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?
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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?
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A \(\sqrt{960}\)
B \(\sqrt{961}\)
C \(\sqrt{962}\)
D \(\sqrt{31}\)
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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?
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A \(32<\sqrt{1155}<33\)
B \(33<\sqrt{1155}<34\)
C \(34<\sqrt{1155}<35\)
D \(35<\sqrt{1155}<36\)
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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?
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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 \(\sqrt{52-1}=\sqrt{53}\)
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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 \(\sqrt{n}\)?
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A \(\sqrt{n+1}\)
B \(\sqrt{n+6}\)
C \(\sqrt{n+36}\)
D \(\sqrt{6n}\)
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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?
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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)
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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?
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#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
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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?
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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?
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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?
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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)
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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?
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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?
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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)?
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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 \(\sqrt{12}\)?
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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?
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#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?
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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 \(\sqrt{m}\)?
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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?
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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?
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A \(\sqrt{79}\)
B (9)
C \(\sqrt{160}\)
D \(\sqrt{82}\)
Explanation opens after your attempt
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 \(40<\sqrt{1520}<41\)
Explanation opens after your attempt
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
Explanation opens after your attempt
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 \(45<\sqrt{1935}<46\)
Explanation opens after your attempt
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 \(51<\sqrt{2499}<52\)
Explanation opens after your attempt
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?
#square-root-spiral
#hard
#next-root
#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
#next-root
#perfect-square
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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
#perfect-square
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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 \(\sqrt{4097}\)
Explanation opens after your attempt
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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