square-root-spiral
#hard
#pythagoras
#next-root
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A (\(\sqrt{20}\)2 +12 =21)
B \(\sqrt{20}+1=\sqrt{21}\)
C (\(\sqrt{20}\)2 -12 =21)
D \(20+1=\sqrt{21}\)
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Correct Answer
A. (\(\sqrt{20}\)2 +12 =21)
Explanation
Simple Explanation
पाइथागोरस प्रमेय में वर्गों का योग लिया जाता है। इसलिए \(\sqrt{20}\) और (1) से कर्ण \(\sqrt{21}\) बनता है। / Pythagoras theorem uses the sum of squares. Therefore \(\sqrt{20}\) and (1) form hypotenuse \(\sqrt{21}\).
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वर्गमूल सर्पिल में \(\sqrt{899}\) के बाद बनने वाला कर्ण क्या होगा और उसका सटीक मान क्या है?
In a square root spiral, what will be the hypotenuse after \(\sqrt{899}\), and what is its exact value?
#square-root-spiral
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A \(\sqrt{898}\), कोई पूर्ण मान नहीं / \(\sqrt{898}\), no whole value
B \(\sqrt{900}\), (30)
C \(\sqrt{1798}\), कोई पूर्ण मान नहीं / \(\sqrt{1798}\), no whole value
D \(\sqrt{901}\), कोई पूर्ण मान नहीं / \(\sqrt{901}\), no whole value
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{900}\), (30)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{900}\) है। क्योंकि \(900=30^2\), इसका सटीक मान (30) है। / The next hypotenuse is \(\sqrt{900}\). Since \(900=30^2\), its exact value is (30).
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वर्गमूल सर्पिल में \(\sqrt{168}\) और \(\sqrt{170}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{168}\) and \(\sqrt{170}\) in a square root spiral?
#square-root-spiral
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#interval
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A \(\sqrt{168}\) (12) और (13) के बीच है, \(\sqrt{170}\) (13) और (14) के बीच है / \(\sqrt{168}\) lies between (12) and (13), \(\sqrt{170}\) lies between (13) and (14)
B \(\sqrt{168}\) (12) और (13) के बीच है, \(\sqrt{170}\) (12) और (13) के बीच है / \(\sqrt{168}\) lies between (12) and (13), \(\sqrt{170}\) lies between (12) and (13)
C \(\sqrt{168}\) (13) और (14) के बीच है, \(\sqrt{170}\) (13) और (14) के बीच है / \(\sqrt{168}\) lies between (13) and (14), \(\sqrt{170}\) lies between (13) and (14)
D \(\sqrt{168}=13\) और \(\sqrt{170}\) अपरिमेय है / \(\sqrt{168}=13\) and \(\sqrt{170}\) is irrational
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Correct Answer
C. \(\sqrt{168}\) (13) और (14) के बीच है, \(\sqrt{170}\) (13) और (14) के बीच है / \(\sqrt{168}\) lies between (13) and (14), \(\sqrt{170}\) lies between (13) and (14)
Explanation
Simple Explanation
क्योंकि \(13^2=169\) है। (168) थोड़ा कम है इसलिए (12) और (13) के बीच, जबकि (170) (13) और (14) के बीच है। / Because \(13^2=169\). The number (168) is slightly less, so it is between (12) and (13), while (170) is between (13) and (14).
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वर्गमूल सर्पिल में यदि नया कर्ण \(\sqrt{n+1}\) है और पिछला कर्ण \(\sqrt{48}\) था, तो नया कर्ण कौन-सा होगा?
In a square root spiral, if the new hypotenuse is \(\sqrt{n+1}\) and the previous hypotenuse was \(\sqrt{48}\), what will the new hypotenuse be?
#square-root-spiral
#hard
#general-rule
#next-root
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A \(\sqrt{47}\)
B \(\sqrt{48}\)
C \(\sqrt{49}\)
D \(\sqrt{96}\)
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Correct Answer
C. \(\sqrt{49}\)
Explanation
Simple Explanation
पिछला कर्ण \(\sqrt{48}\) है, इसलिए (n=48)। नया कर्ण \(\sqrt{48+1}=\sqrt{49}\) होगा। / The previous hypotenuse is \(\sqrt{48}\), so (n=48). The new hypotenuse is \(\sqrt{48+1}=\sqrt{49}\).
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वर्गमूल सर्पिल में \(\sqrt{840}\) की संख्या-रेखा स्थिति कौन-सी है?
What is the number-line position of \(\sqrt{840}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(27<\sqrt{840}<28\)
B \(28<\sqrt{840}<29\)
C \(29<\sqrt{840}<30\)
D \(30<\sqrt{840}<31\)
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Correct Answer
B. \(28<\sqrt{840}<29\)
Explanation
Simple Explanation
क्योंकि \(28^2=784\) और \(29^2=841\) हैं। (840) इनके बीच है, इसलिए \(\sqrt{840}\) (28) और (29) के बीच है। / Because \(28^2=784\) and \(29^2=841\). The number (840) lies between them, so \(\sqrt{840}\) lies between (28) and (29).
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वर्गमूल सर्पिल में \(\sqrt{24}\) से \(\sqrt{25}\) बनने पर कौन-सा संयुक्त निष्कर्ष सही है?
When \(\sqrt{25}\) is formed from \(\sqrt{24}\) in a square root spiral, which combined conclusion is correct?
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A नया कर्ण (5) है और \(\sqrt{24}\) (4) और (5) के बीच है / The new hypotenuse is (5), and \(\sqrt{24}\) lies between (4) and (5)
B नया कर्ण (4) है और \(\sqrt{24}\) (5) और (6) के बीच है / The new hypotenuse is (4), and \(\sqrt{24}\) lies between (5) and (6)
C नया कर्ण \(\sqrt{23}\) है और \(\sqrt{24}=5\) / The new hypotenuse is \(\sqrt{23}\), and \(\sqrt{24}=5\)
D नया कर्ण \(\sqrt{48}\) है और \(\sqrt{25}=4\) / The new hypotenuse is \(\sqrt{48}\), and \(\sqrt{25}=4\)
Explanation opens after your attempt
Correct Answer
A. नया कर्ण (5) है और \(\sqrt{24}\) (4) और (5) के बीच है / The new hypotenuse is (5), and \(\sqrt{24}\) lies between (4) and (5)
Explanation
Simple Explanation
\(\sqrt{24}\) के बाद \(\sqrt{25}=5\) बनता है। साथ ही \(4^2<24<5^2\), इसलिए \(\sqrt{24}\) (4) और (5) के बीच है। / After \(\sqrt{24}\), \(\sqrt{25}=5\) is formed. Also \(4^2<24<5^2\), so \(\sqrt{24}\) lies between (4) and (5).
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वर्गमूल सर्पिल में \(\sqrt{n}\) को संख्या रेखा पर रखने से पहले सबसे विश्वसनीय तरीका क्या है?
Before placing \(\sqrt{n}\) on the number line in a square root spiral, what is the most reliable method?
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#method
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A \(\sqrt{n}\) का दशमलव याद करना / Memorize the decimal of \(\sqrt{n}\)
B निकटतम पूर्ण वर्गों (a-2 <n<(a+1)2 ) की पहचान करना / Identify nearest perfect squares (a-2 <n<(a+1)2 )
C हमेशा उसे (n) पर रखना / Always place it at (n)
D हमेशा उसे (1) और (2) के बीच रखना / Always place it between (1) and (2)
Explanation opens after your attempt
Correct Answer
B. निकटतम पूर्ण वर्गों (a-2 <n<(a+1)2 ) की पहचान करना / Identify nearest perfect squares (a-2 <n<(a+1)2 )
Explanation
Simple Explanation
निकटतम पूर्ण वर्गों से सही अंतराल मिलता है। इसके बाद सर्पिल की लंबाई कंपास से अंकित करें। / Nearest perfect squares give the correct interval. Then mark the spiral length using a compass.
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वर्गमूल सर्पिल में \(\sqrt{440}\) और \(\sqrt{441}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{440}\) and \(\sqrt{441}\) in a square root spiral?
#square-root-spiral
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A \(\sqrt{440}\) (20) और (21) के बीच है, \(\sqrt{441}=21\) है / \(\sqrt{440}\) lies between (20) and (21), \(\sqrt{441}=21\)
B \(\sqrt{440}=21\) और \(\sqrt{441}\) अपरिमेय है / \(\sqrt{440}=21\), and \(\sqrt{441}\) is irrational
C दोनों (20) हैं / Both are (20)
D दोनों (21) से बड़े हैं / Both are greater than (21)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{440}\) (20) और (21) के बीच है, \(\sqrt{441}=21\) है / \(\sqrt{440}\) lies between (20) and (21), \(\sqrt{441}=21\)
Explanation
Simple Explanation
क्योंकि \(20^2<440<21^2\) और \(441=21^2\) है। इसलिए \(\sqrt{441}\) ठीक (21) है। / Because \(20^2<440<21^2\), and \(441=21^2\). Therefore \(\sqrt{441}\) is exactly (21).
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वर्गमूल सर्पिल में यदि \(\sqrt{n}\) कर्ण पर (1) इकाई लंब बनाई जाती है, तो कौन-सा कथन गलत है?
In a square root spiral, if a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{n}\), which statement is incorrect?
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#wrong-statement
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A नया कर्ण \(\sqrt{n+1}\) होगा / The new hypotenuse will be \(\sqrt{n+1}\)
B पाइथागोरस प्रमेय लागू होगा / Pythagoras theorem will apply
C समकोण त्रिभुज बनेगा / A right triangle will be formed
D नया कर्ण \(\sqrt{n}+1\) होगा / The new hypotenuse will be \(\sqrt{n}+1\)
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Correct Answer
D. नया कर्ण \(\sqrt{n}+1\) होगा / The new hypotenuse will be \(\sqrt{n}+1\)
Explanation
Simple Explanation
नया कर्ण सीधे \(\sqrt{n}+1\) नहीं होता। वह (\sqrt{\(\sqrt{n}\)2 +12 }=\sqrt{n+1}) होता है। / The new hypotenuse is not directly \(\sqrt{n}+1\). It is (\sqrt{\(\sqrt{n}\)2 +12 }=\sqrt{n+1}).
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वर्गमूल सर्पिल में \(\sqrt{960}\) का सही अंतराल कौन-सा है?
What is the correct interval for \(\sqrt{960}\) in a square root spiral?
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#interval
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A \(29<\sqrt{960}<30\)
B \(30<\sqrt{960}<31\)
C \(31<\sqrt{960}<32\)
D \(32<\sqrt{960}<33\)
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Correct Answer
B. \(30<\sqrt{960}<31\)
Explanation
Simple Explanation
क्योंकि \(30^2=900\) और \(31^2=961\) हैं। (960) इनके बीच है, इसलिए \(\sqrt{960}\) (30) और (31) के बीच है। / Because \(30^2=900\) and \(31^2=961\). The number (960) lies between them, so \(\sqrt{960}\) lies between (30) and (31).
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वर्गमूल सर्पिल का कठिन स्तर पर सबसे सटीक सार कौन-सा है?
At hard level, which is the most precise summary of a square root spiral?
#square-root-spiral
#hard
#main-idea
#pythagoras
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A यह सीधे वर्गमूलों को जोड़ने की विधि है / It is a method of directly adding square roots
B यह समकोण त्रिभुजों की क्रमिक रचना है जिसमें (\(\sqrt{n}\)2 +12 =n+1) से अगला कर्ण बनता है / It is a successive construction of right triangles where the next hypotenuse is formed by (\(\sqrt{n}\)2 +12 =n+1)
C यह केवल पूर्ण वर्गों को याद करने की सूची है / It is only a list for memorizing perfect squares
D यह बिना कंपास और समकोण के बनने वाली रचना है / It is a construction made without compass and right angle
Explanation opens after your attempt
Correct Answer
B. यह समकोण त्रिभुजों की क्रमिक रचना है जिसमें (\(\sqrt{n}\)2 +12 =n+1) से अगला कर्ण बनता है / It is a successive construction of right triangles where the next hypotenuse is formed by (\(\sqrt{n}\)2 +12 =n+1)
Explanation
Simple Explanation
वर्गमूल सर्पिल पाइथागोरस प्रमेय पर आधारित है। पिछला कर्ण और (1) इकाई लंब मिलकर अगला वर्गमूल बनाते हैं। / A square root spiral is based on Pythagoras theorem. The previous hypotenuse and (1) unit perpendicular form the next square root.
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वर्गमूल सर्पिल में \(\sqrt{34}\) कर्ण पर (1) इकाई लंब बनाने पर नया कर्ण कौन-सा बनेगा?
In a square root spiral, which new hypotenuse is formed by drawing a (1) unit perpendicular on the hypotenuse \(\sqrt{34}\)?
#square-root-spiral
#hard
#next-root
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A \(\sqrt{33}\)
B \(\sqrt{35}\)
C \(\sqrt{68}\)
D \(\sqrt{36}\)
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Correct Answer
B. \(\sqrt{35}\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{34+1}=\sqrt{35}\) होगा। सीधे जोड़ नहीं, पाइथागोरस का नियम लगाएँ। / The new hypotenuse is \(\sqrt{34+1}=\sqrt{35}\). Use Pythagoras rule, not direct addition.
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यदि वर्गमूल सर्पिल में नया कर्ण (14) के बराबर है, तो उससे ठीक पहले वाला कर्ण कौन-सा था?
If the new hypotenuse in a square root spiral is equal to (14), which hypotenuse came immediately before it?
#square-root-spiral
#hard
#reverse-rule
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A \(\sqrt{195}\)
B \(\sqrt{196}\)
C \(\sqrt{197}\)
D \(\sqrt{14}\)
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Correct Answer
A. \(\sqrt{195}\)
Explanation
Simple Explanation
नया कर्ण \(14=\sqrt{196}\) है। इसलिए पिछला कर्ण \(\sqrt{195}\) था। / The new hypotenuse is \(14=\sqrt{196}\). Therefore the previous hypotenuse was \(\sqrt{195}\).
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\(\sqrt{575}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही पहचाना जाएगा?
Before placing \(\sqrt{575}\) on the number line, which interval will be correctly identified?
#square-root-spiral
#hard
#number-line
#interval
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A \(22<\sqrt{575}<23\)
B \(23<\sqrt{575}<24\)
C \(24<\sqrt{575}<25\)
D \(25<\sqrt{575}<26\)
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Correct Answer
B. \(23<\sqrt{575}<24\)
Explanation
Simple Explanation
क्योंकि \(23^2=529\) और \(24^2=576\) हैं। (575) इनके बीच है। / Because \(23^2=529\) and \(24^2=576\). The number (575) lies between them.
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यदि कोई विद्यार्थी \(\sqrt{18}+1=\sqrt{19}\) लिखकर अगला कर्ण बताता है, तो सही सुधार कौन-सा है?
If a student writes \(\sqrt{18}+1=\sqrt{19}\) to find the next hypotenuse, what is the correct correction?
#square-root-spiral
#hard
#error-correction
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A (\sqrt{\(\sqrt{18}\)2 +12 }=\sqrt{19})
B \(\sqrt{18^2+1^2}=\sqrt{19}\)
C \(\sqrt{18}+1=\sqrt{36}\)
D \(\sqrt{18-1}=\sqrt{19}\)
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Correct Answer
A. (\sqrt{\(\sqrt{18}\)2 +12 }=\sqrt{19})
Explanation
Simple Explanation
वर्गमूल सर्पिल में कर्ण वर्गों के योग से बनता है। \(\sqrt{18}+1\) को \(\sqrt{19}\) नहीं मानना चाहिए। / In a square root spiral, the hypotenuse is formed by the sum of squares. Do not treat \(\sqrt{18}+1\) as \(\sqrt{19}\).
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यदि सामान्य वर्गमूल सर्पिल में (1) इकाई की जगह (3) इकाई लंब ली जाए, तो \(\sqrt{n}\) से बनने वाला कर्ण किस रूप में होगा?
If a (3) unit perpendicular is used instead of (1) unit in the usual square root spiral, what will be the hypotenuse formed from \(\sqrt{n}\)?
#square-root-spiral
#hard
#unit-change
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A \(\sqrt{n+1}\)
B \(\sqrt{n+3}\)
C \(\sqrt{n+9}\)
D \(\sqrt{3n}\)
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Correct Answer
C. \(\sqrt{n+9}\)
Explanation
Simple Explanation
पाइथागोरस से (\(\sqrt{n}\)2 +32 =n+9) होगा। इसलिए सामान्य क्रम बदल जाएगा। / By Pythagoras, (\(\sqrt{n}\)2 +32 =n+9). So the usual sequence will change.
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वर्गमूल सर्पिल में \(\sqrt{169}\) पर (1) इकाई लंब बनाने से नया कर्ण कौन-सा होगा और कहाँ स्थित होगा?
In a square root spiral, drawing a (1) unit perpendicular on \(\sqrt{169}\) gives which new hypotenuse and where is it located?
#square-root-spiral
#hard
#next-root
#interval
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A \(\sqrt{170}\), (13) और (14) के बीच / \(\sqrt{170}\), between (13) and (14)
B \(\sqrt{168}\), (12) और (13) के बीच / \(\sqrt{168}\), between (12) and (13)
C \(\sqrt{338}\), (18) और (19) के बीच / \(\sqrt{338}\), between (18) and (19)
D \(\sqrt{170}\), ठीक (13) पर / \(\sqrt{170}\), exactly at (13)
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Correct Answer
A. \(\sqrt{170}\), (13) और (14) के बीच / \(\sqrt{170}\), between (13) and (14)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{170}\) है। क्योंकि \(13^2<170<14^2\), यह (13) और (14) के बीच है। / The new hypotenuse is \(\sqrt{170}\). Since \(13^2<170<14^2\), it lies between (13) and (14).
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वर्गमूल सर्पिल में \(\sqrt{224}\) और \(\sqrt{225}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{224}\) and \(\sqrt{225}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#perfect-square
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A \(\sqrt{224}\) ठीक (15) है और \(\sqrt{225}\) अपरिमेय है / \(\sqrt{224}\) is exactly (15) and \(\sqrt{225}\) is irrational
B \(\sqrt{224}\) (14) और (15) के बीच है और \(\sqrt{225}=15\) है / \(\sqrt{224}\) lies between (14) and (15), and \(\sqrt{225}=15\)
C \(\sqrt{224}\) (15) और (16) के बीच है और \(\sqrt{225}=15\) है / \(\sqrt{224}\) lies between (15) and (16), and \(\sqrt{225}=15\)
D दोनों अपरिमेय हैं / Both are irrational
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{224}\) (14) और (15) के बीच है और \(\sqrt{225}=15\) है / \(\sqrt{224}\) lies between (14) and (15), and \(\sqrt{225}=15\)
Explanation
Simple Explanation
\(14^2<224<15^2\) और \(225=15^2\) है। इसलिए \(\sqrt{225}\) ठीक (15) है।
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वर्गमूल सर्पिल में \(\sqrt{143}\) के बाद बनने वाले कर्ण का सटीक मान क्या होगा?
What will be the exact value of the hypotenuse formed after \(\sqrt{143}\) in a square root spiral?
#square-root-spiral
#hard
#exact-value
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A (11)
B (12)
C (13)
D कोई पूर्ण संख्या नहीं / No whole number
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Explanation
Simple Explanation
अगला कर्ण \(\sqrt{144}\) होगा और \(\sqrt{144}=12\) है। पूर्ण वर्ग पर सटीक मान मिलता है। / The next hypotenuse is \(\sqrt{144}\), and \(\sqrt{144}=12\). A perfect square gives an exact value.
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यदि (k)वाँ कर्ण \(\sqrt{k}\) माना जाए, तो \(\sqrt{36}\) कौन-सा कर्ण होगा और उसका मान क्या होगा?
If the (k)-th hypotenuse is considered \(\sqrt{k}\), which hypotenuse is \(\sqrt{36}\), and what is its value?
#square-root-spiral
#hard
#sequence
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A (35)वाँ, (6) / (35)-th, (6)
B (36)वाँ, (6) / (36)-th, (6)
C (37)वाँ, (6) / (37)-th, (6)
D (36)वाँ, (36) / (36)-th, (36)
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Correct Answer
B. (36)वाँ, (6) / (36)-th, (6)
Explanation
Simple Explanation
यदि (k)वाँ कर्ण \(\sqrt{k}\) है, तो \(\sqrt{36}\) (36)वाँ कर्ण है। \(\sqrt{36}=6\) होता है। / If the (k)-th hypotenuse is \(\sqrt{k}\), then \(\sqrt{36}\) is the (36)-th hypotenuse. Also, \(\sqrt{36}=6\).
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वर्गमूल सर्पिल में \(\sqrt{120}\) बनाने के लिए कौन-सा पिछला कर्ण और कौन-सी नई लंब सही है?
To construct \(\sqrt{120}\) in a square root spiral, which previous hypotenuse and new perpendicular are correct?
#square-root-spiral
#hard
#construction
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A \(\sqrt{118}\) और (2) / \(\sqrt{118}\) and (2)
B \(\sqrt{119}\) और (1) / \(\sqrt{119}\) and (1)
C \(\sqrt{120}\) और (1) / \(\sqrt{120}\) and (1)
D \(\sqrt{121}\) और (1) / \(\sqrt{121}\) and (1)
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Correct Answer
B. \(\sqrt{119}\) और (1) / \(\sqrt{119}\) and (1)
Explanation
Simple Explanation
(\(\sqrt{119}\)2 +12 =120) है। इसलिए \(\sqrt{120}\) के लिए पिछला कर्ण \(\sqrt{119}\) होगा। / (\(\sqrt{119}\)2 +12 =120). So the previous hypotenuse for \(\sqrt{120}\) is \(\sqrt{119}\).
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\(\sqrt{323}\) के बाद बनने वाला कर्ण वर्गमूल सर्पिल में किस सटीक मान पर होगा?
In a square root spiral, the hypotenuse formed after \(\sqrt{323}\) will be at which exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{322}\), कोई पूर्ण मान नहीं / \(\sqrt{322}\), no whole value
B \(\sqrt{324}=18\)
C \(\sqrt{646}\), कोई पूर्ण मान नहीं / \(\sqrt{646}\), no whole value
D \(\sqrt{325}\), (18)
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Correct Answer
B. \(\sqrt{324}=18\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{324}\) होगा। \(324=18^2\), इसलिए इसका मान (18) है। / The next hypotenuse is \(\sqrt{324}\). Since \(324=18^2\), its value is (18).
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वर्गमूल सर्पिल में \(\sqrt{257}\) का स्थान पहचानने के लिए कौन-सी असमानता सही है?
Which inequality is correct to identify the position of \(\sqrt{257}\) in a square root spiral?
#square-root-spiral
#hard
#inequality
#interval
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A \(,15^2<257<16^2,\)
B \(,16^2<257<17^2,\)
C \(,17^2<257<18^2,\)
D \(,18^2<257<19^2,\)
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Correct Answer
B. \(,16^2<257<17^2,\)
Explanation
Simple Explanation
\(16^2=256\) और \(17^2=289\) हैं। (257) इनके बीच है। / \(16^2=256\) and \(17^2=289\). The number (257) lies between them.
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यदि वर्गमूल सर्पिल में \(\sqrt{n}\) के बाद बना कर्ण (25) है, तो (n) का मान क्या होगा?
If the hypotenuse formed after \(\sqrt{n}\) in a square root spiral is (25), what is the value of (n)?
#square-root-spiral
#hard
#reverse-rule
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A (624)
B (625)
C (626)
D (25)
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Explanation
Simple Explanation
नया कर्ण \(25=\sqrt{625}\) है। इसलिए (n+1=625), अतः (n=624)। / The new hypotenuse is \(25=\sqrt{625}\). Therefore (n+1=625), so (n=624).
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वर्गमूल सर्पिल में \(\sqrt{2}\) से \(\sqrt{5}\) तक सामान्य निर्माण का सही क्रम कौन-सा है?
In a square root spiral, which is the correct usual construction order from \(\sqrt{2}\) to \(\sqrt{5}\)?
#square-root-spiral
#hard
#sequence
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A \(\sqrt{2}\rightarrow\sqrt{4}\rightarrow\sqrt{5}\)
B \(\sqrt{2}\rightarrow\sqrt{3}\rightarrow\sqrt{4}\rightarrow\sqrt{5}\)
C \(\sqrt{2}\rightarrow\sqrt{5}\rightarrow\sqrt{3}\)
D \(\sqrt{5}\rightarrow\sqrt{4}\rightarrow\sqrt{3}\)
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Correct Answer
B. \(\sqrt{2}\rightarrow\sqrt{3}\rightarrow\sqrt{4}\rightarrow\sqrt{5}\)
Explanation
Simple Explanation
सर्पिल में कर्ण क्रमिक रूप से बनते हैं। सामान्य निर्माण में बीच के वर्गमूल नहीं छोड़े जाते। / Hypotenuses are formed successively in the spiral. In the usual construction, intermediate square roots are not skipped.
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वर्गमूल सर्पिल में \(\sqrt{170}\) और \(\sqrt{195}\) की संख्या-रेखा स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the number-line positions of \(\sqrt{170}\) and \(\sqrt{195}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A दोनों (13) और (14) के बीच हैं / Both lie between (13) and (14)
B \(\sqrt{170}\) (13) और (14) के बीच, \(\sqrt{195}\) (14) और (15) के बीच है / \(\sqrt{170}\) lies between (13) and (14), \(\sqrt{195}\) lies between (14) and (15)
C \(\sqrt{170}\) (12) और (13) के बीच, \(\sqrt{195}\) (13) और (14) के बीच है / \(\sqrt{170}\) lies between (12) and (13), \(\sqrt{195}\) lies between (13) and (14)
D दोनों ठीक (14) पर हैं / Both are exactly at (14)
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Correct Answer
A. दोनों (13) और (14) के बीच हैं / Both lie between (13) and (14)
Explanation
Simple Explanation
क्योंकि \(13^2<170<14^2\) और \(13^2<195<14^2\) हैं। इसलिए दोनों (13) और (14) के बीच हैं। / Because \(13^2<170<14^2\) and \(13^2<195<14^2\). Therefore both lie between (13) and (14).
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वर्गमूल सर्पिल में \(\sqrt{24}\) से बनने वाले अगले कर्ण और \(\sqrt{26}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the next hypotenuse from \(\sqrt{24}\) and \(\sqrt{26}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#next-root
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A अगला कर्ण \(\sqrt{25}=5\) है और \(\sqrt{26}\) (5) और (6) के बीच है / The next hypotenuse is \(\sqrt{25}=5\), and \(\sqrt{26}\) lies between (5) and (6)
B अगला कर्ण \(\sqrt{23}\) है और \(\sqrt{26}=5\) है / The next hypotenuse is \(\sqrt{23}\), and \(\sqrt{26}=5\)
C दोनों ठीक (5) पर हैं / Both are exactly at (5)
D अगला कर्ण \(\sqrt{48}\) है और \(\sqrt{26}\) (4) और (5) के बीच है / The next hypotenuse is \(\sqrt{48}\), and \(\sqrt{26}\) lies between (4) and (5)
Explanation opens after your attempt
Correct Answer
A. अगला कर्ण \(\sqrt{25}=5\) है और \(\sqrt{26}\) (5) और (6) के बीच है / The next hypotenuse is \(\sqrt{25}=5\), and \(\sqrt{26}\) lies between (5) and (6)
Explanation
Simple Explanation
\(\sqrt{24}\) के बाद \(\sqrt{25}=5\) बनता है। \(5^2<26<6^2\), इसलिए \(\sqrt{26}\) (5) और (6) के बीच है। / After \(\sqrt{24}\), \(\sqrt{25}=5\) is formed. Since \(5^2<26<6^2\), \(\sqrt{26}\) lies between (5) and (6).
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वर्गमूल सर्पिल में यदि (m) पूर्ण वर्ग से ठीक (1) कम है, तो \(\sqrt{m}\) के बाद बनने वाले कर्ण के बारे में सही कथन क्या है?
In a square root spiral, if (m) is exactly (1) less than a perfect square, what is correct about the hypotenuse formed after \(\sqrt{m}\)?
#square-root-spiral
#hard
#pattern
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A वह पूर्ण संख्या होगा / It will be a whole number
B वह हमेशा अपरिमेय होगा / It will always be irrational
C वह शून्य होगा / It will be zero
D वह \(\sqrt{m}\) ही रहेगा / It will remain \(\sqrt{m}\)
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Correct Answer
A. वह पूर्ण संख्या होगा / It will be a whole number
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{m+1}\) होगा। यदि (m+1) पूर्ण वर्ग है, तो उसका वर्गमूल पूर्ण संख्या होगा। / The next hypotenuse is \(\sqrt{m+1}\). If (m+1) is a perfect square, its square root will be a whole number.
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वर्गमूल सर्पिल में \(\sqrt{440}\) और \(\sqrt{441}\) की तुलना में कौन-सा निष्कर्ष सही है?
Which conclusion is correct when comparing \(\sqrt{440}\) and \(\sqrt{441}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#perfect-square
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A \(\sqrt{440}\) (20) और (21) के बीच है और \(\sqrt{441}=21\) है / \(\sqrt{440}\) lies between (20) and (21), and \(\sqrt{441}=21\)
B \(\sqrt{440}=21\) और \(\sqrt{441}\) अपरिमेय है / \(\sqrt{440}=21\), and \(\sqrt{441}\) is irrational
C दोनों (20) हैं / Both are (20)
D दोनों (21) से बड़े हैं / Both are greater than (21)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{440}\) (20) और (21) के बीच है और \(\sqrt{441}=21\) है / \(\sqrt{440}\) lies between (20) and (21), and \(\sqrt{441}=21\)
Explanation
Simple Explanation
\(20^2<440<21^2\) और \(441=21^2\) है। इसलिए \(\sqrt{441}\) ठीक (21) पर है।
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वर्गमूल सर्पिल में \(\sqrt{48}\) के बाद बनने वाले कर्ण का मान क्या है?
What is the value of the hypotenuse formed after \(\sqrt{48}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#exact-value
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A \(\sqrt{47}\)
B (7)
C \(\sqrt{96}\)
D \(\sqrt{50}\)
Explanation opens after your attempt
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{49}\) होगा और \(\sqrt{49}=7\) है। पूर्ण वर्ग पर कर्ण पूर्ण संख्या बनता है। / The next hypotenuse is \(\sqrt{49}\), and \(\sqrt{49}=7\). At a perfect square, the hypotenuse becomes a whole number.
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वर्गमूल सर्पिल में \(\sqrt{624}\) का सही संख्या-रेखा अंतराल कौन-सा है?
What is the correct number-line interval for \(\sqrt{624}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(23<\sqrt{624}<24\)
B \(24<\sqrt{624}<25\)
C \(25<\sqrt{624}<26\)
D \(26<\sqrt{624}<27\)
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Correct Answer
B. \(24<\sqrt{624}<25\)
Explanation
Simple Explanation
क्योंकि \(24^2=576\) और \(25^2=625\) हैं। (624) इनके बीच है। / Because \(24^2=576\) and \(25^2=625\). The number (624) lies between them.
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वर्गमूल सर्पिल में \(\sqrt{899}\) के बाद बनने वाले कर्ण का सटीक मान क्या होगा?
What will be the exact value of the hypotenuse formed after \(\sqrt{899}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#perfect-square
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A (29)
B (30)
C (31)
D कोई पूर्ण संख्या नहीं / No whole number
Explanation opens after your attempt
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{900}\) है। \(900=30^2\), इसलिए इसका सटीक मान (30) है। / The next hypotenuse is \(\sqrt{900}\). Since \(900=30^2\), its exact value is (30).
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वर्गमूल सर्पिल में \(\sqrt{27}\) और \(\sqrt{32}\) के बारे में कौन-सा कथन सही है?
Which statement about \(\sqrt{27}\) and \(\sqrt{32}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A दोनों (5) और (6) के बीच हैं / Both lie between (5) and (6)
B \(\sqrt{27}\) (4) और (5) के बीच है, \(\sqrt{32}\) (5) और (6) के बीच है / \(\sqrt{27}\) lies between (4) and (5), \(\sqrt{32}\) lies between (5) and (6)
C \(\sqrt{27}\) (5) और (6) के बीच है, \(\sqrt{32}\) (6) और (7) के बीच है / \(\sqrt{27}\) lies between (5) and (6), \(\sqrt{32}\) lies between (6) and (7)
D दोनों ठीक (6) पर हैं / Both are exactly at (6)
Explanation opens after your attempt
Correct Answer
A. दोनों (5) और (6) के बीच हैं / Both lie between (5) and (6)
Explanation
Simple Explanation
(25<27<36) और (25<32<36) हैं। इसलिए दोनों के वर्गमूल (5) और (6) के बीच हैं।
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वर्गमूल सर्पिल में \(\sqrt{7}\) से \(\sqrt{8}\) बनने का सही कारण कौन-सा है?
What is the correct reason for \(\sqrt{8}\) being formed from \(\sqrt{7}\) in a square root spiral?
#square-root-spiral
#hard
#pythagoras
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A (\(\sqrt{7}\)2 +12 =8)
B \(\sqrt{7}+1=\sqrt{8}\)
C (\(\sqrt{7}\)2 +22 =8)
D \(\sqrt{7}\times1=\sqrt{8}\)
Explanation opens after your attempt
Correct Answer
A. (\(\sqrt{7}\)2 +12 =8)
Explanation
Simple Explanation
पाइथागोरस प्रमेय में भुजाओं के वर्ग जुड़ते हैं। इसलिए नया कर्ण \(\sqrt{8}\) बनता है। / In Pythagoras theorem, the squares of sides are added. Therefore the new hypotenuse becomes \(\sqrt{8}\).
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वर्गमूल सर्पिल में \(\sqrt{960}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही होगा?
Before placing \(\sqrt{960}\) on the number line using a square root spiral, which interval is correct?
#square-root-spiral
#hard
#number-line
#interval
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A \(29<\sqrt{960}<30\)
B \(30<\sqrt{960}<31\)
C \(31<\sqrt{960}<32\)
D \(32<\sqrt{960}<33\)
Explanation opens after your attempt
Correct Answer
B. \(30<\sqrt{960}<31\)
Explanation
Simple Explanation
क्योंकि \(30^2=900\) और \(31^2=961\) हैं। (960) इनके बीच है। / Because \(30^2=900\) and \(31^2=961\). The number (960) lies between them.
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वर्गमूल सर्पिल में \(\sqrt{n}\) से \(\sqrt{n+1}\) बनने की शर्त में कौन-सी बात आवश्यक है?
Which condition is necessary for \(\sqrt{n}\) to become \(\sqrt{n+1}\) in a square root spiral?
#square-root-spiral
#hard
#general-rule
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A नई लंब (1) इकाई हो और समकोण बने / The new perpendicular is (1) unit and a right angle is formed
B नई लंब (2) इकाई हो / The new perpendicular is (2) units
C कर्ण में सीधे (1) जोड़ा जाए / (1) is directly added to the hypotenuse
D त्रिभुज समबाहु हो / The triangle is equilateral
Explanation opens after your attempt
Correct Answer
A. नई लंब (1) इकाई हो और समकोण बने / The new perpendicular is (1) unit and a right angle is formed
Explanation
Simple Explanation
(1) इकाई लंब और समकोण से (\(\sqrt{n}\)2 +12 =n+1) लागू होता है। यही सर्पिल का नियम है। / With a (1) unit perpendicular and a right angle, (\(\sqrt{n}\)2 +12 =n+1) applies. This is the spiral rule.
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वर्गमूल सर्पिल में यदि \(\sqrt{168}\) से अगला कर्ण बनता है, तो कौन-सा संयुक्त निष्कर्ष सही है?
If the next hypotenuse is formed from \(\sqrt{168}\) in a square root spiral, which combined conclusion is correct?
#square-root-spiral
#hard
#next-root
#exact-value
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A नया कर्ण \(\sqrt{169}=13\) है / The new hypotenuse is \(\sqrt{169}=13\)
B नया कर्ण \(\sqrt{167}\) है / The new hypotenuse is \(\sqrt{167}\)
C नया कर्ण \(\sqrt{336}\) है / The new hypotenuse is \(\sqrt{336}\)
D नया कर्ण \(\sqrt{170}\) है / The new hypotenuse is \(\sqrt{170}\)
Explanation opens after your attempt
Correct Answer
A. नया कर्ण \(\sqrt{169}=13\) है / The new hypotenuse is \(\sqrt{169}=13\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{168+1}=\sqrt{169}\) होता है। \(169=13^2\), इसलिए मान (13) है। / The next hypotenuse is \(\sqrt{168+1}=\sqrt{169}\). Since \(169=13^2\), its value is (13).
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वर्गमूल सर्पिल में \(\sqrt{840}\) का सही स्थान कौन-सा है?
What is the correct position of \(\sqrt{840}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(27<\sqrt{840}<28\)
B \(28<\sqrt{840}<29\)
C \(29<\sqrt{840}<30\)
D \(30<\sqrt{840}<31\)
Explanation opens after your attempt
Correct Answer
B. \(28<\sqrt{840}<29\)
Explanation
Simple Explanation
क्योंकि \(28^2=784\) और \(29^2=841\) हैं। (840) इनके बीच आता है। / Because \(28^2=784\) and \(29^2=841\). The number (840) lies between them.
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वर्गमूल सर्पिल में \(\sqrt{50}\) और \(\sqrt{63}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{50}\) and \(\sqrt{63}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{50}\) (6) और (7) के बीच, \(\sqrt{63}\) (7) और (8) के बीच है / \(\sqrt{50}\) is between (6) and (7), \(\sqrt{63}\) is between (7) and (8)
B दोनों (7) और (8) के बीच हैं / Both lie between (7) and (8)
C \(\sqrt{50}\) (7) और (8) के बीच, \(\sqrt{63}\) (8) और (9) के बीच है / \(\sqrt{50}\) is between (7) and (8), \(\sqrt{63}\) is between (8) and (9)
D दोनों ठीक (8) पर हैं / Both are exactly at (8)
Explanation opens after your attempt
Correct Answer
B. दोनों (7) और (8) के बीच हैं / Both lie between (7) and (8)
Explanation
Simple Explanation
\(7^2<50<8^2\) और \(7^2<63<8^2\) हैं। इसलिए दोनों (7) और (8) के बीच हैं।
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वर्गमूल सर्पिल में \(\sqrt{n+1}\) नया कर्ण है। यदि पिछला कर्ण \(\sqrt{224}\) था, तो नया कर्ण कौन-सा होगा?
In a square root spiral, the new hypotenuse is \(\sqrt{n+1}\). If the previous hypotenuse was \(\sqrt{224}\), what will be the new hypotenuse?
#square-root-spiral
#hard
#general-rule
#next-root
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A \(\sqrt{223}\)
B \(\sqrt{224}\)
C \(\sqrt{225}\)
D \(\sqrt{448}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{225}\)
Explanation
Simple Explanation
पिछला कर्ण \(\sqrt{224}\) है, इसलिए नया कर्ण \(\sqrt{224+1}=\sqrt{225}\) होगा। / The previous hypotenuse is \(\sqrt{224}\), so the new hypotenuse is \(\sqrt{224+1}=\sqrt{225}\).
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वर्गमूल सर्पिल में \(\sqrt{224}\) से \(\sqrt{225}\) बनने पर नया कर्ण किस मान पर होगा?
When \(\sqrt{225}\) is formed from \(\sqrt{224}\) in a square root spiral, at what value will the new hypotenuse be?
#square-root-spiral
#hard
#perfect-square
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A (14)
B (15)
C (16)
D कोई पूर्ण संख्या नहीं / No whole number
Explanation opens after your attempt
Explanation
Simple Explanation
\(\sqrt{225}=15\) होता है। पूर्ण वर्ग बनने पर कर्ण पूर्ण संख्या पर आता है। / \(\sqrt{225}=15\). When a perfect square is formed, the hypotenuse lies at a whole number.
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वर्गमूल सर्पिल में \(\sqrt{399}\) पर (1) इकाई लंब बनाने से कौन-सा कर्ण बनेगा?
In a square root spiral, which hypotenuse is formed by drawing a (1) unit perpendicular on \(\sqrt{399}\)?
#square-root-spiral
#hard
#next-root
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A \(\sqrt{398}\)
B \(\sqrt{400}\)
C \(\sqrt{798}\)
D \(\sqrt{401}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{400}\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{399+1}=\sqrt{400}\) है। इसका सटीक मान (20) है। / The new hypotenuse is \(\sqrt{399+1}=\sqrt{400}\). Its exact value is (20).
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वर्गमूल सर्पिल में \(\sqrt{195}\) का अंतराल पहचानते समय कौन-सा निष्कर्ष सही है?
While identifying the interval of \(\sqrt{195}\) in a square root spiral, which conclusion is correct?
#square-root-spiral
#hard
#interval
#error-analysis
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A \(13<\sqrt{195}<14\)
B \(14<\sqrt{195}<15\)
C \(15<\sqrt{195}<16\)
D \(\sqrt{195}=14\)
Explanation opens after your attempt
Correct Answer
A. \(13<\sqrt{195}<14\)
Explanation
Simple Explanation
क्योंकि \(13^2=169\) और \(14^2=196\) हैं। (195) (196) से कम है। / Because \(13^2=169\) and \(14^2=196\). The number (195) is less than (196).
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वर्गमूल सर्पिल में \(\sqrt{2}\) को संख्या रेखा पर अंकित करने की सबसे सटीक प्रक्रिया कौन-सी है?
What is the most precise process to mark \(\sqrt{2}\) on the number line using a square root spiral?
#square-root-spiral
#hard
#number-line
#compass
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A \(\sqrt{2}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{2}\) hypotenuse length in a compass and draw an arc from the origin
B (2) इकाई दूरी सीधे अंकित करना / Directly mark (2) units
C किसी भी बिंदु से कोई भी चाप खींचना / Draw any arc from any point
D कर्ण को आधा करके अंकित करना / Mark half of the hypotenuse
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{2}\) hypotenuse length in a compass and draw an arc from the origin
Explanation
Simple Explanation
जिस वर्गमूल को अंकित करना है, उसी कर्ण की लंबाई कंपास में ली जाती है। मूल बिंदु से चाप सही स्थान देता है। / The hypotenuse length of the square root to be marked is taken in the compass. An arc from the origin gives the correct location.
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वर्गमूल सर्पिल में \(\sqrt{440}\) बनाने से ठीक पहले कौन-सा कर्ण होना चाहिए?
Which hypotenuse should be present just before constructing \(\sqrt{440}\) in a square root spiral?
#square-root-spiral
#hard
#previous-root
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A \(\sqrt{438}\)
B \(\sqrt{439}\)
C \(\sqrt{440}\)
D \(\sqrt{441}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{439}\)
Explanation
Simple Explanation
\(\sqrt{439}\) पर (1) इकाई लंब बनाने से \(\sqrt{440}\) बनता है। पिछला कर्ण एक कम संख्या का होता है। / Drawing a (1) unit perpendicular on \(\sqrt{439}\) forms \(\sqrt{440}\). The previous hypotenuse has one less number.
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वर्गमूल सर्पिल में \(\sqrt{150}\) और \(\sqrt{169}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{150}\) and \(\sqrt{169}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#perfect-square
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A \(\sqrt{150}\) (11) और (12) के बीच है और \(\sqrt{169}=13\) है / \(\sqrt{150}\) lies between (11) and (12), and \(\sqrt{169}=13\)
B \(\sqrt{150}\) (12) और (13) के बीच है और \(\sqrt{169}=13\) है / \(\sqrt{150}\) lies between (12) and (13), and \(\sqrt{169}=13\)
C \(\sqrt{150}=13\) और \(\sqrt{169}\) अपरिमेय है / \(\sqrt{150}=13\), and \(\sqrt{169}\) is irrational
D दोनों (13) हैं / Both are (13)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{150}\) (12) और (13) के बीच है और \(\sqrt{169}=13\) है / \(\sqrt{150}\) lies between (12) and (13), and \(\sqrt{169}=13\)
Explanation
Simple Explanation
\(12^2<150<13^2\) और \(169=13^2\) है। इसलिए \(\sqrt{150}\) (13) से कम है।
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वर्गमूल सर्पिल में \(\sqrt{5}\) बनाने के लिए \(\sqrt{4}\) और (1) का प्रयोग क्यों सही है?
Why is using \(\sqrt{4}\) and (1) correct for constructing \(\sqrt{5}\) in a square root spiral?
#square-root-spiral
#hard
#pythagoras
#construction
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A क्योंकि (\(\sqrt{4}\)2 +12 =5) / Because (\(\sqrt{4}\)2 +12 =5)
B क्योंकि \(\sqrt{4}+1=\sqrt{5}\) / Because \(\sqrt{4}+1=\sqrt{5}\)
C क्योंकि \(4+1=\sqrt{5}\) / Because \(4+1=\sqrt{5}\)
D क्योंकि (\(\sqrt{4}\)2 -12 =5) / Because (\(\sqrt{4}\)2 -12 =5)
Explanation opens after your attempt
Correct Answer
A. क्योंकि (\(\sqrt{4}\)2 +12 =5) / Because (\(\sqrt{4}\)2 +12 =5)
Explanation
Simple Explanation
\(\sqrt{4}\) पिछला कर्ण है और (1) नई लंब है। पाइथागोरस से कर्ण \(\sqrt{5}\) मिलता है। / \(\sqrt{4}\) is the previous hypotenuse and (1) is the new perpendicular. Pythagoras gives hypotenuse \(\sqrt{5}\).
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वर्गमूल सर्पिल में \(\sqrt{255}\) के बाद बनने वाला कर्ण किस विशेष मान पर स्थित होगा?
In a square root spiral, the hypotenuse formed after \(\sqrt{255}\) will be located at which special value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{254}\)
B \(\sqrt{256}=16\)
C \(\sqrt{510}\)
D \(\sqrt{257}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{256}=16\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{256}\) है। \(256=16^2\), इसलिए यह ठीक (16) पर स्थित है। / The next hypotenuse is \(\sqrt{256}\). Since \(256=16^2\), it is located exactly at (16).
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वर्गमूल सर्पिल में \(\sqrt{24}\) और \(\sqrt{26}\) की स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the positions of \(\sqrt{24}\) and \(\sqrt{26}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{24}\) (4) और (5) के बीच है, \(\sqrt{26}\) (5) और (6) के बीच है / \(\sqrt{24}\) lies between (4) and (5), \(\sqrt{26}\) lies between (5) and (6)
B दोनों (4) और (5) के बीच हैं / Both lie between (4) and (5)
C दोनों (5) और (6) के बीच हैं / Both lie between (5) and (6)
D \(\sqrt{24}=5\) और \(\sqrt{26}\) अपरिमेय है / \(\sqrt{24}=5\) and \(\sqrt{26}\) is irrational
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{24}\) (4) और (5) के बीच है, \(\sqrt{26}\) (5) और (6) के बीच है / \(\sqrt{24}\) lies between (4) and (5), \(\sqrt{26}\) lies between (5) and (6)
Explanation
Simple Explanation
\(4^2<24<5^2\) और \(5^2<26<6^2\) हैं। इसलिए दोनों अलग अंतरालों में आते हैं।
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वर्गमूल सर्पिल में \(\sqrt{624}\) के बाद कौन-सा कर्ण बनेगा और उसका सटीक मान क्या है?
In a square root spiral, which hypotenuse is formed after \(\sqrt{624}\), and what is its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{625}=25\)
B \(\sqrt{623}\), कोई पूर्ण मान नहीं / \(\sqrt{623}\), no whole value
C \(\sqrt{1248}\), कोई पूर्ण मान नहीं / \(\sqrt{1248}\), no whole value
D \(\sqrt{626}\), कोई पूर्ण मान नहीं / \(\sqrt{626}\), no whole value
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{625}=25\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{625}\) है। क्योंकि \(625=25^2\), इसका सटीक मान (25) है। / The next hypotenuse is \(\sqrt{625}\). Since \(625=25^2\), its exact value is (25).
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वर्गमूल सर्पिल में \(\sqrt{80}\) और \(\sqrt{82}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{80}\) and \(\sqrt{82}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#number-line
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A \(\sqrt{80}\) (8) और (9) के बीच है, \(\sqrt{82}\) (9) और (10) के बीच है / \(\sqrt{80}\) lies between (8) and (9), \(\sqrt{82}\) lies between (9) and (10)
B \(\sqrt{80}\) (8) और (9) के बीच है, \(\sqrt{82}\) भी (9) और (10) के बीच है / \(\sqrt{80}\) lies between (8) and (9), \(\sqrt{82}\) also lies between (9) and (10)
C \(\sqrt{80}\) (8) और (9) के बीच है, \(\sqrt{82}\) (9) और (10) के बीच है क्योंकि (82>81) / \(\sqrt{80}\) lies between (8) and (9), \(\sqrt{82}\) lies between (9) and (10) because (82>81)
D दोनों ठीक (9) पर हैं / Both are exactly at (9)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{80}\) (8) और (9) के बीच है, \(\sqrt{82}\) (9) और (10) के बीच है क्योंकि (82>81) / \(\sqrt{80}\) lies between (8) and (9), \(\sqrt{82}\) lies between (9) and (10) because (82>81)
Explanation
Simple Explanation
(80<81) होने से \(\sqrt{80}<9\), और (81<82<100) होने से \(\sqrt{82}\) (9) और (10) के बीच है। / Since (80<81), \(\sqrt{80}<9\), and since (81<82<100), \(\sqrt{82}\) lies between (9) and (10).
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वर्गमूल सर्पिल में यदि \(\sqrt{n+1}\) अपरिमेय है, तो (n+1) के बारे में कौन-सा निष्कर्ष सही है?
In a square root spiral, if \(\sqrt{n+1}\) is irrational, what conclusion about (n+1) is correct?
#square-root-spiral
#hard
#irrational
#concept
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A (n+1) पूर्ण वर्ग नहीं है / (n+1) is not a perfect square
B (n+1) हमेशा सम है / (n+1) is always even
C (n+1) हमेशा अभाज्य है / (n+1) is always prime
D (n+1=0) है / (n+1=0)
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Correct Answer
A. (n+1) पूर्ण वर्ग नहीं है / (n+1) is not a perfect square
Explanation
Simple Explanation
पूर्णांक का वर्गमूल पूर्ण संख्या तभी होता है जब वह पूर्ण वर्ग हो। पूर्ण वर्ग न हो तो वर्गमूल अपरिमेय हो सकता है। / The square root of an integer is a whole number only when it is a perfect square. If it is not a perfect square, the square root can be irrational.
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वर्गमूल सर्पिल में \(\sqrt{168}\) और \(\sqrt{170}\) की सही तुलना कौन-सी है?
Which is the correct comparison of \(\sqrt{168}\) and \(\sqrt{170}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{168}\) (12) और (13) के बीच, \(\sqrt{170}\) (13) और (14) के बीच है / \(\sqrt{168}\) lies between (12) and (13), \(\sqrt{170}\) lies between (13) and (14)
B दोनों (13) और (14) के बीच हैं / Both lie between (13) and (14)
C \(\sqrt{168}=13\) और \(\sqrt{170}\) अपरिमेय है / \(\sqrt{168}=13\) and \(\sqrt{170}\) is irrational
D दोनों (12) और (13) के बीच हैं / Both lie between (12) and (13)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{168}\) (12) और (13) के बीच, \(\sqrt{170}\) (13) और (14) के बीच है / \(\sqrt{168}\) lies between (12) and (13), \(\sqrt{170}\) lies between (13) and (14)
Explanation
Simple Explanation
\(168<169=13^2\), इसलिए \(\sqrt{168}<13\)। (170>169), इसलिए \(\sqrt{170}>13\)। / Since \(168<169=13^2\), \(\sqrt{168}<13\). Since (170>169), \(\sqrt{170}>13\).
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वर्गमूल सर्पिल में \(\sqrt{12}\) से अगला कर्ण निकालने में कौन-सा विकल्प तर्कसंगत है?
Which option is logical for finding the next hypotenuse from \(\sqrt{12}\) in a square root spiral?
#square-root-spiral
#hard
#logic
#pythagoras
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A (\(\sqrt{12}\)2 +12 =13), इसलिए नया कर्ण \(\sqrt{13}\) / (\(\sqrt{12}\)2 +12 =13), so the new hypotenuse is \(\sqrt{13}\)
B \(\sqrt{12}+1=\sqrt{13}\), इसलिए नया कर्ण \(\sqrt{13}\) / \(\sqrt{12}+1=\sqrt{13}\), so the new hypotenuse is \(\sqrt{13}\)
C \(12^2+1^2=13\), इसलिए नया कर्ण \(\sqrt{13}\) / \(12^2+1^2=13\), so the new hypotenuse is \(\sqrt{13}\)
D \(\sqrt{12}-1=\sqrt{13}\), इसलिए नया कर्ण \(\sqrt{13}\) / \(\sqrt{12}-1=\sqrt{13}\), so the new hypotenuse is \(\sqrt{13}\)
Explanation opens after your attempt
Correct Answer
A. (\(\sqrt{12}\)2 +12 =13), इसलिए नया कर्ण \(\sqrt{13}\) / (\(\sqrt{12}\)2 +12 =13), so the new hypotenuse is \(\sqrt{13}\)
Explanation
Simple Explanation
सही तर्क (\(\sqrt{12}\)2 +12 =13) है। सर्पिल में पाइथागोरस प्रमेय लागू होता है। / The correct reasoning is (\(\sqrt{12}\)2 +12 =13). Pythagoras theorem applies in the spiral.
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वर्गमूल सर्पिल में \(\sqrt{1023}\) के बाद बनने वाला कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?
In a square root spiral, which hypotenuse is formed after \(\sqrt{1023}\), and what is its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{1024}=32\)
B \(\sqrt{1022}\), कोई पूर्ण मान नहीं / \(\sqrt{1022}\), no whole value
C \(\sqrt{2046}\), कोई पूर्ण मान नहीं / \(\sqrt{2046}\), no whole value
D \(\sqrt{1025}=32\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{1024}=32\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{1024}\) है। \(1024=32^2\), इसलिए सटीक मान (32) है। / The next hypotenuse is \(\sqrt{1024}\). Since \(1024=32^2\), the exact value is (32).
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वर्गमूल सर्पिल में \(\sqrt{35}\) के बाद बनने वाले कर्ण और \(\sqrt{37}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the hypotenuse formed after \(\sqrt{35}\) and \(\sqrt{37}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#next-root
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A अगला कर्ण \(\sqrt{36}=6\) है और \(\sqrt{37}\) (6) और (7) के बीच है / The next hypotenuse is \(\sqrt{36}=6\), and \(\sqrt{37}\) lies between (6) and (7)
B अगला कर्ण \(\sqrt{34}\) है और \(\sqrt{37}=6\) / The next hypotenuse is \(\sqrt{34}\), and \(\sqrt{37}=6\)
C दोनों ठीक (6) पर हैं / Both are exactly at (6)
D अगला कर्ण \(\sqrt{70}\) है और \(\sqrt{37}\) (5) और (6) के बीच है / The next hypotenuse is \(\sqrt{70}\), and \(\sqrt{37}\) lies between (5) and (6)
Explanation opens after your attempt
Correct Answer
A. अगला कर्ण \(\sqrt{36}=6\) है और \(\sqrt{37}\) (6) और (7) के बीच है / The next hypotenuse is \(\sqrt{36}=6\), and \(\sqrt{37}\) lies between (6) and (7)
Explanation
Simple Explanation
\(\sqrt{35}\) के बाद \(\sqrt{36}=6\) बनता है। \(6^2<37<7^2\), इसलिए \(\sqrt{37}\) (6) और (7) के बीच है। / After \(\sqrt{35}\), \(\sqrt{36}=6\) is formed. Since \(6^2<37<7^2\), \(\sqrt{37}\) lies between (6) and (7).
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वर्गमूल सर्पिल में \(\sqrt{1368}\) का सही अंतराल कौन-सा है?
What is the correct interval for \(\sqrt{1368}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(35<\sqrt{1368}<36\)
B \(36<\sqrt{1368}<37\)
C \(37<\sqrt{1368}<38\)
D \(38<\sqrt{1368}<39\)
Explanation opens after your attempt
Correct Answer
B. \(36<\sqrt{1368}<37\)
Explanation
Simple Explanation
\(36^2=1296\) और \(37^2=1369\) हैं। (1368) इनके बीच है, इसलिए \(\sqrt{1368}\) (36) और (37) के बीच है। / \(36^2=1296\) and \(37^2=1369\). The number (1368) lies between them, so \(\sqrt{1368}\) lies between (36) and (37).
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वर्गमूल सर्पिल में कौन-सा कथन निर्माण की दृष्टि से सबसे गलत है?
Which statement is most incorrect from the construction point of view in a square root spiral?
#square-root-spiral
#hard
#wrong-method
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A हर नए चरण में समकोण बनाना / Making a right angle at every new step
B नई लंब भुजा को (1) इकाई रखना / Keeping the new perpendicular side (1) unit
C पिछले कर्ण को नई भुजा की तरह लेना / Taking the previous hypotenuse as a new side
D अगला कर्ण पिछले कर्ण में सीधे (1) जोड़कर निकालना / Finding the next hypotenuse by directly adding (1) to the previous hypotenuse
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Correct Answer
D. अगला कर्ण पिछले कर्ण में सीधे (1) जोड़कर निकालना / Finding the next hypotenuse by directly adding (1) to the previous hypotenuse
Explanation
Simple Explanation
वर्गमूल सर्पिल में सीधे जोड़ नहीं होता। नया कर्ण समकोण त्रिभुज और पाइथागोरस से मिलता है। / Direct addition is not used in a square root spiral. The new hypotenuse is found using a right triangle and Pythagoras theorem.
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वर्गमूल सर्पिल में \(\sqrt{n}\) को संख्या रेखा पर रखने से पहले सबसे विश्वसनीय जाँच कौन-सी है?
Before placing \(\sqrt{n}\) on the number line in a square root spiral, what is the most reliable check?
#square-root-spiral
#hard
#number-line
#method
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A निकटतम पूर्ण वर्गों (a-2 <n<(a+1)2 ) की पहचान करना / Identify nearest perfect squares (a-2 <n<(a+1)2 )
B \(\sqrt{n}\) को हमेशा (n) पर रखना / Always place \(\sqrt{n}\) at (n)
C हर वर्गमूल को (1) और (2) के बीच रखना / Place every square root between (1) and (2)
D दशमलव याद करके बिना निर्माण के अंकित करना / Memorize decimal and mark without construction
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Correct Answer
A. निकटतम पूर्ण वर्गों (a-2 <n<(a+1)2 ) की पहचान करना / Identify nearest perfect squares (a-2 <n<(a+1)2 )
Explanation
Simple Explanation
निकटतम पूर्ण वर्ग सही अंतराल बताते हैं। फिर सर्पिल की लंबाई कंपास से संख्या रेखा पर रखी जाती है। / Nearest perfect squares give the correct interval. Then the spiral length is placed on the number line using a compass.
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वर्गमूल सर्पिल का कठिन स्तर पर सबसे सटीक गणितीय सार कौन-सा है?
At hard level, which is the most precise mathematical summary of a square root spiral?
#square-root-spiral
#hard
#main-idea
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A यह सीधे वर्गमूलों को जोड़ने की विधि है / It is a method of directly adding square roots
B यह समकोण त्रिभुजों की क्रमिक रचना है जिसमें (\(\sqrt{n}\)2 +12 =n+1) से अगला कर्ण बनता है / It is a successive construction of right triangles where the next hypotenuse is formed by (\(\sqrt{n}\)2 +12 =n+1)
C यह केवल पूर्ण वर्गों को याद करने की सूची है / It is only a list for memorizing perfect squares
D यह बिना समकोण के बनने वाली रचना है / It is a construction made without a right angle
Explanation opens after your attempt
Correct Answer
B. यह समकोण त्रिभुजों की क्रमिक रचना है जिसमें (\(\sqrt{n}\)2 +12 =n+1) से अगला कर्ण बनता है / It is a successive construction of right triangles where the next hypotenuse is formed by (\(\sqrt{n}\)2 +12 =n+1)
Explanation
Simple Explanation
वर्गमूल सर्पिल पाइथागोरस प्रमेय पर आधारित है। पिछला कर्ण और (1) इकाई लंब मिलकर अगला वर्गमूल बनाते हैं। / A square root spiral is based on Pythagoras theorem. The previous hypotenuse and (1) unit perpendicular form the next square root.
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वर्गमूल सर्पिल में यदि किसी चरण पर कर्ण \(\sqrt{728}\) है, तो अगले कर्ण को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही होगा?
In a square root spiral, if the hypotenuse at a step is \(\sqrt{728}\), which interval is correct before placing the next hypotenuse on the number line?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(25<\sqrt{729}<26\)
B \(26<\sqrt{729}<27\)
C \(\sqrt{729}=27\)
D \(27<\sqrt{729}<28\)
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Correct Answer
C. \(\sqrt{729}=27\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{728+1}=\sqrt{729}\) होगा। \(729=27^2\), इसलिए यह ठीक (27) पर स्थित होगा। / The next hypotenuse is \(\sqrt{728+1}=\sqrt{729}\). Since \(729=27^2\), it will lie exactly at (27).
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वर्गमूल सर्पिल में यदि पिछले कर्ण की लंबाई \(\sqrt{899}\) है, तो (1) इकाई लंब जोड़ने पर नया कर्ण किस सटीक मान पर होगा?
In a square root spiral, if the previous hypotenuse is \(\sqrt{899}\), at what exact value will the new hypotenuse be after adding a (1) unit perpendicular?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{898}\), कोई पूर्ण मान नहीं / \(\sqrt{898}\), no whole value
B \(\sqrt{900}=30\)
C \(\sqrt{1800}\), कोई पूर्ण मान नहीं / \(\sqrt{1800}\), no whole value
D \(\sqrt{901}\), कोई पूर्ण मान नहीं / \(\sqrt{901}\), no whole value
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{900}=30\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{899+1}=\sqrt{900}\) होगा। \(900=30^2\), इसलिए सटीक मान (30) है। / The new hypotenuse is \(\sqrt{899+1}=\sqrt{900}\). Since \(900=30^2\), the exact value is (30).
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यदि वर्गमूल सर्पिल में नया कर्ण (40) के बराबर है, तो उससे ठीक पहले वाला कर्ण कौन-सा था?
If the new hypotenuse in a square root spiral is equal to (40), which hypotenuse came immediately before it?
#square-root-spiral
#hard
#reverse-rule
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A \(\sqrt{1599}\)
B \(\sqrt{1600}\)
C \(\sqrt{1601}\)
D \(\sqrt{40}\)
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Correct Answer
A. \(\sqrt{1599}\)
Explanation
Simple Explanation
नया कर्ण \(40=\sqrt{1600}\) है। इसलिए पिछले चरण का कर्ण \(\sqrt{1599}\) था। / The new hypotenuse is \(40=\sqrt{1600}\). Therefore the previous hypotenuse was \(\sqrt{1599}\).
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\(\sqrt{2023}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही पहचाना जाएगा?
Before placing \(\sqrt{2023}\) on the number line, which interval will be correctly identified?
#square-root-spiral
#hard
#number-line
#interval
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A \(41<\sqrt{2023}<42\)
B \(42<\sqrt{2023}<43\)
C \(43<\sqrt{2023}<44\)
D \(44<\sqrt{2023}<45\)
Explanation opens after your attempt
Correct Answer
D. \(44<\sqrt{2023}<45\)
Explanation
Simple Explanation
क्योंकि \(44^2=1936\) और \(45^2=2025\) हैं। (2023) इनके बीच है। / Because \(44^2=1936\) and \(45^2=2025\). The number (2023) lies between them.
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यदि कोई विद्यार्थी \(\sqrt{98}+1=\sqrt{99}\) लिखकर अगला कर्ण बताता है, तो सही सुधार कौन-सा है?
If a student writes \(\sqrt{98}+1=\sqrt{99}\) to find the next hypotenuse, what is the correct correction?
#square-root-spiral
#hard
#error-correction
#pythagoras
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A \(\sqrt{98^2+1^2}=\sqrt{99}\)
B \(\sqrt{98+2}=\sqrt{99}\)
C (\sqrt{\(\sqrt{98}\)2 +12 }=\sqrt{99})
D \(\sqrt{98-1}=\sqrt{99}\)
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Correct Answer
C. (\sqrt{\(\sqrt{98}\)2 +12 }=\sqrt{99})
Explanation
Simple Explanation
वर्गमूल सर्पिल में सीधे लंबाइयाँ नहीं जोड़ी जातीं। सही विधि पाइथागोरस प्रमेय से वर्गों का योग लेना है। / Lengths are not added directly in a square root spiral. The correct method is to add squares using Pythagoras theorem.
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यदि सामान्य वर्गमूल सर्पिल में (1) इकाई की जगह (7) इकाई लंब ली जाए, तो \(\sqrt{n}\) से बनने वाला कर्ण किस रूप में होगा?
If a (7) unit perpendicular is used instead of (1) unit in the usual square root spiral, what will be the hypotenuse formed from \(\sqrt{n}\)?
#square-root-spiral
#hard
#unit-change
#general-rule
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A \(\sqrt{n+49}\)
B \(\sqrt{n+7}\)
C \(\sqrt{7n}\)
D \(\sqrt{n+14}\)
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Correct Answer
A. \(\sqrt{n+49}\)
Explanation
Simple Explanation
पाइथागोरस से (\(\sqrt{n}\)2 +72 =n+49) होगा। नई लंब बदलने से सामान्य क्रम बदल जाता है। / By Pythagoras, (\(\sqrt{n}\)2 +72 =n+49). Changing the perpendicular changes the usual sequence.
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वर्गमूल सर्पिल में \(\sqrt{1224}\) पर (1) इकाई लंब बनाने से नया कर्ण कौन-सा होगा और कहाँ स्थित होगा?
In a square root spiral, drawing a (1) unit perpendicular on \(\sqrt{1224}\) gives which new hypotenuse and where is it located?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{1223}\), (34) और (35) के बीच / \(\sqrt{1223}\), between (34) and (35)
B \(\sqrt{2448}\), (49) और (50) के बीच / \(\sqrt{2448}\), between (49) and (50)
C \(\sqrt{1226}\), (35) और (36) के बीच / \(\sqrt{1226}\), between (35) and (36)
D \(\sqrt{1225}\), ठीक (35) पर / \(\sqrt{1225}\), exactly at (35)
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Correct Answer
D. \(\sqrt{1225}\), ठीक (35) पर / \(\sqrt{1225}\), exactly at (35)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{1225}\) है। क्योंकि \(\sqrt{1225}=35\), यह ठीक (35) पर स्थित होगा। / The new hypotenuse is \(\sqrt{1225}\). Since \(\sqrt{1225}=35\), it will be located exactly at (35).
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वर्गमूल सर्पिल में \(\sqrt{528}\) और \(\sqrt{530}\) की संख्या-रेखा स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the number-line positions of \(\sqrt{528}\) and \(\sqrt{530}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A दोनों (22) और (23) के बीच हैं / Both lie between (22) and (23)
B \(\sqrt{528}\) (22) और (23) के बीच है, \(\sqrt{530}\) (23) और (24) के बीच है / \(\sqrt{528}\) lies between (22) and (23), \(\sqrt{530}\) lies between (23) and (24)
C दोनों (23) और (24) के बीच हैं / Both lie between (23) and (24)
D \(\sqrt{528}=23\) और \(\sqrt{530}\) अपरिमेय है / \(\sqrt{528}=23\) and \(\sqrt{530}\) is irrational
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{528}\) (22) और (23) के बीच है, \(\sqrt{530}\) (23) और (24) के बीच है / \(\sqrt{528}\) lies between (22) and (23), \(\sqrt{530}\) lies between (23) and (24)
Explanation
Simple Explanation
\(528<529=23^2\), इसलिए \(\sqrt{528}<23\)। (530>529), इसलिए \(\sqrt{530}>23\)। / Since \(528<529=23^2\), \(\sqrt{528}<23\). Since (530>529), \(\sqrt{530}>23\).
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वर्गमूल सर्पिल में \(\sqrt{1520}\) के बाद बनने वाले कर्ण का सटीक मान क्या होगा?
What will be the exact value of the hypotenuse formed after \(\sqrt{1520}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#exact-value
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A (38)
B कोई पूर्ण संख्या नहीं / No whole number
C (39)
D (40)
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Explanation
Simple Explanation
अगला कर्ण \(\sqrt{1521}\) होगा। \(1521=39^2\), इसलिए इसका सटीक मान (39) है। / The next hypotenuse is \(\sqrt{1521}\). Since \(1521=39^2\), its exact value is (39).
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यदि (k)वाँ कर्ण \(\sqrt{k}\) माना जाए, तो \(\sqrt{144}\) कौन-सा कर्ण होगा और उसका मान क्या होगा?
If the (k)-th hypotenuse is considered \(\sqrt{k}\), which hypotenuse is \(\sqrt{144}\), and what is its value?
#square-root-spiral
#hard
#sequence
#perfect-square
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A (143)वाँ, (12) / (143)-th, (12)
B (145)वाँ, (12) / (145)-th, (12)
C (144)वाँ, (144) / (144)-th, (144)
D (144)वाँ, (12) / (144)-th, (12)
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Correct Answer
D. (144)वाँ, (12) / (144)-th, (12)
Explanation
Simple Explanation
यदि (k)वाँ कर्ण \(\sqrt{k}\) है, तो \(\sqrt{144}\) (144)वाँ कर्ण है। \(\sqrt{144}=12\) होता है। / If the (k)-th hypotenuse is \(\sqrt{k}\), then \(\sqrt{144}\) is the (144)-th hypotenuse. Also, \(\sqrt{144}=12\).
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वर्गमूल सर्पिल में \(\sqrt{390}\) बनाने के लिए कौन-सा पिछला कर्ण और कौन-सी नई लंब सही है?
To construct \(\sqrt{390}\) in a square root spiral, which previous hypotenuse and new perpendicular are correct?
#square-root-spiral
#hard
#construction
#previous-root
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A \(\sqrt{388}\) और (2) / \(\sqrt{388}\) and (2)
B \(\sqrt{390}\) और (1) / \(\sqrt{390}\) and (1)
C \(\sqrt{389}\) और (1) / \(\sqrt{389}\) and (1)
D \(\sqrt{391}\) और (1) / \(\sqrt{391}\) and (1)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{389}\) और (1) / \(\sqrt{389}\) and (1)
Explanation
Simple Explanation
(\(\sqrt{389}\)2 +12 =390) है। इसलिए \(\sqrt{390}\) के लिए पिछला कर्ण \(\sqrt{389}\) होगा। / (\(\sqrt{389}\)2 +12 =390). So the previous hypotenuse for \(\sqrt{390}\) is \(\sqrt{389}\).
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\(\sqrt{1295}\) के बाद बनने वाला कर्ण वर्गमूल सर्पिल में किस सटीक मान पर होगा?
In a square root spiral, the hypotenuse formed after \(\sqrt{1295}\) will be at which exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{1296}=36\)
B \(\sqrt{1294}\), कोई पूर्ण मान नहीं / \(\sqrt{1294}\), no whole value
C \(\sqrt{2590}\), कोई पूर्ण मान नहीं / \(\sqrt{2590}\), no whole value
D \(\sqrt{1297}=36\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{1296}=36\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{1296}\) होगा। \(1296=36^2\), इसलिए इसका मान (36) है। / The next hypotenuse is \(\sqrt{1296}\). Since \(1296=36^2\), its value is (36).
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वर्गमूल सर्पिल में \(\sqrt{675}\) का स्थान पहचानने के लिए कौन-सी असमानता सही है?
Which inequality is correct to identify the position of \(\sqrt{675}\) in a square root spiral?
#square-root-spiral
#hard
#inequality
#interval
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A \(,24^2<675<25^2,\)
B \(,25^2<675<26^2,\)
C \(,26^2<675<27^2,\)
D \(,27^2<675<28^2,\)
Explanation opens after your attempt
Correct Answer
B. \(,25^2<675<26^2,\)
Explanation
Simple Explanation
\(25^2=625\) और \(26^2=676\) हैं। (675) इनके बीच है। / \(25^2=625\) and \(26^2=676\). The number (675) lies between them.
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यदि वर्गमूल सर्पिल में \(\sqrt{n}\) के बाद बना कर्ण (52) है, तो (n) का मान क्या होगा?
If the hypotenuse formed after \(\sqrt{n}\) in a square root spiral is (52), what is the value of (n)?
#square-root-spiral
#hard
#reverse-rule
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A (52)
B (2705)
C (2703)
D (2704)
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Explanation
Simple Explanation
नया कर्ण \(52=\sqrt{2704}\) है। इसलिए (n+1=2704), अतः (n=2703)। / The new hypotenuse is \(52=\sqrt{2704}\). Therefore (n+1=2704), so (n=2703).
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वर्गमूल सर्पिल में \(\sqrt{18}\) से \(\sqrt{22}\) तक सामान्य निर्माण का सही क्रम कौन-सा है?
In a square root spiral, which is the correct usual construction order from \(\sqrt{18}\) to \(\sqrt{22}\)?
#square-root-spiral
#hard
#sequence
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A \(\sqrt{18}\rightarrow\sqrt{20}\rightarrow\sqrt{22}\)
B \(\sqrt{18}\rightarrow\sqrt{22}\rightarrow\sqrt{19}\)
C \(\sqrt{18}\rightarrow\sqrt{19}\rightarrow\sqrt{20}\rightarrow\sqrt{21}\rightarrow\sqrt{22}\)
D \(\sqrt{22}\rightarrow\sqrt{21}\rightarrow\sqrt{20}\)
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Correct Answer
C. \(\sqrt{18}\rightarrow\sqrt{19}\rightarrow\sqrt{20}\rightarrow\sqrt{21}\rightarrow\sqrt{22}\)
Explanation
Simple Explanation
सर्पिल में कर्ण क्रमिक रूप से एक-एक बढ़ते हैं। सामान्य निर्माण में बीच के चरण नहीं छोड़े जाते। / Hypotenuses increase one by one in the spiral. In the usual construction, intermediate steps are not skipped.
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वर्गमूल सर्पिल में \(\sqrt{440}\) और \(\sqrt{442}\) की संख्या-रेखा स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the number-line positions of \(\sqrt{440}\) and \(\sqrt{442}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{440}=21\) और \(\sqrt{442}\) अपरिमेय है / \(\sqrt{440}=21\) and \(\sqrt{442}\) is irrational
B \(\sqrt{440}\) (20) और (21) के बीच है, \(\sqrt{442}\) (21) और (22) के बीच है / \(\sqrt{440}\) lies between (20) and (21), \(\sqrt{442}\) lies between (21) and (22)
C दोनों (20) और (21) के बीच हैं / Both lie between (20) and (21)
D दोनों (21) और (22) के बीच हैं / Both lie between (21) and (22)
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Correct Answer
B. \(\sqrt{440}\) (20) और (21) के बीच है, \(\sqrt{442}\) (21) और (22) के बीच है / \(\sqrt{440}\) lies between (20) and (21), \(\sqrt{442}\) lies between (21) and (22)
Explanation
Simple Explanation
\(440<441=21^2\), इसलिए \(\sqrt{440}<21\)। (442>441), इसलिए \(\sqrt{442}>21\)। / Since \(440<441=21^2\), \(\sqrt{440}<21\). Since (442>441), \(\sqrt{442}>21\).
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वर्गमूल सर्पिल में \(\sqrt{624}\) से बनने वाले अगले कर्ण और \(\sqrt{626}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the next hypotenuse from \(\sqrt{624}\) and \(\sqrt{626}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#next-root
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A अगला कर्ण \(\sqrt{625}=25\) है और \(\sqrt{626}\) (25) और (26) के बीच है / The next hypotenuse is \(\sqrt{625}=25\), and \(\sqrt{626}\) lies between (25) and (26)
B अगला कर्ण \(\sqrt{623}\) है और \(\sqrt{626}=25\) है / The next hypotenuse is \(\sqrt{623}\), and \(\sqrt{626}=25\)
C दोनों ठीक (25) पर हैं / Both are exactly at (25)
D अगला कर्ण \(\sqrt{1248}\) है और \(\sqrt{626}\) (24) और (25) के बीच है / The next hypotenuse is \(\sqrt{1248}\), and \(\sqrt{626}\) lies between (24) and (25)
Explanation opens after your attempt
Correct Answer
A. अगला कर्ण \(\sqrt{625}=25\) है और \(\sqrt{626}\) (25) और (26) के बीच है / The next hypotenuse is \(\sqrt{625}=25\), and \(\sqrt{626}\) lies between (25) and (26)
Explanation
Simple Explanation
\(\sqrt{624}\) के बाद \(\sqrt{625}=25\) बनता है। \(25^2<626<26^2\), इसलिए \(\sqrt{626}\) (25) और (26) के बीच है। / After \(\sqrt{624}\), \(\sqrt{625}=25\) is formed. Since \(25^2<626<26^2\), \(\sqrt{626}\) lies between (25) and (26).
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वर्गमूल सर्पिल में \(\sqrt{2499}\) और \(\sqrt{2500}\) की तुलना में कौन-सा निष्कर्ष सही है?
Which conclusion is correct when comparing \(\sqrt{2499}\) and \(\sqrt{2500}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#perfect-square
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A \(\sqrt{2499}=50\) और \(\sqrt{2500}\) अपरिमेय है / \(\sqrt{2499}=50\) and \(\sqrt{2500}\) is irrational
B दोनों (49) हैं / Both are (49)
C \(\sqrt{2499}\) (49) और (50) के बीच है और \(\sqrt{2500}=50\) है / \(\sqrt{2499}\) lies between (49) and (50), and \(\sqrt{2500}=50\)
D दोनों (50) से बड़े हैं / Both are greater than (50)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{2499}\) (49) और (50) के बीच है और \(\sqrt{2500}=50\) है / \(\sqrt{2499}\) lies between (49) and (50), and \(\sqrt{2500}=50\)
Explanation
Simple Explanation
\(49^2<2499<50^2\) और \(2500=50^2\) है। इसलिए \(\sqrt{2500}\) ठीक (50) है।
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वर्गमूल सर्पिल में \(\sqrt{255}\) के बाद बनने वाले कर्ण का मान क्या है?
What is the value of the hypotenuse formed after \(\sqrt{255}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#exact-value
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A \(\sqrt{254}\)
B (16)
C \(\sqrt{510}\)
D \(\sqrt{257}\)
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Explanation
Simple Explanation
अगला कर्ण \(\sqrt{256}\) होगा और \(\sqrt{256}=16\) है। पूर्ण वर्ग पर कर्ण पूर्ण संख्या बनता है। / The next hypotenuse is \(\sqrt{256}\), and \(\sqrt{256}=16\). At a perfect square, the hypotenuse becomes a whole number.
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\(\sqrt{2400}\) का सही संख्या-रेखा अंतराल कौन-सा है?
What is the correct number-line interval for \(\sqrt{2400}\)?
#square-root-spiral
#hard
#number-line
#interval
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A \(47<\sqrt{2400}<48\)
B \(48<\sqrt{2400}<49\)
C \(49<\sqrt{2400}<50\)
D \(50<\sqrt{2400}<51\)
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Correct Answer
B. \(48<\sqrt{2400}<49\)
Explanation
Simple Explanation
क्योंकि \(48^2=2304\) और \(49^2=2401\) हैं। (2400) इनके बीच है। / Because \(48^2=2304\) and \(49^2=2401\). The number (2400) lies between them.
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वर्गमूल सर्पिल में \(\sqrt{3480}\) के बाद बनने वाले कर्ण का सटीक मान क्या होगा?
What will be the exact value of the hypotenuse formed after \(\sqrt{3480}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#perfect-square
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A (58)
B (59)
C (60)
D कोई पूर्ण संख्या नहीं / No whole number
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Explanation
Simple Explanation
अगला कर्ण \(\sqrt{3481}\) है। \(3481=59^2\), इसलिए इसका सटीक मान (59) है। / The next hypotenuse is \(\sqrt{3481}\). Since \(3481=59^2\), its exact value is (59).
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वर्गमूल सर्पिल में \(\sqrt{143}\) और \(\sqrt{170}\) के बारे में कौन-सा कथन सही है?
Which statement about \(\sqrt{143}\) and \(\sqrt{170}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{143}\) (11) और (12) के बीच है, \(\sqrt{170}\) (13) और (14) के बीच है / \(\sqrt{143}\) lies between (11) and (12), \(\sqrt{170}\) lies between (13) and (14)
B दोनों (12) और (13) के बीच हैं / Both lie between (12) and (13)
C दोनों (13) और (14) के बीच हैं / Both lie between (13) and (14)
D दोनों ठीक पूर्ण संख्या पर हैं / Both are exactly at whole numbers
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{143}\) (11) और (12) के बीच है, \(\sqrt{170}\) (13) और (14) के बीच है / \(\sqrt{143}\) lies between (11) and (12), \(\sqrt{170}\) lies between (13) and (14)
Explanation
Simple Explanation
\(11^2<143<12^2\) और \(13^2<170<14^2\) हैं। इसलिए दोनों अलग अंतरालों में हैं।
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वर्गमूल सर्पिल में \(\sqrt{84}\) से \(\sqrt{85}\) बनने का सही कारण कौन-सा है?
What is the correct reason for \(\sqrt{85}\) being formed from \(\sqrt{84}\) in a square root spiral?
#square-root-spiral
#hard
#pythagoras
#next-root
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A \(\sqrt{84}+1=\sqrt{85}\)
B (\(\sqrt{84}\)2 +22 =85)
C \(\sqrt{84}\times1=\sqrt{85}\)
D (\(\sqrt{84}\)2 +12 =85)
Explanation opens after your attempt
Correct Answer
D. (\(\sqrt{84}\)2 +12 =85)
Explanation
Simple Explanation
पाइथागोरस प्रमेय में भुजाओं के वर्ग जुड़ते हैं। इसलिए नया कर्ण \(\sqrt{85}\) बनता है। / In Pythagoras theorem, the squares of sides are added. Therefore the new hypotenuse becomes \(\sqrt{85}\).
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वर्गमूल सर्पिल में \(\sqrt{4224}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही होगा?
Before placing \(\sqrt{4224}\) on the number line using a square root spiral, which interval is correct?
#square-root-spiral
#hard
#number-line
#interval
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A \(62<\sqrt{4224}<63\)
B \(63<\sqrt{4224}<64\)
C \(64<\sqrt{4224}<65\)
D \(65<\sqrt{4224}<66\)
Explanation opens after your attempt
Correct Answer
C. \(64<\sqrt{4224}<65\)
Explanation
Simple Explanation
क्योंकि \(64^2=4096\) और \(65^2=4225\) हैं। (4224) इनके बीच है। / Because \(64^2=4096\) and \(65^2=4225\). The number (4224) lies between them.
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वर्गमूल सर्पिल में यदि \(\sqrt{1935}\) से अगला कर्ण बनता है, तो कौन-सा संयुक्त निष्कर्ष सही है?
If the next hypotenuse is formed from \(\sqrt{1935}\) in a square root spiral, which combined conclusion is correct?
#square-root-spiral
#hard
#next-root
#exact-value
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A नया कर्ण \(\sqrt{1936}=44\) है / The new hypotenuse is \(\sqrt{1936}=44\)
B नया कर्ण \(\sqrt{1934}\) है / The new hypotenuse is \(\sqrt{1934}\)
C नया कर्ण \(\sqrt{3870}\) है / The new hypotenuse is \(\sqrt{3870}\)
D नया कर्ण \(\sqrt{1937}\) है / The new hypotenuse is \(\sqrt{1937}\)
Explanation opens after your attempt
Correct Answer
A. नया कर्ण \(\sqrt{1936}=44\) है / The new hypotenuse is \(\sqrt{1936}=44\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{1935+1}=\sqrt{1936}\) होता है। \(1936=44^2\), इसलिए मान (44) है। / The next hypotenuse is \(\sqrt{1935+1}=\sqrt{1936}\). Since \(1936=44^2\), its value is (44).
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वर्गमूल सर्पिल में \(\sqrt{3599}\) का सही स्थान कौन-सा है?
What is the correct position of \(\sqrt{3599}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(57<\sqrt{3599}<58\)
B \(58<\sqrt{3599}<59\)
C \(59<\sqrt{3599}<60\)
D \(60<\sqrt{3599}<61\)
Explanation opens after your attempt
Correct Answer
C. \(59<\sqrt{3599}<60\)
Explanation
Simple Explanation
क्योंकि \(59^2=3481\) और \(60^2=3600\) हैं। (3599) इनके बीच आता है। / Because \(59^2=3481\) and \(60^2=3600\). The number (3599) lies between them.
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वर्गमूल सर्पिल में \(\sqrt{1520}\) और \(\sqrt{1522}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{1520}\) and \(\sqrt{1522}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#number-line
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A \(\sqrt{1520}\) (38) और (39) के बीच है, \(\sqrt{1522}\) (39) और (40) के बीच है / \(\sqrt{1520}\) lies between (38) and (39), \(\sqrt{1522}\) lies between (39) and (40)
B दोनों (39) और (40) के बीच हैं / Both lie between (39) and (40)
C दोनों (38) और (39) के बीच हैं / Both lie between (38) and (39)
D दोनों ठीक (39) पर हैं / Both are exactly at (39)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{1520}\) (38) और (39) के बीच है, \(\sqrt{1522}\) (39) और (40) के बीच है / \(\sqrt{1520}\) lies between (38) and (39), \(\sqrt{1522}\) lies between (39) and (40)
Explanation
Simple Explanation
\(1520<1521=39^2\), इसलिए \(\sqrt{1520}<39\)। (1522>1521), इसलिए \(\sqrt{1522}>39\)। / Since \(1520<1521=39^2\), \(\sqrt{1520}<39\). Since (1522>1521), \(\sqrt{1522}>39\).
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वर्गमूल सर्पिल में \(\sqrt{n+1}\) नया कर्ण है। यदि पिछला कर्ण \(\sqrt{1368}\) था, तो नया कर्ण कौन-सा होगा?
In a square root spiral, the new hypotenuse is \(\sqrt{n+1}\). If the previous hypotenuse was \(\sqrt{1368}\), what will the new hypotenuse be?
#square-root-spiral
#hard
#general-rule
#next-root
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A \(\sqrt{1367}\)
B \(\sqrt{1369}\)
C \(\sqrt{1368}\)
D \(\sqrt{2736}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{1369}\)
Explanation
Simple Explanation
पिछला कर्ण \(\sqrt{1368}\) है, इसलिए नया कर्ण \(\sqrt{1368+1}=\sqrt{1369}\) होगा। / The previous hypotenuse is \(\sqrt{1368}\), so the new hypotenuse is \(\sqrt{1368+1}=\sqrt{1369}\).
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वर्गमूल सर्पिल में \(\sqrt{1368}\) से \(\sqrt{1369}\) बनने पर नया कर्ण किस मान पर होगा?
When \(\sqrt{1369}\) is formed from \(\sqrt{1368}\) in a square root spiral, at what value will the new hypotenuse be?
#square-root-spiral
#hard
#perfect-square
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A (36)
B (38)
C कोई पूर्ण संख्या नहीं / No whole number
D (37)
Explanation opens after your attempt
Explanation
Simple Explanation
\(\sqrt{1369}=37\) होता है। पूर्ण वर्ग बनने पर कर्ण पूर्ण संख्या पर आता है। / \(\sqrt{1369}=37\). When a perfect square is formed, the hypotenuse lies at a whole number.
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वर्गमूल सर्पिल में \(\sqrt{3024}\) पर (1) इकाई लंब बनाने से कौन-सा कर्ण बनेगा?
In a square root spiral, which hypotenuse is formed by drawing a (1) unit perpendicular on \(\sqrt{3024}\)?
#square-root-spiral
#hard
#next-root
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A \(\sqrt{3023}\)
B \(\sqrt{6048}\)
C \(\sqrt{3025}\)
D \(\sqrt{3026}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{3025}\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{3024+1}=\sqrt{3025}\) है। इसका सटीक मान (55) है। / The new hypotenuse is \(\sqrt{3024+1}=\sqrt{3025}\). Its exact value is (55).
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वर्गमूल सर्पिल में \(\sqrt{2600}\) का अंतराल पहचानते समय कौन-सा निष्कर्ष सही है?
While identifying the interval of \(\sqrt{2600}\) in a square root spiral, which conclusion is correct?
#square-root-spiral
#hard
#interval
#error-analysis
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A \(50<\sqrt{2600}<51\)
B \(49<\sqrt{2600}<50\)
C \(51<\sqrt{2600}<52\)
D \(\sqrt{2600}=51\)
Explanation opens after your attempt
Correct Answer
A. \(50<\sqrt{2600}<51\)
Explanation
Simple Explanation
क्योंकि \(50^2=2500\) और \(51^2=2601\) हैं। (2600) (2601) से कम है। / Because \(50^2=2500\) and \(51^2=2601\). The number (2600) is less than (2601).
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वर्गमूल सर्पिल में \(\sqrt{5}\) को संख्या रेखा पर अंकित करने की सबसे सटीक प्रक्रिया कौन-सी है?
What is the most precise process to mark \(\sqrt{5}\) on the number line using a square root spiral?
#square-root-spiral
#hard
#number-line
#compass
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A \(\sqrt{5}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{5}\) hypotenuse length in a compass and draw an arc from the origin
B (5) इकाई दूरी सीधे अंकित करना / Directly mark (5) units
C किसी भी बिंदु से कोई भी चाप खींचना / Draw any arc from any point
D कर्ण को दोगुना करके अंकित करना / Mark double the hypotenuse
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{5}\) hypotenuse length in a compass and draw an arc from the origin
Explanation
Simple Explanation
जिस वर्गमूल को अंकित करना है, उसी कर्ण की लंबाई कंपास में ली जाती है। मूल बिंदु से चाप सही स्थान देता है। / The hypotenuse length of the square root to be marked is taken in the compass. An arc from the origin gives the correct location.
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वर्गमूल सर्पिल में \(\sqrt{1800}\) बनाने से ठीक पहले कौन-सा कर्ण होना चाहिए?
Which hypotenuse should be present just before constructing \(\sqrt{1800}\) in a square root spiral?
#square-root-spiral
#hard
#previous-root
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A \(\sqrt{1798}\)
B \(\sqrt{1800}\)
C \(\sqrt{1799}\)
D \(\sqrt{1801}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{1799}\)
Explanation
Simple Explanation
\(\sqrt{1799}\) पर (1) इकाई लंब बनाने से \(\sqrt{1800}\) बनता है। पिछला कर्ण एक कम संख्या का होता है। / Drawing a (1) unit perpendicular on \(\sqrt{1799}\) forms \(\sqrt{1800}\). The previous hypotenuse has one less number.
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वर्गमूल सर्पिल में \(\sqrt{624}\) और \(\sqrt{729}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{624}\) and \(\sqrt{729}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#perfect-square
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A \(\sqrt{624}\) (24) और (25) के बीच है और \(\sqrt{729}=27\) है / \(\sqrt{624}\) lies between (24) and (25), and \(\sqrt{729}=27\)
B \(\sqrt{624}=25\) और \(\sqrt{729}\) अपरिमेय है / \(\sqrt{624}=25\), and \(\sqrt{729}\) is irrational
C दोनों (25) हैं / Both are (25)
D दोनों (27) से बड़े हैं / Both are greater than (27)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{624}\) (24) और (25) के बीच है और \(\sqrt{729}=27\) है / \(\sqrt{624}\) lies between (24) and (25), and \(\sqrt{729}=27\)
Explanation
Simple Explanation
\(24^2<624<25^2\) और \(729=27^2\) है। इसलिए तुलना में पहला कथन सही है।
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वर्गमूल सर्पिल में \(\sqrt{17}\) बनाने के लिए \(\sqrt{16}\) और (1) का प्रयोग क्यों सही है?
Why is using \(\sqrt{16}\) and (1) correct for constructing \(\sqrt{17}\) in a square root spiral?
#square-root-spiral
#hard
#pythagoras
#construction
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A क्योंकि \(\sqrt{16}+1=\sqrt{17}\) / Because \(\sqrt{16}+1=\sqrt{17}\)
B क्योंकि (\(\sqrt{16}\)2 +12 =17) / Because (\(\sqrt{16}\)2 +12 =17)
C क्योंकि \(16+1=\sqrt{17}\) / Because \(16+1=\sqrt{17}\)
D क्योंकि (\(\sqrt{16}\)2 -12 =17) / Because (\(\sqrt{16}\)2 -12 =17)
Explanation opens after your attempt
Correct Answer
B. क्योंकि (\(\sqrt{16}\)2 +12 =17) / Because (\(\sqrt{16}\)2 +12 =17)
Explanation
Simple Explanation
\(\sqrt{16}\) पिछला कर्ण है और (1) नई लंब है। पाइथागोरस से कर्ण \(\sqrt{17}\) मिलता है। / \(\sqrt{16}\) is the previous hypotenuse and (1) is the new perpendicular. Pythagoras gives hypotenuse \(\sqrt{17}\).
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वर्गमूल सर्पिल में \(\sqrt{2115}\) के बाद बनने वाला कर्ण किस विशेष मान पर स्थित होगा?
In a square root spiral, the hypotenuse formed after \(\sqrt{2115}\) will be located at which special value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{2114}\)
B \(\sqrt{4230}\)
C \(\sqrt{2117}\)
D \(\sqrt{2116}=46\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{2116}=46\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{2116}\) है। \(2116=46^2\), इसलिए यह ठीक (46) पर स्थित है। / The next hypotenuse is \(\sqrt{2116}\). Since \(2116=46^2\), it is located exactly at (46).
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वर्गमूल सर्पिल में \(\sqrt{99}\) और \(\sqrt{101}\) की स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the positions of \(\sqrt{99}\) and \(\sqrt{101}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{99}\) (9) और (10) के बीच है, \(\sqrt{101}\) (10) और (11) के बीच है / \(\sqrt{99}\) lies between (9) and (10), \(\sqrt{101}\) lies between (10) and (11)
B दोनों (9) और (10) के बीच हैं / Both lie between (9) and (10)
C दोनों (10) और (11) के बीच हैं / Both lie between (10) and (11)
D \(\sqrt{99}=10\) और \(\sqrt{101}\) अपरिमेय है / \(\sqrt{99}=10\) and \(\sqrt{101}\) is irrational
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{99}\) (9) और (10) के बीच है, \(\sqrt{101}\) (10) और (11) के बीच है / \(\sqrt{99}\) lies between (9) and (10), \(\sqrt{101}\) lies between (10) and (11)
Explanation
Simple Explanation
\(99<100=10^2\), इसलिए \(\sqrt{99}<10\)। (101>100), इसलिए \(\sqrt{101}>10\)। / Since \(99<100=10^2\), \(\sqrt{99}<10\). Since (101>100), \(\sqrt{101}>10\).
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वर्गमूल सर्पिल में \(\sqrt{3968}\) के बाद कौन-सा कर्ण बनेगा और उसका सटीक मान क्या है?
In a square root spiral, which hypotenuse is formed after \(\sqrt{3968}\), and what is its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{3969}=63\)
B \(\sqrt{3967}\), कोई पूर्ण मान नहीं / \(\sqrt{3967}\), no whole value
C \(\sqrt{7936}\), कोई पूर्ण मान नहीं / \(\sqrt{7936}\), no whole value
D \(\sqrt{3970}\), कोई पूर्ण मान नहीं / \(\sqrt{3970}\), no whole value
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3969}=63\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{3969}\) है। क्योंकि \(3969=63^2\), इसका सटीक मान (63) है। / The next hypotenuse is \(\sqrt{3969}\). Since \(3969=63^2\), its exact value is (63).
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वर्गमूल सर्पिल में \(\sqrt{3024}\) और \(\sqrt{3026}\) की सही तुलना कौन-सी है?
Which is the correct comparison of \(\sqrt{3024}\) and \(\sqrt{3026}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{3024}\) (54) और (55) के बीच है, \(\sqrt{3026}\) (55) और (56) के बीच है / \(\sqrt{3024}\) lies between (54) and (55), \(\sqrt{3026}\) lies between (55) and (56)
B दोनों (55) हैं / Both are (55)
C \(\sqrt{3024}=55\) और \(\sqrt{3026}\) अपरिमेय है / \(\sqrt{3024}=55\) and \(\sqrt{3026}\) is irrational
D दोनों (55) से बड़े हैं / Both are greater than (55)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3024}\) (54) और (55) के बीच है, \(\sqrt{3026}\) (55) और (56) के बीच है / \(\sqrt{3024}\) lies between (54) and (55), \(\sqrt{3026}\) lies between (55) and (56)
Explanation
Simple Explanation
\(3024<3025=55^2\), इसलिए \(\sqrt{3024}<55\)। (3026>3025), इसलिए \(\sqrt{3026}>55\)। / Since \(3024<3025=55^2\), \(\sqrt{3024}<55\). Since (3026>3025), \(\sqrt{3026}>55\).
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वर्गमूल सर्पिल में \(\sqrt{132}\) से अगला कर्ण निकालने में कौन-सा विकल्प तर्कसंगत है?
Which option is logical for finding the next hypotenuse from \(\sqrt{132}\) in a square root spiral?
#square-root-spiral
#hard
#logic
#pythagoras
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A \(\sqrt{132}+1=\sqrt{133}\), इसलिए नया कर्ण \(\sqrt{133}\) / \(\sqrt{132}+1=\sqrt{133}\), so the new hypotenuse is \(\sqrt{133}\)
B \(132^2+1^2=133\), इसलिए नया कर्ण \(\sqrt{133}\) / \(132^2+1^2=133\), so the new hypotenuse is \(\sqrt{133}\)
C (\(\sqrt{132}\)2 +12 =133), इसलिए नया कर्ण \(\sqrt{133}\) / (\(\sqrt{132}\)2 +12 =133), so the new hypotenuse is \(\sqrt{133}\)
D \(\sqrt{132}-1=\sqrt{133}\), इसलिए नया कर्ण \(\sqrt{133}\) / \(\sqrt{132}-1=\sqrt{133}\), so the new hypotenuse is \(\sqrt{133}\)
Explanation opens after your attempt
Correct Answer
C. (\(\sqrt{132}\)2 +12 =133), इसलिए नया कर्ण \(\sqrt{133}\) / (\(\sqrt{132}\)2 +12 =133), so the new hypotenuse is \(\sqrt{133}\)
Explanation
Simple Explanation
सही तर्क (\(\sqrt{132}\)2 +12 =133) है। सर्पिल में पाइथागोरस प्रमेय लागू होता है। / The correct reasoning is (\(\sqrt{132}\)2 +12 =133). Pythagoras theorem applies in the spiral.
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वर्गमूल सर्पिल में \(\sqrt{4623}\) के बाद बनने वाला कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?
In a square root spiral, which hypotenuse is formed after \(\sqrt{4623}\), and what is its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{4624}=68\)
B \(\sqrt{4622}\), कोई पूर्ण मान नहीं / \(\sqrt{4622}\), no whole value
C \(\sqrt{9246}\), कोई पूर्ण मान नहीं / \(\sqrt{9246}\), no whole value
D \(\sqrt{4625}=68\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{4624}=68\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{4624}\) है। \(4624=68^2\), इसलिए सटीक मान (68) है। / The next hypotenuse is \(\sqrt{4624}\). Since \(4624=68^2\), the exact value is (68).
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वर्गमूल सर्पिल में \(\sqrt{48}\) के बाद बनने वाले कर्ण और \(\sqrt{50}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the hypotenuse formed after \(\sqrt{48}\) and \(\sqrt{50}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#next-root
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A अगला कर्ण \(\sqrt{49}=7\) है और \(\sqrt{50}\) (7) और (8) के बीच है / The next hypotenuse is \(\sqrt{49}=7\), and \(\sqrt{50}\) lies between (7) and (8)
B अगला कर्ण \(\sqrt{47}\) है और \(\sqrt{50}=7\) / The next hypotenuse is \(\sqrt{47}\), and \(\sqrt{50}=7\)
C दोनों ठीक (7) पर हैं / Both are exactly at (7)
D अगला कर्ण \(\sqrt{96}\) है और \(\sqrt{50}\) (6) और (7) के बीच है / The next hypotenuse is \(\sqrt{96}\), and \(\sqrt{50}\) lies between (6) and (7)
Explanation opens after your attempt
Correct Answer
A. अगला कर्ण \(\sqrt{49}=7\) है और \(\sqrt{50}\) (7) और (8) के बीच है / The next hypotenuse is \(\sqrt{49}=7\), and \(\sqrt{50}\) lies between (7) and (8)
Explanation
Simple Explanation
\(\sqrt{48}\) के बाद \(\sqrt{49}=7\) बनता है। \(7^2<50<8^2\), इसलिए \(\sqrt{50}\) (7) और (8) के बीच है। / After \(\sqrt{48}\), \(\sqrt{49}=7\) is formed. Since \(7^2<50<8^2\), \(\sqrt{50}\) lies between (7) and (8).
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वर्गमूल सर्पिल में \(\sqrt{4899}\) का सही अंतराल कौन-सा है?
What is the correct interval for \(\sqrt{4899}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(67<\sqrt{4899}<68\)
B \(68<\sqrt{4899}<69\)
C \(69<\sqrt{4899}<70\)
D \(70<\sqrt{4899}<71\)
Explanation opens after your attempt
Correct Answer
C. \(69<\sqrt{4899}<70\)
Explanation
Simple Explanation
\(69^2=4761\) और \(70^2=4900\) हैं। (4899) इनके बीच है, इसलिए \(\sqrt{4899}\) (69) और (70) के बीच है। / \(69^2=4761\) and \(70^2=4900\). The number (4899) lies between them, so \(\sqrt{4899}\) lies between (69) and (70).
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वर्गमूल सर्पिल में \(\sqrt{4096}\) का सटीक मान और उसके बाद बनने वाले कर्ण का रूप कौन-सा है?
In a square root spiral, what is the exact value of \(\sqrt{4096}\), and what is the form of the next hypotenuse?
#square-root-spiral
#hard
#perfect-square
#next-root
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A \(\sqrt{4096}=64\), अगला कर्ण \(\sqrt{4097}\) / \(\sqrt{4096}=64\), next hypotenuse \(\sqrt{4097}\)
B \(\sqrt{4096}=63\), अगला कर्ण \(\sqrt{4097}\) / \(\sqrt{4096}=63\), next hypotenuse \(\sqrt{4097}\)
C \(\sqrt{4096}=64\), अगला कर्ण \(\sqrt{8192}\) / \(\sqrt{4096}=64\), next hypotenuse \(\sqrt{8192}\)
D \(\sqrt{4096}\) अपरिमेय है, अगला कर्ण \(\sqrt{4097}\) / \(\sqrt{4096}\) is irrational, next hypotenuse \(\sqrt{4097}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{4096}=64\), अगला कर्ण \(\sqrt{4097}\) / \(\sqrt{4096}=64\), next hypotenuse \(\sqrt{4097}\)
Explanation
Simple Explanation
\(4096=64^2\) है। इसके बाद (1) इकाई लंब जोड़ने पर अगला कर्ण \(\sqrt{4097}\) होगा। / \(4096=64^2\). After adding a (1) unit perpendicular, the next hypotenuse will be \(\sqrt{4097}\).
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वर्गमूल सर्पिल में \(\sqrt{3600}\) तक पहुँचने से ठीक पहले कौन-सा कर्ण होगा और \(\sqrt{3600}\) का मान क्या होगा?
In a square root spiral, which hypotenuse comes just before reaching \(\sqrt{3600}\), and what is the value of \(\sqrt{3600}\)?
#square-root-spiral
#hard
#sequence
#perfect-square
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A \(\sqrt{3598}\), (60)
B \(\sqrt{3599}\), (60)
C \(\sqrt{3601}\), (60)
D \(\sqrt{3599}\), (59)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3599}\), (60)
Explanation
Simple Explanation
\(\sqrt{3600}\) से पहले \(\sqrt{3599}\) आता है और \(3600=60^2\) है। इसलिए \(\sqrt{3600}=60\) होगा। / Before \(\sqrt{3600}\), \(\sqrt{3599}\) comes, and \(3600=60^2\). Therefore \(\sqrt{3600}=60\).
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वर्गमूल सर्पिल में यदि \(\sqrt{8099}\) कर्ण पर (1) इकाई लंब बनाई जाए, तो नया कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?
If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{8099}\) in a square root spiral, what will be the new hypotenuse and its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{8100}=90\)
B \(\sqrt{8098}\), कोई पूर्ण मान नहीं / \(\sqrt{8098}\), no whole value
C \(\sqrt{16198}\), कोई पूर्ण मान नहीं / \(\sqrt{16198}\), no whole value
D \(\sqrt{8101}=90\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{8100}=90\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{8099+1}=\sqrt{8100}\) होगा। \(8100=90^2\), इसलिए सटीक मान (90) है। / The new hypotenuse is \(\sqrt{8099+1}=\sqrt{8100}\). Since \(8100=90^2\), the exact value is (90).
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वर्गमूल सर्पिल में \(\sqrt{8463}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही होगा?
Before placing \(\sqrt{8463}\) on the number line using a square root spiral, which interval is correct?
#square-root-spiral
#hard
#number-line
#interval
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A \(90<\sqrt{8463}<91\)
B \(91<\sqrt{8463}<92\)
C \(92<\sqrt{8463}<93\)
D \(93<\sqrt{8463}<94\)
Explanation opens after your attempt
Correct Answer
B. \(91<\sqrt{8463}<92\)
Explanation
Simple Explanation
क्योंकि \(91^2=8281\) और \(92^2=8464\) हैं। (8463) इनके बीच है। / Because \(91^2=8281\) and \(92^2=8464\). The number (8463) lies between them.
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यदि वर्गमूल सर्पिल में नया कर्ण (95) के बराबर है, तो पिछले चरण का कर्ण कौन-सा था?
If the new hypotenuse in a square root spiral is equal to (95), which was the hypotenuse in the previous step?
#square-root-spiral
#hard
#reverse-rule
#perfect-square
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A \(\sqrt{9023}\)
B \(\sqrt{9024}\)
C \(\sqrt{9025}\)
D \(\sqrt{9026}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{9024}\)
Explanation
Simple Explanation
नया कर्ण \(95=\sqrt{9025}\) है। इसलिए पिछले चरण का कर्ण \(\sqrt{9024}\) था। / The new hypotenuse is \(95=\sqrt{9025}\). Therefore the previous hypotenuse was \(\sqrt{9024}\).
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वर्गमूल सर्पिल में \(\sqrt{9998}\) और \(\sqrt{10000}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{9998}\) and \(\sqrt{10000}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#number-line
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A \(\sqrt{9998}\) (99) और (100) के बीच है और \(\sqrt{10000}=100\) है / \(\sqrt{9998}\) lies between (99) and (100), and \(\sqrt{10000}=100\)
B \(\sqrt{9998}=100\) और \(\sqrt{10000}\) अपरिमेय है / \(\sqrt{9998}=100\), and \(\sqrt{10000}\) is irrational
C दोनों ठीक (100) पर हैं / Both are exactly at (100)
D दोनों (100) से बड़े हैं / Both are greater than (100)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{9998}\) (99) और (100) के बीच है और \(\sqrt{10000}=100\) है / \(\sqrt{9998}\) lies between (99) and (100), and \(\sqrt{10000}=100\)
Explanation
Simple Explanation
\(99^2<9998<100^2\) और \(10000=100^2\) है। इसलिए \(\sqrt{9998}\) (100) से कम है।
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वर्गमूल सर्पिल में यदि \(\sqrt{9603}\) कर्ण पर (1) इकाई लंब बनाई जाए, तो नया कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?
If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{9603}\) in a square root spiral, what will be the new hypotenuse and its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{9604}=98\)
B \(\sqrt{9602}\), कोई पूर्ण मान नहीं / \(\sqrt{9602}\), no whole value
C \(\sqrt{19206}\), कोई पूर्ण मान नहीं / \(\sqrt{19206}\), no whole value
D \(\sqrt{9605}=98\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{9604}=98\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{9603+1}=\sqrt{9604}\) होगा। \(9604=98^2\), इसलिए सटीक मान (98) है। / The new hypotenuse is \(\sqrt{9603+1}=\sqrt{9604}\). Since \(9604=98^2\), the exact value is (98).
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वर्गमूल सर्पिल में \(\sqrt{10199}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही होगा?
Before placing \(\sqrt{10199}\) on the number line using a square root spiral, which interval is correct?
#square-root-spiral
#hard
#number-line
#interval
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A \(99<\sqrt{10199}<100\)
B \(100<\sqrt{10199}<101\)
C \(101<\sqrt{10199}<102\)
D \(102<\sqrt{10199}<103\)
Explanation opens after your attempt
Correct Answer
B. \(100<\sqrt{10199}<101\)
Explanation
Simple Explanation
क्योंकि \(100^2=10000\) और \(101^2=10201\) हैं। (10199) इनके बीच है। / Because \(100^2=10000\) and \(101^2=10201\). The number (10199) lies between them.
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वर्गमूल सर्पिल में यदि पिछले कर्ण की लंबाई \(\sqrt{483}\) है, तो (1) इकाई लंब जोड़ने पर नया कर्ण किस सटीक मान पर होगा?
In a square root spiral, if the previous hypotenuse is \(\sqrt{483}\), at what exact value will the new hypotenuse be after adding a (1) unit perpendicular?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{484}=22\)
B \(\sqrt{482}\)
C \(\sqrt{966}\)
D \(\sqrt{485}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{484}=22\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{483+1}=\sqrt{484}\) होगा। \(484=22^2\), इसलिए सटीक मान (22) है। / The new hypotenuse is \(\sqrt{483+1}=\sqrt{484}\). Since \(484=22^2\), the exact value is (22).
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यदि वर्गमूल सर्पिल में नया कर्ण (31) के बराबर है, तो उससे ठीक पहले वाला कर्ण कौन-सा था?
If the new hypotenuse in a square root spiral is equal to (31), which hypotenuse came immediately before it?
#square-root-spiral
#hard
#reverse-rule
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A \(\sqrt{960}\)
B \(\sqrt{961}\)
C \(\sqrt{962}\)
D \(\sqrt{31}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{960}\)
Explanation
Simple Explanation
नया कर्ण \(31=\sqrt{961}\) है। इसलिए पिछले चरण का कर्ण \(\sqrt{960}\) था। / The new hypotenuse is \(31=\sqrt{961}\). Therefore the previous hypotenuse was \(\sqrt{960}\).
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\(\sqrt{1155}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही पहचाना जाएगा?
Before placing \(\sqrt{1155}\) on the number line, which interval will be correctly identified?
#square-root-spiral
#hard
#number-line
#interval
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A \(32<\sqrt{1155}<33\)
B \(33<\sqrt{1155}<34\)
C \(34<\sqrt{1155}<35\)
D \(35<\sqrt{1155}<36\)
Explanation opens after your attempt
Correct Answer
B. \(33<\sqrt{1155}<34\)
Explanation
Simple Explanation
क्योंकि \(33^2=1089\) और \(34^2=1156\) हैं। (1155) इनके बीच है। / Because \(33^2=1089\) and \(34^2=1156\). The number (1155) lies between them.
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यदि कोई विद्यार्थी \(\sqrt{52}+1=\sqrt{53}\) लिखकर अगला कर्ण बताता है, तो सही सुधार कौन-सा है?
If a student writes \(\sqrt{52}+1=\sqrt{53}\) to find the next hypotenuse, what is the correct correction?
#square-root-spiral
#hard
#error-correction
#pythagoras
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A \(\sqrt{52^2+1^2}=\sqrt{53}\)
B (\sqrt{\(\sqrt{52}\)2 +12 }=\sqrt{53})
C \(\sqrt{52+2}=\sqrt{53}\)
D \(\sqrt{52-1}=\sqrt{53}\)
Explanation opens after your attempt
Correct Answer
B. (\sqrt{\(\sqrt{52}\)2 +12 }=\sqrt{53})
Explanation
Simple Explanation
वर्गमूल सर्पिल में सीधे लंबाइयाँ नहीं जोड़ी जातीं। सही तरीका पाइथागोरस प्रमेय से वर्गों का योग लेना है। / Lengths are not added directly in a square root spiral. The correct method is to add squares by Pythagoras theorem.
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यदि सामान्य वर्गमूल सर्पिल में (1) इकाई की जगह (6) इकाई लंब ली जाए, तो \(\sqrt{n}\) से बनने वाला कर्ण किस रूप में होगा?
If a (6) unit perpendicular is used instead of (1) unit in the usual square root spiral, what will be the hypotenuse formed from \(\sqrt{n}\)?
#square-root-spiral
#hard
#unit-change
#general-rule
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A \(\sqrt{n+1}\)
B \(\sqrt{n+6}\)
C \(\sqrt{n+36}\)
D \(\sqrt{6n}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{n+36}\)
Explanation
Simple Explanation
पाइथागोरस से (\(\sqrt{n}\)2 +62 =n+36) होगा। इसलिए सामान्य \(\sqrt{n+1}\) क्रम बदल जाएगा। / By Pythagoras, (\(\sqrt{n}\)2 +62 =n+36). So the usual \(\sqrt{n+1}\) sequence will change.
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वर्गमूल सर्पिल में \(\sqrt{624}\) पर (1) इकाई लंब बनाने से नया कर्ण कौन-सा होगा और कहाँ स्थित होगा?
In a square root spiral, drawing a (1) unit perpendicular on \(\sqrt{624}\) gives which new hypotenuse and where is it located?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{625}\), ठीक (25) पर / \(\sqrt{625}\), exactly at (25)
B \(\sqrt{623}\), (24) और (25) के बीच / \(\sqrt{623}\), between (24) and (25)
C \(\sqrt{1248}\), (35) और (36) के बीच / \(\sqrt{1248}\), between (35) and (36)
D \(\sqrt{626}\), (25) और (26) के बीच / \(\sqrt{626}\), between (25) and (26)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{625}\), ठीक (25) पर / \(\sqrt{625}\), exactly at (25)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{625}\) है। क्योंकि \(\sqrt{625}=25\), यह ठीक (25) पर स्थित होगा। / The new hypotenuse is \(\sqrt{625}\). Since \(\sqrt{625}=25\), it will be located exactly at (25).
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वर्गमूल सर्पिल में \(\sqrt{120}\) और \(\sqrt{122}\) की संख्या-रेखा स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the number-line positions of \(\sqrt{120}\) and \(\sqrt{122}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A दोनों (10) और (11) के बीच हैं / Both lie between (10) and (11)
B \(\sqrt{120}\) (10) और (11) के बीच है, \(\sqrt{122}\) (11) और (12) के बीच है / \(\sqrt{120}\) lies between (10) and (11), \(\sqrt{122}\) lies between (11) and (12)
C दोनों (11) और (12) के बीच हैं / Both lie between (11) and (12)
D \(\sqrt{120}=11\) और \(\sqrt{122}\) अपरिमेय है / \(\sqrt{120}=11\) and \(\sqrt{122}\) is irrational
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{120}\) (10) और (11) के बीच है, \(\sqrt{122}\) (11) और (12) के बीच है / \(\sqrt{120}\) lies between (10) and (11), \(\sqrt{122}\) lies between (11) and (12)
Explanation
Simple Explanation
\(120<121=11^2\), इसलिए \(\sqrt{120}<11\)। (122>121), इसलिए \(\sqrt{122}>11\)। / Since \(120<121=11^2\), \(\sqrt{120}<11\). Since (122>121), \(\sqrt{122}>11\).
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वर्गमूल सर्पिल में \(\sqrt{675}\) के बाद बनने वाले कर्ण का सटीक मान क्या होगा?
What will be the exact value of the hypotenuse formed after \(\sqrt{675}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#exact-value
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A (25)
B (26)
C (27)
D कोई पूर्ण संख्या नहीं / No whole number
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Explanation
Simple Explanation
अगला कर्ण \(\sqrt{676}\) होगा। \(676=26^2\), इसलिए इसका सटीक मान (26) है। / The next hypotenuse is \(\sqrt{676}\). Since \(676=26^2\), its exact value is (26).
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यदि (k)वाँ कर्ण \(\sqrt{k}\) माना जाए, तो \(\sqrt{81}\) कौन-सा कर्ण होगा और उसका मान क्या होगा?
If the (k)-th hypotenuse is considered \(\sqrt{k}\), which hypotenuse is \(\sqrt{81}\), and what is its value?
#square-root-spiral
#hard
#sequence
#perfect-square
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A (80)वाँ, (9) / (80)-th, (9)
B (81)वाँ, (9) / (81)-th, (9)
C (82)वाँ, (9) / (82)-th, (9)
D (81)वाँ, (81) / (81)-th, (81)
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Correct Answer
B. (81)वाँ, (9) / (81)-th, (9)
Explanation
Simple Explanation
यदि (k)वाँ कर्ण \(\sqrt{k}\) है, तो \(\sqrt{81}\) (81)वाँ कर्ण है। \(\sqrt{81}=9\) होता है। / If the (k)-th hypotenuse is \(\sqrt{k}\), then \(\sqrt{81}\) is the (81)-th hypotenuse. Also, \(\sqrt{81}=9\).
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वर्गमूल सर्पिल में \(\sqrt{210}\) बनाने के लिए कौन-सा पिछला कर्ण और कौन-सी नई लंब सही है?
To construct \(\sqrt{210}\) in a square root spiral, which previous hypotenuse and new perpendicular are correct?
#square-root-spiral
#hard
#construction
#previous-root
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A \(\sqrt{208}\) और (2) / \(\sqrt{208}\) and (2)
B \(\sqrt{209}\) और (1) / \(\sqrt{209}\) and (1)
C \(\sqrt{210}\) और (1) / \(\sqrt{210}\) and (1)
D \(\sqrt{211}\) और (1) / \(\sqrt{211}\) and (1)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{209}\) और (1) / \(\sqrt{209}\) and (1)
Explanation
Simple Explanation
(\(\sqrt{209}\)2 +12 =210) है। इसलिए \(\sqrt{210}\) के लिए पिछला कर्ण \(\sqrt{209}\) होगा। / (\(\sqrt{209}\)2 +12 =210). So the previous hypotenuse for \(\sqrt{210}\) is \(\sqrt{209}\).
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\(\sqrt{1088}\) के बाद बनने वाला कर्ण वर्गमूल सर्पिल में किस सटीक मान पर होगा?
In a square root spiral, the hypotenuse formed after \(\sqrt{1088}\) will be at which exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{1089}=33\)
B \(\sqrt{1087}\), कोई पूर्ण मान नहीं / \(\sqrt{1087}\), no whole value
C \(\sqrt{2176}\), कोई पूर्ण मान नहीं / \(\sqrt{2176}\), no whole value
D \(\sqrt{1090}=33\)
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Correct Answer
A. \(\sqrt{1089}=33\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{1089}\) होगा। \(1089=33^2\), इसलिए इसका मान (33) है। / The next hypotenuse is \(\sqrt{1089}\). Since \(1089=33^2\), its value is (33).
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वर्गमूल सर्पिल में \(\sqrt{899}\) का स्थान पहचानने के लिए कौन-सी असमानता सही है?
Which inequality is correct to identify the position of \(\sqrt{899}\) in a square root spiral?
#square-root-spiral
#hard
#inequality
#interval
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A \(,28^2<899<29^2,\)
B \(,29^2<899<30^2,\)
C \(,30^2<899<31^2,\)
D \(,31^2<899<32^2,\)
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Correct Answer
B. \(,29^2<899<30^2,\)
Explanation
Simple Explanation
\(29^2=841\) और \(30^2=900\) हैं। (899) इनके बीच है। / \(29^2=841\) and \(30^2=900\). The number (899) lies between them.
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यदि वर्गमूल सर्पिल में \(\sqrt{n}\) के बाद बना कर्ण (41) है, तो (n) का मान क्या होगा?
If the hypotenuse formed after \(\sqrt{n}\) in a square root spiral is (41), what is the value of (n)?
#square-root-spiral
#hard
#reverse-rule
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A (1680)
B (1681)
C (1682)
D (41)
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Explanation
Simple Explanation
नया कर्ण \(41=\sqrt{1681}\) है। इसलिए (n+1=1681), अतः (n=1680)। / The new hypotenuse is \(41=\sqrt{1681}\). Therefore (n+1=1681), so (n=1680).
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वर्गमूल सर्पिल में \(\sqrt{8}\) से \(\sqrt{12}\) तक सामान्य निर्माण का सही क्रम कौन-सा है?
In a square root spiral, which is the correct usual construction order from \(\sqrt{8}\) to \(\sqrt{12}\)?
#square-root-spiral
#hard
#sequence
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A \(\sqrt{8}\rightarrow\sqrt{10}\rightarrow\sqrt{12}\)
B \(\sqrt{8}\rightarrow\sqrt{9}\rightarrow\sqrt{10}\rightarrow\sqrt{11}\rightarrow\sqrt{12}\)
C \(\sqrt{8}\rightarrow\sqrt{12}\rightarrow\sqrt{9}\)
D \(\sqrt{12}\rightarrow\sqrt{11}\rightarrow\sqrt{10}\)
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Correct Answer
B. \(\sqrt{8}\rightarrow\sqrt{9}\rightarrow\sqrt{10}\rightarrow\sqrt{11}\rightarrow\sqrt{12}\)
Explanation
Simple Explanation
सर्पिल में कर्ण क्रमिक रूप से एक-एक बढ़ते हैं। सामान्य निर्माण में बीच के चरण नहीं छोड़े जाते। / Hypotenuses increase one by one in the spiral. In the usual construction, intermediate steps are not skipped.
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वर्गमूल सर्पिल में \(\sqrt{255}\) और \(\sqrt{257}\) की संख्या-रेखा स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the number-line positions of \(\sqrt{255}\) and \(\sqrt{257}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{255}\) (15) और (16) के बीच है, \(\sqrt{257}\) (16) और (17) के बीच है / \(\sqrt{255}\) lies between (15) and (16), \(\sqrt{257}\) lies between (16) and (17)
B दोनों (16) और (17) के बीच हैं / Both lie between (16) and (17)
C दोनों (15) और (16) के बीच हैं / Both lie between (15) and (16)
D \(\sqrt{255}=16\) और \(\sqrt{257}\) अपरिमेय है / \(\sqrt{255}=16\) and \(\sqrt{257}\) is irrational
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Correct Answer
A. \(\sqrt{255}\) (15) और (16) के बीच है, \(\sqrt{257}\) (16) और (17) के बीच है / \(\sqrt{255}\) lies between (15) and (16), \(\sqrt{257}\) lies between (16) and (17)
Explanation
Simple Explanation
\(255<256=16^2\), इसलिए \(\sqrt{255}<16\)। (257>256), इसलिए \(\sqrt{257}>16\)। / Since \(255<256=16^2\), \(\sqrt{255}<16\). Since (257>256), \(\sqrt{257}>16\).
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वर्गमूल सर्पिल में \(\sqrt{323}\) से बनने वाले अगले कर्ण और \(\sqrt{325}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the next hypotenuse from \(\sqrt{323}\) and \(\sqrt{325}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#next-root
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A अगला कर्ण \(\sqrt{324}=18\) है और \(\sqrt{325}\) (18) और (19) के बीच है / The next hypotenuse is \(\sqrt{324}=18\), and \(\sqrt{325}\) lies between (18) and (19)
B अगला कर्ण \(\sqrt{322}\) है और \(\sqrt{325}=18\) है / The next hypotenuse is \(\sqrt{322}\), and \(\sqrt{325}=18\)
C दोनों ठीक (18) पर हैं / Both are exactly at (18)
D अगला कर्ण \(\sqrt{646}\) है और \(\sqrt{325}\) (17) और (18) के बीच है / The next hypotenuse is \(\sqrt{646}\), and \(\sqrt{325}\) lies between (17) and (18)
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Correct Answer
A. अगला कर्ण \(\sqrt{324}=18\) है और \(\sqrt{325}\) (18) और (19) के बीच है / The next hypotenuse is \(\sqrt{324}=18\), and \(\sqrt{325}\) lies between (18) and (19)
Explanation
Simple Explanation
\(\sqrt{323}\) के बाद \(\sqrt{324}=18\) बनता है। \(18^2<325<19^2\), इसलिए \(\sqrt{325}\) (18) और (19) के बीच है। / After \(\sqrt{323}\), \(\sqrt{324}=18\) is formed. Since \(18^2<325<19^2\), \(\sqrt{325}\) lies between (18) and (19).
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वर्गमूल सर्पिल में यदि (m) अगले पूर्ण वर्ग से ठीक (1) कम है, तो \(\sqrt{m}\) के बाद बनने वाले कर्ण के बारे में क्या निश्चित है?
In a square root spiral, if (m) is exactly (1) less than the next perfect square, what is certain about the hypotenuse formed after \(\sqrt{m}\)?
#square-root-spiral
#hard
#pattern
#perfect-square
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A वह पूर्ण संख्या होगा / It will be a whole number
B वह हमेशा अपरिमेय होगा / It will always be irrational
C वह शून्य होगा / It will be zero
D वह \(\sqrt{m}\) ही रहेगा / It will remain \(\sqrt{m}\)
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Correct Answer
A. वह पूर्ण संख्या होगा / It will be a whole number
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{m+1}\) होगा। यदि (m+1) पूर्ण वर्ग है, तो उसका वर्गमूल पूर्ण संख्या होगा। / The next hypotenuse is \(\sqrt{m+1}\). If (m+1) is a perfect square, its square root will be a whole number.
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वर्गमूल सर्पिल में \(\sqrt{1680}\) और \(\sqrt{1681}\) की तुलना में कौन-सा निष्कर्ष सही है?
Which conclusion is correct when comparing \(\sqrt{1680}\) and \(\sqrt{1681}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#perfect-square
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A \(\sqrt{1680}\) (40) और (41) के बीच है और \(\sqrt{1681}=41\) है / \(\sqrt{1680}\) lies between (40) and (41), and \(\sqrt{1681}=41\)
B \(\sqrt{1680}=41\) और \(\sqrt{1681}\) अपरिमेय है / \(\sqrt{1680}=41\), and \(\sqrt{1681}\) is irrational
C दोनों (40) हैं / Both are (40)
D दोनों (41) से बड़े हैं / Both are greater than (41)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{1680}\) (40) और (41) के बीच है और \(\sqrt{1681}=41\) है / \(\sqrt{1680}\) lies between (40) and (41), and \(\sqrt{1681}=41\)
Explanation
Simple Explanation
\(40^2<1680<41^2\) और \(1681=41^2\) है। इसलिए \(\sqrt{1681}\) ठीक (41) है।
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वर्गमूल सर्पिल में \(\sqrt{80}\) के बाद बनने वाले कर्ण का मान क्या है?
What is the value of the hypotenuse formed after \(\sqrt{80}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#exact-value
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A \(\sqrt{79}\)
B (9)
C \(\sqrt{160}\)
D \(\sqrt{82}\)
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Explanation
Simple Explanation
अगला कर्ण \(\sqrt{81}\) होगा और \(\sqrt{81}=9\) है। पूर्ण वर्ग पर कर्ण पूर्ण संख्या बनता है। / The next hypotenuse is \(\sqrt{81}\), and \(\sqrt{81}=9\). At a perfect square, the hypotenuse becomes a whole number.
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\(\sqrt{1520}\) का सही संख्या-रेखा अंतराल कौन-सा है?
What is the correct number-line interval for \(\sqrt{1520}\)?
#square-root-spiral
#hard
#number-line
#interval
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A \(37<\sqrt{1520}<38\)
B \(38<\sqrt{1520}<39\)
C \(39<\sqrt{1520}<40\)
D \(40<\sqrt{1520}<41\)
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Correct Answer
B. \(38<\sqrt{1520}<39\)
Explanation
Simple Explanation
क्योंकि \(38^2=1444\) और \(39^2=1521\) हैं। (1520) इनके बीच है। / Because \(38^2=1444\) and \(39^2=1521\). The number (1520) lies between them.
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वर्गमूल सर्पिल में \(\sqrt{2024}\) के बाद बनने वाले कर्ण का सटीक मान क्या होगा?
What will be the exact value of the hypotenuse formed after \(\sqrt{2024}\) in a square root spiral?
#square-root-spiral
#hard
#next-root
#perfect-square
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A (44)
B (45)
C (46)
D कोई पूर्ण संख्या नहीं / No whole number
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Explanation
Simple Explanation
अगला कर्ण \(\sqrt{2025}\) है। \(2025=45^2\), इसलिए इसका सटीक मान (45) है। / The next hypotenuse is \(\sqrt{2025}\). Since \(2025=45^2\), its exact value is (45).
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वर्गमूल सर्पिल में \(\sqrt{50}\) और \(\sqrt{80}\) के बारे में कौन-सा कथन सही है?
Which statement about \(\sqrt{50}\) and \(\sqrt{80}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{50}\) (7) और (8) के बीच है, \(\sqrt{80}\) (8) और (9) के बीच है / \(\sqrt{50}\) lies between (7) and (8), \(\sqrt{80}\) lies between (8) and (9)
B दोनों (7) और (8) के बीच हैं / Both lie between (7) and (8)
C दोनों (8) और (9) के बीच हैं / Both lie between (8) and (9)
D दोनों ठीक (8) पर हैं / Both are exactly at (8)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{50}\) (7) और (8) के बीच है, \(\sqrt{80}\) (8) और (9) के बीच है / \(\sqrt{50}\) lies between (7) and (8), \(\sqrt{80}\) lies between (8) and (9)
Explanation
Simple Explanation
\(7^2<50<8^2\) और \(8^2<80<9^2\) हैं। इसलिए दोनों अलग अंतरालों में हैं।
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वर्गमूल सर्पिल में \(\sqrt{41}\) से \(\sqrt{42}\) बनने का सही कारण कौन-सा है?
What is the correct reason for \(\sqrt{42}\) being formed from \(\sqrt{41}\) in a square root spiral?
#square-root-spiral
#hard
#pythagoras
#next-root
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A (\(\sqrt{41}\)2 +12 =42)
B \(\sqrt{41}+1=\sqrt{42}\)
C (\(\sqrt{41}\)2 +22 =42)
D \(\sqrt{41}\times1=\sqrt{42}\)
Explanation opens after your attempt
Correct Answer
A. (\(\sqrt{41}\)2 +12 =42)
Explanation
Simple Explanation
पाइथागोरस प्रमेय में भुजाओं के वर्ग जुड़ते हैं। इसलिए नया कर्ण \(\sqrt{42}\) बनता है। / In Pythagoras theorem, the squares of sides are added. Therefore the new hypotenuse becomes \(\sqrt{42}\).
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वर्गमूल सर्पिल में \(\sqrt{1935}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही होगा?
Before placing \(\sqrt{1935}\) on the number line using a square root spiral, which interval is correct?
#square-root-spiral
#hard
#number-line
#interval
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A \(42<\sqrt{1935}<43\)
B \(43<\sqrt{1935}<44\)
C \(44<\sqrt{1935}<45\)
D \(45<\sqrt{1935}<46\)
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Correct Answer
B. \(43<\sqrt{1935}<44\)
Explanation
Simple Explanation
क्योंकि \(43^2=1849\) और \(44^2=1936\) हैं। (1935) इनके बीच है। / Because \(43^2=1849\) and \(44^2=1936\). The number (1935) lies between them.
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वर्गमूल सर्पिल में यदि \(\sqrt{288}\) से अगला कर्ण बनता है, तो कौन-सा संयुक्त निष्कर्ष सही है?
If the next hypotenuse is formed from \(\sqrt{288}\) in a square root spiral, which combined conclusion is correct?
#square-root-spiral
#hard
#next-root
#exact-value
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A नया कर्ण \(\sqrt{289}=17\) है / The new hypotenuse is \(\sqrt{289}=17\)
B नया कर्ण \(\sqrt{287}\) है / The new hypotenuse is \(\sqrt{287}\)
C नया कर्ण \(\sqrt{576}\) है / The new hypotenuse is \(\sqrt{576}\)
D नया कर्ण \(\sqrt{290}\) है / The new hypotenuse is \(\sqrt{290}\)
Explanation opens after your attempt
Correct Answer
A. नया कर्ण \(\sqrt{289}=17\) है / The new hypotenuse is \(\sqrt{289}=17\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{288+1}=\sqrt{289}\) होता है। \(289=17^2\), इसलिए मान (17) है। / The next hypotenuse is \(\sqrt{288+1}=\sqrt{289}\). Since \(289=17^2\), its value is (17).
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वर्गमूल सर्पिल में \(\sqrt{2499}\) का सही स्थान कौन-सा है?
What is the correct position of \(\sqrt{2499}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(48<\sqrt{2499}<49\)
B \(49<\sqrt{2499}<50\)
C \(50<\sqrt{2499}<51\)
D \(51<\sqrt{2499}<52\)
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Correct Answer
B. \(49<\sqrt{2499}<50\)
Explanation
Simple Explanation
क्योंकि \(49^2=2401\) और \(50^2=2500\) हैं। (2499) इनके बीच आता है। / Because \(49^2=2401\) and \(50^2=2500\). The number (2499) lies between them.
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वर्गमूल सर्पिल में \(\sqrt{399}\) और \(\sqrt{401}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{399}\) and \(\sqrt{401}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#number-line
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A \(\sqrt{399}\) (19) और (20) के बीच है, \(\sqrt{401}\) (20) और (21) के बीच है / \(\sqrt{399}\) lies between (19) and (20), \(\sqrt{401}\) lies between (20) and (21)
B दोनों (20) और (21) के बीच हैं / Both lie between (20) and (21)
C दोनों (19) और (20) के बीच हैं / Both lie between (19) and (20)
D दोनों ठीक (20) पर हैं / Both are exactly at (20)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{399}\) (19) और (20) के बीच है, \(\sqrt{401}\) (20) और (21) के बीच है / \(\sqrt{399}\) lies between (19) and (20), \(\sqrt{401}\) lies between (20) and (21)
Explanation
Simple Explanation
\(399<400=20^2\), इसलिए \(\sqrt{399}<20\)। (401>400), इसलिए \(\sqrt{401}>20\)। / Since \(399<400=20^2\), \(\sqrt{399}<20\). Since (401>400), \(\sqrt{401}>20\).
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वर्गमूल सर्पिल में \(\sqrt{n+1}\) नया कर्ण है। यदि पिछला कर्ण \(\sqrt{728}\) था, तो नया कर्ण कौन-सा होगा?
In a square root spiral, the new hypotenuse is \(\sqrt{n+1}\). If the previous hypotenuse was \(\sqrt{728}\), what will the new hypotenuse be?
#square-root-spiral
#hard
#general-rule
#next-root
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A \(\sqrt{727}\)
B \(\sqrt{728}\)
C \(\sqrt{729}\)
D \(\sqrt{1456}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{729}\)
Explanation
Simple Explanation
पिछला कर्ण \(\sqrt{728}\) है, इसलिए नया कर्ण \(\sqrt{728+1}=\sqrt{729}\) होगा। / The previous hypotenuse is \(\sqrt{728}\), so the new hypotenuse is \(\sqrt{728+1}=\sqrt{729}\).
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वर्गमूल सर्पिल में \(\sqrt{728}\) से \(\sqrt{729}\) बनने पर नया कर्ण किस मान पर होगा?
When \(\sqrt{729}\) is formed from \(\sqrt{728}\) in a square root spiral, at what value will the new hypotenuse be?
#square-root-spiral
#hard
#perfect-square
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A (26)
B (27)
C (28)
D कोई पूर्ण संख्या नहीं / No whole number
Explanation opens after your attempt
Explanation
Simple Explanation
\(\sqrt{729}=27\) होता है। पूर्ण वर्ग बनने पर कर्ण पूर्ण संख्या पर आता है। / \(\sqrt{729}=27\). When a perfect square is formed, the hypotenuse lies at a whole number.
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वर्गमूल सर्पिल में \(\sqrt{1599}\) पर (1) इकाई लंब बनाने से कौन-सा कर्ण बनेगा?
In a square root spiral, which hypotenuse is formed by drawing a (1) unit perpendicular on \(\sqrt{1599}\)?
#square-root-spiral
#hard
#next-root
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A \(\sqrt{1598}\)
B \(\sqrt{1600}\)
C \(\sqrt{3198}\)
D \(\sqrt{1601}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{1600}\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{1599+1}=\sqrt{1600}\) है। इसका सटीक मान (40) है। / The new hypotenuse is \(\sqrt{1599+1}=\sqrt{1600}\). Its exact value is (40).
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वर्गमूल सर्पिल में \(\sqrt{1368}\) का अंतराल पहचानते समय कौन-सा निष्कर्ष सही है?
While identifying the interval of \(\sqrt{1368}\) in a square root spiral, which conclusion is correct?
#square-root-spiral
#hard
#interval
#error-analysis
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A \(35<\sqrt{1368}<36\)
B \(36<\sqrt{1368}<37\)
C \(37<\sqrt{1368}<38\)
D \(\sqrt{1368}=37\)
Explanation opens after your attempt
Correct Answer
B. \(36<\sqrt{1368}<37\)
Explanation
Simple Explanation
क्योंकि \(36^2=1296\) और \(37^2=1369\) हैं। (1368) (1369) से कम है। / Because \(36^2=1296\) and \(37^2=1369\). The number (1368) is less than (1369).
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वर्गमूल सर्पिल में \(\sqrt{3}\) को संख्या रेखा पर अंकित करने की सबसे सटीक प्रक्रिया कौन-सी है?
What is the most precise process to mark \(\sqrt{3}\) on the number line using a square root spiral?
#square-root-spiral
#hard
#number-line
#compass
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A \(\sqrt{3}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{3}\) hypotenuse length in a compass and draw an arc from the origin
B (3) इकाई दूरी सीधे अंकित करना / Directly mark (3) units
C किसी भी बिंदु से कोई भी चाप खींचना / Draw any arc from any point
D कर्ण को दोगुना करके अंकित करना / Mark double the hypotenuse
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{3}\) hypotenuse length in a compass and draw an arc from the origin
Explanation
Simple Explanation
जिस वर्गमूल को अंकित करना है, उसी कर्ण की लंबाई कंपास में ली जाती है। मूल बिंदु से चाप सही स्थान देता है। / The hypotenuse length of the square root to be marked is taken in the compass. An arc from the origin gives the correct location.
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वर्गमूल सर्पिल में \(\sqrt{840}\) बनाने से ठीक पहले कौन-सा कर्ण होना चाहिए?
Which hypotenuse should be present just before constructing \(\sqrt{840}\) in a square root spiral?
#square-root-spiral
#hard
#previous-root
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A \(\sqrt{838}\)
B \(\sqrt{839}\)
C \(\sqrt{840}\)
D \(\sqrt{841}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{839}\)
Explanation
Simple Explanation
\(\sqrt{839}\) पर (1) इकाई लंब बनाने से \(\sqrt{840}\) बनता है। पिछला कर्ण एक कम संख्या का होता है। / Drawing a (1) unit perpendicular on \(\sqrt{839}\) forms \(\sqrt{840}\). The previous hypotenuse has one less number.
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वर्गमूल सर्पिल में \(\sqrt{960}\) और \(\sqrt{1024}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{960}\) and \(\sqrt{1024}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#perfect-square
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A \(\sqrt{960}\) (30) और (31) के बीच है और \(\sqrt{1024}=32\) है / \(\sqrt{960}\) lies between (30) and (31), and \(\sqrt{1024}=32\)
B \(\sqrt{960}=32\) और \(\sqrt{1024}\) अपरिमेय है / \(\sqrt{960}=32\), and \(\sqrt{1024}\) is irrational
C दोनों (31) हैं / Both are (31)
D दोनों (32) से बड़े हैं / Both are greater than (32)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{960}\) (30) और (31) के बीच है और \(\sqrt{1024}=32\) है / \(\sqrt{960}\) lies between (30) and (31), and \(\sqrt{1024}=32\)
Explanation
Simple Explanation
\(30^2<960<31^2\) और \(1024=32^2\) है। इसलिए तुलना में पहला कथन सही है।
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वर्गमूल सर्पिल में \(\sqrt{10}\) बनाने के लिए \(\sqrt{9}\) और (1) का प्रयोग क्यों सही है?
Why is using \(\sqrt{9}\) and (1) correct for constructing \(\sqrt{10}\) in a square root spiral?
#square-root-spiral
#hard
#pythagoras
#construction
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A क्योंकि (\(\sqrt{9}\)2 +12 =10) / Because (\(\sqrt{9}\)2 +12 =10)
B क्योंकि \(\sqrt{9}+1=\sqrt{10}\) / Because \(\sqrt{9}+1=\sqrt{10}\)
C क्योंकि \(9+1=\sqrt{10}\) / Because \(9+1=\sqrt{10}\)
D क्योंकि (\(\sqrt{9}\)2 -12 =10) / Because (\(\sqrt{9}\)2 -12 =10)
Explanation opens after your attempt
Correct Answer
A. क्योंकि (\(\sqrt{9}\)2 +12 =10) / Because (\(\sqrt{9}\)2 +12 =10)
Explanation
Simple Explanation
\(\sqrt{9}\) पिछला कर्ण है और (1) नई लंब है। पाइथागोरस से कर्ण \(\sqrt{10}\) मिलता है। / \(\sqrt{9}\) is the previous hypotenuse and (1) is the new perpendicular. Pythagoras gives hypotenuse \(\sqrt{10}\).
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वर्गमूल सर्पिल में \(\sqrt{1848}\) के बाद बनने वाला कर्ण किस विशेष मान पर स्थित होगा?
In a square root spiral, the hypotenuse formed after \(\sqrt{1848}\) will be located at which special value?
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#hard
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#perfect-square
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A \(\sqrt{1847}\)
B \(\sqrt{1849}=43\)
C \(\sqrt{3696}\)
D \(\sqrt{1850}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{1849}=43\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{1849}\) है। \(1849=43^2\), इसलिए यह ठीक (43) पर स्थित है। / The next hypotenuse is \(\sqrt{1849}\). Since \(1849=43^2\), it is located exactly at (43).
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वर्गमूल सर्पिल में \(\sqrt{35}\) और \(\sqrt{37}\) की स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the positions of \(\sqrt{35}\) and \(\sqrt{37}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{35}\) (5) और (6) के बीच है, \(\sqrt{37}\) (6) और (7) के बीच है / \(\sqrt{35}\) lies between (5) and (6), \(\sqrt{37}\) lies between (6) and (7)
B दोनों (5) और (6) के बीच हैं / Both lie between (5) and (6)
C दोनों (6) और (7) के बीच हैं / Both lie between (6) and (7)
D \(\sqrt{35}=6\) और \(\sqrt{37}\) अपरिमेय है / \(\sqrt{35}=6\) and \(\sqrt{37}\) is irrational
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{35}\) (5) और (6) के बीच है, \(\sqrt{37}\) (6) और (7) के बीच है / \(\sqrt{35}\) lies between (5) and (6), \(\sqrt{37}\) lies between (6) and (7)
Explanation
Simple Explanation
\(35<36=6^2\), इसलिए \(\sqrt{35}<6\)। (37>36), इसलिए \(\sqrt{37}>6\)। / Since \(35<36=6^2\), \(\sqrt{35}<6\). Since (37>36), \(\sqrt{37}>6\).
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वर्गमूल सर्पिल में \(\sqrt{2208}\) के बाद कौन-सा कर्ण बनेगा और उसका सटीक मान क्या है?
In a square root spiral, which hypotenuse is formed after \(\sqrt{2208}\), and what is its exact value?
#square-root-spiral
#hard
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A \(\sqrt{2209}=47\)
B \(\sqrt{2207}\), कोई पूर्ण मान नहीं / \(\sqrt{2207}\), no whole value
C \(\sqrt{4416}\), कोई पूर्ण मान नहीं / \(\sqrt{4416}\), no whole value
D \(\sqrt{2210}\), कोई पूर्ण मान नहीं / \(\sqrt{2210}\), no whole value
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2209}=47\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{2209}\) है। क्योंकि \(2209=47^2\), इसका सटीक मान (47) है। / The next hypotenuse is \(\sqrt{2209}\). Since \(2209=47^2\), its exact value is (47).
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वर्गमूल सर्पिल में \(\sqrt{48}\) और \(\sqrt{50}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{48}\) and \(\sqrt{50}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#number-line
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A \(\sqrt{48}\) (6) और (7) के बीच है, \(\sqrt{50}\) (7) और (8) के बीच है / \(\sqrt{48}\) lies between (6) and (7), \(\sqrt{50}\) lies between (7) and (8)
B दोनों (7) और (8) के बीच हैं / Both lie between (7) and (8)
C दोनों (6) और (7) के बीच हैं / Both lie between (6) and (7)
D दोनों ठीक (7) पर हैं / Both are exactly at (7)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{48}\) (6) और (7) के बीच है, \(\sqrt{50}\) (7) और (8) के बीच है / \(\sqrt{48}\) lies between (6) and (7), \(\sqrt{50}\) lies between (7) and (8)
Explanation
Simple Explanation
\(48<49=7^2\), इसलिए \(\sqrt{48}<7\)। (50>49), इसलिए \(\sqrt{50}>7\)। / Since \(48<49=7^2\), \(\sqrt{48}<7\). Since (50>49), \(\sqrt{50}>7\).
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वर्गमूल सर्पिल में \(\sqrt{9999}\) और \(\sqrt{10000}\) की सही तुलना कौन-सी है?
Which is the correct comparison of \(\sqrt{9999}\) and \(\sqrt{10000}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#interval
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A \(\sqrt{9999}\) (99) और (100) के बीच है, \(\sqrt{10000}=100\) है / \(\sqrt{9999}\) lies between (99) and (100), and \(\sqrt{10000}=100\)
B दोनों (100) हैं / Both are (100)
C \(\sqrt{9999}=100\) और \(\sqrt{10000}\) अपरिमेय है / \(\sqrt{9999}=100\) and \(\sqrt{10000}\) is irrational
D दोनों (100) से बड़े हैं / Both are greater than (100)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{9999}\) (99) और (100) के बीच है, \(\sqrt{10000}=100\) है / \(\sqrt{9999}\) lies between (99) and (100), and \(\sqrt{10000}=100\)
Explanation
Simple Explanation
\(99^2<9999<100^2\) और \(10000=100^2\) है। इसलिए \(\sqrt{9999}\) (100) से थोड़ा कम है।
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वर्गमूल सर्पिल में \(\sqrt{72}\) से अगला कर्ण निकालने में कौन-सा विकल्प तर्कसंगत है?
Which option is logical for finding the next hypotenuse from \(\sqrt{72}\) in a square root spiral?
#square-root-spiral
#hard
#logic
#pythagoras
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A (\(\sqrt{72}\)2 +12 =73), इसलिए नया कर्ण \(\sqrt{73}\) / (\(\sqrt{72}\)2 +12 =73), so the new hypotenuse is \(\sqrt{73}\)
B \(\sqrt{72}+1=\sqrt{73}\), इसलिए नया कर्ण \(\sqrt{73}\) / \(\sqrt{72}+1=\sqrt{73}\), so the new hypotenuse is \(\sqrt{73}\)
C \(72^2+1^2=73\), इसलिए नया कर्ण \(\sqrt{73}\) / \(72^2+1^2=73\), so the new hypotenuse is \(\sqrt{73}\)
D \(\sqrt{72}-1=\sqrt{73}\), इसलिए नया कर्ण \(\sqrt{73}\) / \(\sqrt{72}-1=\sqrt{73}\), so the new hypotenuse is \(\sqrt{73}\)
Explanation opens after your attempt
Correct Answer
A. (\(\sqrt{72}\)2 +12 =73), इसलिए नया कर्ण \(\sqrt{73}\) / (\(\sqrt{72}\)2 +12 =73), so the new hypotenuse is \(\sqrt{73}\)
Explanation
Simple Explanation
सही तर्क (\(\sqrt{72}\)2 +12 =73) है। सर्पिल में पाइथागोरस प्रमेय लागू होता है। / The correct reasoning is (\(\sqrt{72}\)2 +12 =73). Pythagoras theorem applies in the spiral.
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वर्गमूल सर्पिल में \(\sqrt{2600}\) के बाद बनने वाला कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?
In a square root spiral, which hypotenuse is formed after \(\sqrt{2600}\), and what is its exact value?
#square-root-spiral
#hard
#next-root
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A \(\sqrt{2601}=51\)
B \(\sqrt{2599}\), कोई पूर्ण मान नहीं / \(\sqrt{2599}\), no whole value
C \(\sqrt{5200}\), कोई पूर्ण मान नहीं / \(\sqrt{5200}\), no whole value
D \(\sqrt{2602}=51\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2601}=51\)
Explanation
Simple Explanation
अगला कर्ण \(\sqrt{2601}\) है। \(2601=51^2\), इसलिए सटीक मान (51) है। / The next hypotenuse is \(\sqrt{2601}\). Since \(2601=51^2\), the exact value is (51).
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वर्गमूल सर्पिल में \(\sqrt{15}\) के बाद बनने वाले कर्ण और \(\sqrt{17}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing the hypotenuse formed after \(\sqrt{15}\) and \(\sqrt{17}\) in a square root spiral?
#square-root-spiral
#hard
#comparison
#next-root
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A अगला कर्ण \(\sqrt{16}=4\) है और \(\sqrt{17}\) (4) और (5) के बीच है / The next hypotenuse is \(\sqrt{16}=4\), and \(\sqrt{17}\) lies between (4) and (5)
B अगला कर्ण \(\sqrt{14}\) है और \(\sqrt{17}=4\) / The next hypotenuse is \(\sqrt{14}\), and \(\sqrt{17}=4\)
C दोनों ठीक (4) पर हैं / Both are exactly at (4)
D अगला कर्ण \(\sqrt{30}\) है और \(\sqrt{17}\) (3) और (4) के बीच है / The next hypotenuse is \(\sqrt{30}\), and \(\sqrt{17}\) lies between (3) and (4)
Explanation opens after your attempt
Correct Answer
A. अगला कर्ण \(\sqrt{16}=4\) है और \(\sqrt{17}\) (4) और (5) के बीच है / The next hypotenuse is \(\sqrt{16}=4\), and \(\sqrt{17}\) lies between (4) and (5)
Explanation
Simple Explanation
\(\sqrt{15}\) के बाद \(\sqrt{16}=4\) बनता है। \(4^2<17<5^2\), इसलिए \(\sqrt{17}\) (4) और (5) के बीच है। / After \(\sqrt{15}\), \(\sqrt{16}=4\) is formed. Since \(4^2<17<5^2\), \(\sqrt{17}\) lies between (4) and (5).
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वर्गमूल सर्पिल में \(\sqrt{3480}\) का सही अंतराल कौन-सा है?
What is the correct interval for \(\sqrt{3480}\) in a square root spiral?
#square-root-spiral
#hard
#number-line
#interval
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A \(57<\sqrt{3480}<58\)
B \(58<\sqrt{3480}<59\)
C \(59<\sqrt{3480}<60\)
D \(60<\sqrt{3480}<61\)
Explanation opens after your attempt
Correct Answer
B. \(58<\sqrt{3480}<59\)
Explanation
Simple Explanation
\(58^2=3364\) और \(59^2=3481\) हैं। (3480) इनके बीच है, इसलिए \(\sqrt{3480}\) (58) और (59) के बीच है। / \(58^2=3364\) and \(59^2=3481\). The number (3480) lies between them, so \(\sqrt{3480}\) lies between (58) and (59).
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वर्गमूल सर्पिल में यदि \(\sqrt{3024}\) कर्ण पर (1) इकाई लंब बनाई जाए, तो नया कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?
If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{3024}\) in a square root spiral, what will be the new hypotenuse and its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{3025}=55\)
B \(\sqrt{3023}\), कोई पूर्ण मान नहीं / \(\sqrt{3023}\), no whole value
C \(\sqrt{6048}\), कोई पूर्ण मान नहीं / \(\sqrt{6048}\), no whole value
D \(\sqrt{3026}=55\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3025}=55\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{3024+1}=\sqrt{3025}\) होगा। \(3025=55^2\), इसलिए सटीक मान (55) है। / The new hypotenuse is \(\sqrt{3024+1}=\sqrt{3025}\). Since \(3025=55^2\), the exact value is (55).
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वर्गमूल सर्पिल में \(\sqrt{2207}\) और \(\sqrt{2209}\) की संख्या-रेखा स्थिति के बारे में सही कथन कौन-सा है?
Which statement about the number-line positions of \(\sqrt{2207}\) and \(\sqrt{2209}\) in a square root spiral is correct?
#square-root-spiral
#hard
#comparison
#number-line
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A \(\sqrt{2207}\) (46) और (47) के बीच है और \(\sqrt{2209}=47\) है / \(\sqrt{2207}\) lies between (46) and (47), and \(\sqrt{2209}=47\)
B \(\sqrt{2207}=47\) और \(\sqrt{2209}\) अपरिमेय है / \(\sqrt{2207}=47\), and \(\sqrt{2209}\) is irrational
C दोनों (47) और (48) के बीच हैं / Both lie between (47) and (48)
D दोनों ठीक (47) पर हैं / Both are exactly at (47)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2207}\) (46) और (47) के बीच है और \(\sqrt{2209}=47\) है / \(\sqrt{2207}\) lies between (46) and (47), and \(\sqrt{2209}=47\)
Explanation
Simple Explanation
\(46^2<2207<47^2\) और \(2209=47^2\) है। इसलिए \(\sqrt{2209}\) ठीक (47) पर है।
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यदि सामान्य वर्गमूल सर्पिल में \(\sqrt{n}\) पर (8) इकाई लंब बनाई जाए, तो बनने वाला कर्ण किस रूप में होगा?
If an (8) unit perpendicular is drawn on \(\sqrt{n}\) in the usual square root spiral setup, what form will the formed hypotenuse have?
#square-root-spiral
#hard
#unit-change
#pythagoras
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A \(\sqrt{n+8}\)
B \(\sqrt{n+16}\)
C \(\sqrt{n+64}\)
D \(\sqrt{8n}\)
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Correct Answer
C. \(\sqrt{n+64}\)
Explanation
Simple Explanation
पाइथागोरस से (\(\sqrt{n}\)2 +82 =n+64) होगा। इसलिए नई लंब बदलने से सामान्य क्रम बदल जाता है। / By Pythagoras, (\(\sqrt{n}\)2 +82 =n+64). So changing the perpendicular changes the usual sequence.
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वर्गमूल सर्पिल में यदि नया कर्ण \(\sqrt{4096}\) है, तो उससे ठीक पहले कौन-सा कर्ण था?
In a square root spiral, if the new hypotenuse is \(\sqrt{4096}\), which hypotenuse was immediately before it?
#square-root-spiral
#hard
#previous-root
#reverse-rule
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A \(\sqrt{4094}\)
B \(\sqrt{4095}\)
C \(\sqrt{4096}\)
D \(\sqrt{4097}\)
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Correct Answer
B. \(\sqrt{4095}\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{n+1}\) हो तो पिछला कर्ण \(\sqrt{n}\) होता है। इसलिए \(\sqrt{4096}\) से पहले \(\sqrt{4095}\) था। / If the new hypotenuse is \(\sqrt{n+1}\), the previous hypotenuse is \(\sqrt{n}\). Therefore before \(\sqrt{4096}\), it was \(\sqrt{4095}\).
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वर्गमूल सर्पिल में \(\sqrt{9800}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल सही होगा?
Before placing \(\sqrt{9800}\) on the number line using a square root spiral, which interval is correct?
#square-root-spiral
#hard
#number-line
#interval
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A \(97<\sqrt{9800}<98\)
B \(98<\sqrt{9800}<99\)
C \(99<\sqrt{9800}<100\)
D \(100<\sqrt{9800}<101\)
Explanation opens after your attempt
Correct Answer
B. \(98<\sqrt{9800}<99\)
Explanation
Simple Explanation
क्योंकि \(98^2=9604\) और \(99^2=9801\) हैं। (9800) इनके बीच है। / Because \(98^2=9604\) and \(99^2=9801\). The number (9800) lies between them.
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वर्गमूल सर्पिल में यदि \(\sqrt{10403}\) कर्ण पर (1) इकाई लंब बनाई जाए, तो नया कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?
If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{10403}\) in a square root spiral, what will be the new hypotenuse and its exact value?
#square-root-spiral
#hard
#next-root
#perfect-square
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A \(\sqrt{10402}\), कोई पूर्ण मान नहीं / \(\sqrt{10402}\), no whole value
B \(\sqrt{20806}\), कोई पूर्ण मान नहीं / \(\sqrt{20806}\), no whole value
C \(\sqrt{10404}=102\)
D \(\sqrt{10405}=102\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{10404}=102\)
Explanation
Simple Explanation
नया कर्ण \(\sqrt{10403+1}=\sqrt{10404}\) होगा। \(10404=102^2\), इसलिए सटीक मान (102) है। / The new hypotenuse is \(\sqrt{10403+1}=\sqrt{10404}\). Since \(10404=102^2\), the exact value is (102).
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