100 results found for "integer-interval" in Class 10.
संख्या रेखा पर \( \sqrt{156} \) किस पूर्णांक के सबसे निकट है?
On the number line, \( \sqrt{156} \) is closest to which integer?
#number-line
#nearest-integer
#square-root
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{156}\approx12.49 \), so it is slightly closer to (12). Check distance for the nearest integer.
Step 2
Why this answer is correct
The correct answer is B. (12). \( \sqrt{156}\approx12.49 \), so it is slightly closer to (12). Check distance for the nearest integer.
Step 3
Exam Tip
\( \sqrt{156}\approx12.49 \), इसलिए यह (12) के थोड़ा अधिक निकट है। निकटतम पूर्णांक के लिए दूरी जाँचें।
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संख्या रेखा पर \( \sqrt{132} \) किस पूर्णांक के सबसे निकट है?
On the number line, \( \sqrt{132} \) is closest to which integer?
#number-line
#nearest-integer
#square-root
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{132}\approx11.49 \), so it is slightly closer to (11). Check distance for the nearest integer.
Step 2
Why this answer is correct
The correct answer is B. (11). \( \sqrt{132}\approx11.49 \), so it is slightly closer to (11). Check distance for the nearest integer.
Step 3
Exam Tip
\( \sqrt{132}\approx11.49 \), इसलिए यह (11) के थोड़ा अधिक निकट है। निकटतम पूर्णांक के लिए दूरी जाँचें।
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यदि (m) पूर्णांक है और \(m<\sqrt{145}<m+1\), तो (m) का मान क्या है?
If (m) is an integer and \(m<\sqrt{145}<m+1\), what is the value of (m)?
#number-line
#integer-bounds
#square-roots
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
Since (144<145<169), \(12<\sqrt{145}<13\). Perfect squares give (m) quickly.
Step 2
Why this answer is correct
The correct answer is B. (12). Since (144<145<169), \(12<\sqrt{145}<13\). Perfect squares give (m) quickly.
Step 3
Exam Tip
क्योंकि (144<145<169), इसलिए \(12<\sqrt{145}<13\)। पूर्ण वर्गों से (m) तुरंत मिलता है।
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संख्या रेखा पर \( \sqrt{98} \) किस पूर्णांक के सबसे निकट है?
On the number line, \( \sqrt{98} \) is closest to which integer?
#number-line
#nearest-integer
#square-root
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{98}\approx9.899 \), so it is closest to (10). Check distance for the nearest integer.
Step 2
Why this answer is correct
The correct answer is C. (10). \( \sqrt{98}\approx9.899 \), so it is closest to (10). Check distance for the nearest integer.
Step 3
Exam Tip
\( \sqrt{98}\approx9.899 \), इसलिए यह (10) के सबसे निकट है। निकटतम पूर्णांक के लिए दूरी देखें।
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संख्या रेखा पर \( \sqrt{90} \) किस पूर्णांक के सबसे निकट है?
On the number line, \( \sqrt{90} \) is closest to which integer?
#number-line
#nearest-integer
#square-root
A (9)
B (10)
C (8)
D (11)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{90}\approx9.49 \), which is closer to (10) than to (9). Check distance for the nearest integer.
Step 2
Why this answer is correct
The correct answer is B. (10). \( \sqrt{90}\approx9.49 \), which is closer to (10) than to (9). Check distance for the nearest integer.
Step 3
Exam Tip
\( \sqrt{90}\approx9.49 \) है जो (9) की तुलना में (10) के अधिक निकट है। निकटतम पूर्णांक के लिए दूरी जाँचें।
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यदि (m) ऐसा पूर्णांक है कि \(m<\sqrt{57}<m+1\), तो (m) का मान क्या है?
If (m) is an integer such that \(m<\sqrt{57}<m+1\), what is the value of (m)?
#number-line
#integer-bounds
#square-roots
A (7)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Since (49<57<64), \(7<\sqrt{57}<8\). Therefore (m=7).
Step 2
Why this answer is correct
The correct answer is A. (7). Since (49<57<64), \(7<\sqrt{57}<8\). Therefore (m=7).
Step 3
Exam Tip
क्योंकि (49<57<64), इसलिए \(7<\sqrt{57}<8\)। अतः (m=7) होगा।
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संख्या रेखा पर \( \sqrt{99} \) का सबसे निकटतम पूर्णांक कौन सा है?
Which integer is closest to \( \sqrt{99} \) on the number line?
#number-line
#nearest-integer
#square-roots
A (10)
B (9)
C (11)
D (8)
Explanation opens after your attempt
Step 1
Concept
(99) is very close to (100), so \( \sqrt{99}\) is about (10). The nearest perfect square gives a quick answer.
Step 2
Why this answer is correct
The correct answer is A. (10). (99) is very close to (100), so \( \sqrt{99}\) is about (10). The nearest perfect square gives a quick answer.
Step 3
Exam Tip
(99) संख्या (100) के बहुत निकट है, इसलिए \( \sqrt{99}\) लगभग (10) है। निकटतम पूर्ण वर्ग तेजी से उत्तर देता है।
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संख्या रेखा पर \(\sqrt{32}\) किस पूर्णांक के सबसे निकट है?
On the number line, \(\sqrt{32}\) is closest to which integer?
#number-line
#estimation
#square-root
#nearest-integer
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{32}\approx5.66\), so it is closer to (6). Compare distances for the nearest integer.
Step 2
Why this answer is correct
The correct answer is C. (6). \(\sqrt{32}\approx5.66\), so it is closer to (6). Compare distances for the nearest integer.
Step 3
Exam Tip
\(\sqrt{32}\approx5.66\) है इसलिए यह (6) के अधिक पास है। निकटतम पूर्णांक के लिए दूरी की तुलना करें।
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संख्या रेखा पर \(\sqrt{45}\) किस पूर्णांक के सबसे निकट होगा?
On the number line, \(\sqrt{45}\) will be closest to which integer?
#number-line
#estimation
#square-root
#nearest-integer
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{45}\) is about (6.7), so it is closer to (7). Nearby perfect squares (36) and (49) help in estimation.
Step 2
Why this answer is correct
The correct answer is C. (7). \(\sqrt{45}\) is about (6.7), so it is closer to (7). Nearby perfect squares (36) and (49) help in estimation.
Step 3
Exam Tip
\(\sqrt{45}\) लगभग (6.7) है इसलिए यह (7) के अधिक पास है। अनुमान में पास के पूर्ण वर्ग (36) और (49) उपयोगी हैं।
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संख्या रेखा पर \(\sqrt{20}\) किस पूर्णांक के सबसे निकट है?
On the number line, \(\sqrt{20}\) is closest to which integer?
#number-line
#nearest-integer
#square-root
#estimation
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{20}\) is about (4.47), so it is closer to (4). Place \(\sqrt{20}\) between (4) and (5) and compare distances.
Step 2
Why this answer is correct
The correct answer is B. (4). \(\sqrt{20}\) is about (4.47), so it is closer to (4). Place \(\sqrt{20}\) between (4) and (5) and compare distances.
Step 3
Exam Tip
\(\sqrt{20}\) लगभग (4.47) है इसलिए यह (4) के अधिक पास है। \(\sqrt{20}\) को (4) और (5) के बीच रखकर दूरी सोचें।
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संख्या रेखा पर \(\sqrt{18}\) के सबसे निकट कौन सा पूर्णांक है?
Which integer is closest to \(\sqrt{18}\) on the number line?
#number-line
#estimation
#square-root
#nearest-integer
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}\) is about (4.24), so it is closer to (4). For estimation, check nearby perfect squares (16) and (25).
Step 2
Why this answer is correct
The correct answer is B. (4). \(\sqrt{18}\) is about (4.24), so it is closer to (4). For estimation, check nearby perfect squares (16) and (25).
Step 3
Exam Tip
\(\sqrt{18}\) लगभग (4.24) है इसलिए यह (4) के अधिक पास है। अनुमान के लिए पास के पूर्ण वर्ग (16) और (25) देखें।
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एक संख्या को उसके अगले पूर्णांक से गुणा करने पर (552) मिलता है। संख्या क्या है?
A number multiplied by its next integer gives (552). What is the number?
#quadratic-equations
#word-problems
#next-integer
A (23)
B (24)
C (22)
D (21)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x+1)=552). Since \(23\times24=552\), the number is (23).
Step 2
Why this answer is correct
The correct answer is A. (23). If the number is (x), then (x(x+1)=552). Since \(23\times24=552\), the number is (23).
Step 3
Exam Tip
यदि संख्या (x) है, तो (x(x+1)=552)। \(23\times24=552\), इसलिए संख्या (23) है।
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एक संख्या को उसके अगले पूर्णांक से गुणा करने पर (210) मिलता है। संख्या क्या है?
A number multiplied by its next integer gives (210). What is the number?
#quadratic-equations
#word-problems
#next-integer
A (14)
B (15)
C (13)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x+1)=210). Since \(14\times15=210\), the number is (14).
Step 2
Why this answer is correct
The correct answer is A. (14). If the number is (x), then (x(x+1)=210). Since \(14\times15=210\), the number is (14).
Step 3
Exam Tip
यदि संख्या (x) है, तो (x(x+1)=210)। \(14\times15=210\), इसलिए संख्या (14) है।
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एक संख्या और उसके अगले पूर्णांक का गुणनफल (56) है। वह संख्या क्या है?
A number multiplied by its next integer gives (56). What is the number?
#quadratic equations
#integer application
#word problems
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x+1)=56), giving (x=7). In the question, next integer means (x+1).
Step 2
Why this answer is correct
The correct answer is B. (7). If the number is (x), then (x(x+1)=56), giving (x=7). In the question, next integer means (x+1).
Step 3
Exam Tip
संख्या (x) हो तो (x(x+1)=56) बनता है, जिससे (x=7) मिलता है। प्रश्न में अगले पूर्णांक का अर्थ (x+1) है।
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किस कथन से पता चलता है कि \(\sqrt{2}\) पूर्णांक नहीं हो सकता?
Which statement shows that \(\sqrt{2}\) cannot be an integer?
#real-numbers
#root2
#integer-square
#concept
A ऐसा कोई पूर्णांक नहीं है जिसका वर्ग (2) हो / There is no integer whose square is (2)
B (2) ऋणात्मक है / (2) is negative
C \(\sqrt{2}=2\) है / \(\sqrt{2}=2\)
D हर वर्गमूल पूर्णांक होता है / Every square root is an integer
Explanation opens after your attempt
Correct Answer
A. ऐसा कोई पूर्णांक नहीं है जिसका वर्ग (2) हो / There is no integer whose square is (2)
Step 1
Concept
Squares of integers are like (0,1,4,9).
Step 2
Why this answer is correct
No integer has square (2).
Step 3
Exam Tip
Still, to prove irrationality, the full rational-form proof is needed. चरण 1: पूर्णांकों के वर्ग (0,1,4,9) जैसे होते हैं। चरण 2: कोई पूर्णांक ऐसा नहीं जिसका वर्ग (2) हो। चरण 3: फिर भी अपरिमेयता सिद्ध करने के लिए परिमेय रूप वाला पूरा प्रमाण चाहिए।
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यदि संख्या रेखा पर \(u=-\sqrt{27}-3\), तो (u) किस अंतराल में है?
If \(u=-\sqrt{27}-3\) on the number line, in which interval does (u) lie?
#number-line
#negative-expression
#interval
A ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 )
B ( -8 ) और ( -7 ) के बीच / Between ( -8 ) and ( -7 )
C ( -9 ) और ( -8 ) के बीच / Between ( -9 ) and ( -8 )
D (6) और (7) के बीच / Between (6) and (7)
Explanation opens after your attempt
Correct Answer
B. ( -8 ) और ( -7 ) के बीच / Between ( -8 ) and ( -7 )
Step 1
Concept
\( -\sqrt{27}\approx-5.196 \), so \( -\sqrt{27}-3\approx-8.196 \). Therefore it lies between (-9) and (-8).
Step 2
Why this answer is correct
The correct answer is B. ( -8 ) और ( -7 ) के बीच / Between ( -8 ) and ( -7 ). \( -\sqrt{27}\approx-5.196 \), so \( -\sqrt{27}-3\approx-8.196 \). Therefore it lies between (-9) and (-8).
Step 3
Exam Tip
\( -\sqrt{27}-3\approx-8.196 \) नहीं, बल्कि \( -\sqrt{27}\approx-5.196 \) होने से योग लगभग (-8.196) है। इसलिए यह (-9) और (-8) के बीच है।
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संख्या रेखा पर \(6-\sqrt{39}\) का सही स्थान किस अंतराल में है?
In which interval is \(6-\sqrt{39}\) correctly located on the number line?
#number-line
#root-expression
#interval
A ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
B (0) और (1) के बीच / Between (0) and (1)
C (1) और (2) के बीच / Between (1) and (2)
D ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
Explanation opens after your attempt
Correct Answer
A. ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Step 1
Concept
\( \sqrt{39}\approx6.245 \), so \(6-\sqrt{39}\approx-0.245\). Always check the sign in root subtraction.
Step 2
Why this answer is correct
The correct answer is A. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). \( \sqrt{39}\approx6.245 \), so \(6-\sqrt{39}\approx-0.245\). Always check the sign in root subtraction.
Step 3
Exam Tip
\( \sqrt{39}\approx6.245 \), इसलिए \(6-\sqrt{39}\approx-0.245\) है। घटाव वाले मूल में चिह्न जरूर जाँचें।
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यदि संख्या रेखा पर \(u=-\sqrt{18}-2\), तो (u) किस अंतराल में है?
If \(u=-\sqrt{18}-2\) on the number line, in which interval does (u) lie?
#number-line
#negative-expression
#interval
A ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
B ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
C ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 )
D (4) और (5) के बीच / Between (4) and (5)
Explanation opens after your attempt
Correct Answer
C. ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 )
Step 1
Concept
\( -\sqrt{18}-2\approx-6.243 \), so it lies between (-7) and (-6). Estimate negative sums carefully.
Step 2
Why this answer is correct
The correct answer is C. ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 ). \( -\sqrt{18}-2\approx-6.243 \), so it lies between (-7) and (-6). Estimate negative sums carefully.
Step 3
Exam Tip
\( -\sqrt{18}-2\approx-6.243 \), इसलिए यह (-7) और (-6) के बीच है। ऋणात्मक योगों में अनुमान सावधानी से करें।
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संख्या रेखा पर \(5-\sqrt{31}\) का सही स्थान किस अंतराल में है?
In which interval is \(5-\sqrt{31}\) correctly located on the number line?
#number-line
#root-expression
#interval
A (0) और (1) के बीच / Between (0) and (1)
B ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
C (1) और (2) के बीच / Between (1) and (2)
D ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
Explanation opens after your attempt
Correct Answer
B. ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Step 1
Concept
\( \sqrt{31}\approx5.568 \), so \(5-\sqrt{31}\approx-0.568\). Always check the sign in root subtraction.
Step 2
Why this answer is correct
The correct answer is B. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). \( \sqrt{31}\approx5.568 \), so \(5-\sqrt{31}\approx-0.568\). Always check the sign in root subtraction.
Step 3
Exam Tip
\( \sqrt{31}\approx5.568 \), इसलिए \(5-\sqrt{31}\approx-0.568\) है। घटाव वाले मूलों में चिह्न अवश्य जाँचें।
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यदि संख्या रेखा पर \(u=-2-\sqrt{7}\), तो (u) किस अंतराल में स्थित है?
If \(u=-2-\sqrt{7}\), in which interval is (u) located on the number line?
#number-line
#negative-expression
#interval
A ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
B ( -4 ) और ( -3 ) के बीच / Between ( -4 ) and ( -3 )
C ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
D (2) और (3) के बीच / Between (2) and (3)
Explanation opens after your attempt
Correct Answer
C. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
Step 1
Concept
\( \sqrt{7}\approx2.646 \), so \(u\approx-4.646\). Therefore it lies between (-5) and (-4).
Step 2
Why this answer is correct
The correct answer is C. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 ). \( \sqrt{7}\approx2.646 \), so \(u\approx-4.646\). Therefore it lies between (-5) and (-4).
Step 3
Exam Tip
\( \sqrt{7}\approx2.646 \), इसलिए \(u\approx-4.646\) है। अतः यह (-5) और (-4) के बीच होगा।
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यदि \(x=-5+\sqrt{22}\), तो संख्या रेखा पर (x) किस अंतराल में है?
If \(x=-5+\sqrt{22}\), in which interval is (x) on the number line?
#number-line
#root-expression
#interval
A ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
B (0) और (1) के बीच / Between (0) and (1)
C ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
D (1) और (2) के बीच / Between (1) and (2)
Explanation opens after your attempt
Correct Answer
C. ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Step 1
Concept
Since \(4<\sqrt{22}<5\), \(-1<-5+\sqrt{22}<0\). Add bounds carefully in mixed expressions.
Step 2
Why this answer is correct
The correct answer is C. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). Since \(4<\sqrt{22}<5\), \(-1<-5+\sqrt{22}<0\). Add bounds carefully in mixed expressions.
Step 3
Exam Tip
\(4<\sqrt{22}<5\), इसलिए \(-1<-5+\sqrt{22}<0\)। मिश्रित अभिव्यक्ति में सीमा जोड़ें।
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यदि संख्या रेखा पर \(x=-\sqrt{29}\), तो (x) किस अंतराल में होगा?
If \(x=-\sqrt{29}\) on the number line, in which interval will (x) lie?
#number-line
#negative-square-root
#interval
A ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
B ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
C (4) और (5) के बीच / Between (4) and (5)
D (5) और (6) के बीच / Between (5) and (6)
Explanation opens after your attempt
Correct Answer
B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
Step 1
Concept
Since \(5<\sqrt{29}<6\), \(-6<-\sqrt{29}<-5\). For negative roots, write the reversed interval carefully.
Step 2
Why this answer is correct
The correct answer is B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 ). Since \(5<\sqrt{29}<6\), \(-6<-\sqrt{29}<-5\). For negative roots, write the reversed interval carefully.
Step 3
Exam Tip
क्योंकि \(5<\sqrt{29}<6\), इसलिए \(-6<-\sqrt{29}<-5\)। ऋणात्मक मूलों में क्रम उलटकर लिखें।
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यदि संख्या रेखा पर \(u=-\sqrt{2}-1\), तो (u) किस अंतराल में है?
If \(u=-\sqrt{2}-1\) on the number line, in which interval does (u) lie?
#number-line
#negative-expression
#interval
A ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
B ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
C ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
D (2) और (3) के बीच / Between (2) and (3)
Explanation opens after your attempt
Correct Answer
A. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
Step 1
Concept
\( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 2
Why this answer is correct
The correct answer is A. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 ). \( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 3
Exam Tip
\( -\sqrt{2}-1\approx-2.414 \), इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक योगों में अनुमान सावधानी से करें।
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संख्या रेखा पर \(2-\sqrt{10}\) का सही स्थान किस अंतराल में है?
In which interval is \(2-\sqrt{10}\) correctly located on the number line?
#number-line
#root-expression
#interval
A (-2) और (-1) के बीच / Between (-2) and (-1)
B (-1) और (0) के बीच / Between (-1) and (0)
C (0) और (1) के बीच / Between (0) and (1)
D (1) और (2) के बीच / Between (1) and (2)
Explanation opens after your attempt
Correct Answer
A. (-2) और (-1) के बीच / Between (-2) and (-1)
Step 1
Concept
\( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) के बीच / Between (-2) and (-1). \( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 3
Exam Tip
\( \sqrt{10}\approx3.162 \) इसलिए \(2-\sqrt{10}\approx-1.162\) है। घटाव वाले मूल में अनुमान जरूरी है।
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संख्या रेखा पर (x) का स्थान ( -4 ) से \( \sqrt{13} \) इकाई दाईं ओर है। (x) किस अंतराल में है?
The point (x) is \( \sqrt{13} \) units to the right of (-4) on the number line. In which interval does (x) lie?
#number-line
#interval
#root-expression
A (-1) और (0) के बीच / Between (-1) and (0)
B (0) और (1) के बीच / Between (0) and (1)
C (-2) और (-1) के बीच / Between (-2) and (-1)
D (-4) और (-3) के बीच / Between (-4) and (-3)
Explanation opens after your attempt
Correct Answer
A. (-1) और (0) के बीच / Between (-1) and (0)
Step 1
Concept
\(x=-4+\sqrt{13}\), and \(3<\sqrt{13}<4\), so (-1<x<0). Add bounds in combined expressions.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (0) के बीच / Between (-1) and (0). \(x=-4+\sqrt{13}\), and \(3<\sqrt{13}<4\), so (-1<x<0). Add bounds in combined expressions.
Step 3
Exam Tip
\(x=-4+\sqrt{13}\) और \(3<\sqrt{13}<4\), इसलिए (-1<x<0)। संयुक्त अभिव्यक्ति में सीमा जोड़ें।
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संख्या रेखा पर \(\sqrt{5}-\sqrt{2}\) किस अंतराल में स्थित होगा?
On the number line, in which interval will \(\sqrt{5}-\sqrt{2}\) lie?
#polynomials
#number-line
#irrational-difference
#interval
A ((0,1))
B ((1,2))
C ((2,3))
D ((-1,0))
Explanation opens after your attempt
Correct Answer
A. ((0,1))
Step 1
Concept
\(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 2
Why this answer is correct
The correct answer is A. ((0,1)). \(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 3
Exam Tip
\(\sqrt{5}\approx2.236\) और \(\sqrt{2}\approx1.414\), इसलिए अंतर लगभग (0.822) है। अपरिमेयों के अंतर का स्थान निकालने के लिए छोटे अनुमान उपयोग करें।
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किस विकल्प में संख्या रेखा पर \(-\sqrt{12}\) का सही सरल अंतराल है?
Which option gives the correct simple interval for \(-\sqrt{12}\) on the number line?
#polynomials
#number-line
#negative-surd
#interval
A ((-4,-3))
B ((-3,-2))
C ((3,4))
D ((-5,-4))
Explanation opens after your attempt
Correct Answer
A. ((-4,-3))
Step 1
Concept
Since \(3<\sqrt{12}<4\), \(-4<-\sqrt{12}<-3\). Multiplying by a negative reverses the inequality.
Step 2
Why this answer is correct
The correct answer is A. ((-4,-3)). Since \(3<\sqrt{12}<4\), \(-4<-\sqrt{12}<-3\). Multiplying by a negative reverses the inequality.
Step 3
Exam Tip
क्योंकि \(3<\sqrt{12}<4\), इसलिए \(-4<-\sqrt{12}<-3\)। ऋणात्मक करने पर असमानता की दिशा बदलती है।
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संख्या रेखा पर \(\sqrt{2}+\sqrt{3}\) किस अंतराल में होगा?
On the number line, in which interval will \(\sqrt{2}+\sqrt{3}\) lie?
#polynomials
#number-line
#surd-addition
#interval
A ((3,4))
B ((2,3))
C ((4,5))
D ((1,2))
Explanation opens after your attempt
Correct Answer
A. ((3,4))
Step 1
Concept
\(\sqrt{2}\approx1.414\) and \(\sqrt{3}\approx1.732\), so the sum is about (3.146). Add approximate values for sums.
Step 2
Why this answer is correct
The correct answer is A. ((3,4)). \(\sqrt{2}\approx1.414\) and \(\sqrt{3}\approx1.732\), so the sum is about (3.146). Add approximate values for sums.
Step 3
Exam Tip
\(\sqrt{2}\approx1.414\) और \(\sqrt{3}\approx1.732\), इसलिए योग लगभग (3.146) है। योग के लिए अनुमानित मान जोड़ें।
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किस विकल्प में संख्या रेखा पर \(-1+\sqrt{5}\) का सही अंतराल है?
Which option gives the correct interval of \(-1+\sqrt{5}\) on the number line?
#polynomials
#number-line
#irrational-expression
#interval
A ((1,2))
B ((0,1))
C ((2,3))
D ((-1,0))
Explanation opens after your attempt
Correct Answer
A. ((1,2))
Step 1
Concept
Since \(2<\sqrt{5}<3\), \(1<-1+\sqrt{5}<2\). When adding or subtracting a constant, adjust the whole inequality.
Step 2
Why this answer is correct
The correct answer is A. ((1,2)). Since \(2<\sqrt{5}<3\), \(1<-1+\sqrt{5}<2\). When adding or subtracting a constant, adjust the whole inequality.
Step 3
Exam Tip
क्योंकि \(2<\sqrt{5}<3\), इसलिए \(1<-1+\sqrt{5}<2\)। स्थिर संख्या जोड़ने या घटाने पर पूरी असमानता बदलें।
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संख्या रेखा पर \(2-\sqrt{3}\) किस अंतराल में स्थित होगा?
On the number line, in which interval will \(2-\sqrt{3}\) lie?
#polynomials
#number-line
#irrational-expression
#interval
A ((0,1))
B ((1,2))
C ((-1,0))
D ((2,3))
Explanation opens after your attempt
Correct Answer
A. ((0,1))
Step 1
Concept
Since \(1<\sqrt{3}<2\), \(0<2-\sqrt{3}<1\). Be careful with inequalities when subtracting.
Step 2
Why this answer is correct
The correct answer is A. ((0,1)). Since \(1<\sqrt{3}<2\), \(0<2-\sqrt{3}<1\). Be careful with inequalities when subtracting.
Step 3
Exam Tip
क्योंकि \(1<\sqrt{3}<2\), इसलिए \(0<2-\sqrt{3}<1\)। घटाव में असमानता की दिशा सावधानी से देखें।
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किस विकल्प में \(\sqrt{20}\) का संख्या रेखा पर सही अंतराल दिया गया है?
Which option gives the correct interval for \(\sqrt{20}\) on the number line?
#polynomials
#number-line
#square-root
#interval
A ((4,5))
B ((3,4))
C ((5,6))
D ((2,3))
Explanation opens after your attempt
Correct Answer
A. ((4,5))
Step 1
Concept
Because \(4^2=16\) and \(5^2=25\), \(4<\sqrt{20}<5\). Perfect-square bounds quickly give the interval.
Step 2
Why this answer is correct
The correct answer is A. ((4,5)). Because \(4^2=16\) and \(5^2=25\), \(4<\sqrt{20}<5\). Perfect-square bounds quickly give the interval.
Step 3
Exam Tip
क्योंकि \(4^2=16\) और \(5^2=25\), इसलिए \(4<\sqrt{20}<5\)। पूर्ण वर्गों की सीमा तुरंत अंतराल देती है।
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संख्या रेखा पर \(-\sqrt{5}\) की स्थिति किस अंतराल में होगी?
On the number line, in which interval will \(-\sqrt{5}\) lie?
#polynomials
#number-line
#negative-irrational
#interval
A ((-3,-2))
B ((-2,-1))
C ((1,2))
D ((2,3))
Explanation opens after your attempt
Correct Answer
A. ((-3,-2))
Step 1
Concept
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 2
Why this answer is correct
The correct answer is A. ((-3,-2)). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\) (2) और (3) के बीच है और ऋणात्मक मान (-3) और (-2) के बीच होगा। ऋणात्मक दिशा में क्रम उलट जाता है।
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समीकरण (x-2 -2(4t+1)x+\(7t^2+2t+5\)=0) के कोई वास्तविक मूल नहीं हैं। (t) के लिए सही अंतराल क्या है?
The equation (x-2 -2(4t+1)x+\(7t^2+2t+5\)=0) has no real roots. What is the correct interval for (t)?
#quadratic-equations
#no-real-roots
#parameter-interval
A \(-1<t<\frac{2}{9}\)
B (t<-1) या \(t>\frac{2}{9}\) / (t<-1) or \(t>\frac{2}{9}\)
C (t=-1) या \(t=\frac{2}{9}\) / (t=-1) or \(t=\frac{2}{9}\)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. \(-1<t<\frac{2}{9}\)
Step 1
Concept
Here (D=4(4t+1)2 -4\(7t^2+2t+5\)=36t-2 +24t-16). From (D<0), \(-1<t<\frac{2}{9}\).
Step 2
Why this answer is correct
The correct answer is A. \(-1<t<\frac{2}{9}\). Here (D=4(4t+1)2 -4\(7t^2+2t+5\)=36t-2 +24t-16). From (D<0), \(-1<t<\frac{2}{9}\).
Step 3
Exam Tip
यहाँ (D=4(4t+1)2 -4\(7t^2+2t+5\)=36t-2 +24t-16) है। (D<0) से \(-1<t<\frac{2}{9}\) मिलता है।
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यदि (x-2 +2(v+2)x+(4v+11)=0) के कोई वास्तविक मूल नहीं हों, तो (v) किस अंतराल में होगा?
If (x-2 +2(v+2)x+(4v+11)=0) has no real roots, in which interval will (v) lie?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-3<v<1)
B (v<-3) या (v>1) / (v<-3) or (v>1)
C (v=-3) या (v=1) / (v=-3) or (v=1)
D हर (v) / Every (v)
Explanation opens after your attempt
Correct Answer
A. (-3<v<1)
Step 1
Concept
Here (D=4(v+2)2 -4(4v+11)) must be expanded carefully. Always verify the middle term before solving the interval.
Step 2
Why this answer is correct
The correct answer is A. (-3<v<1). Here (D=4(v+2)2 -4(4v+11)) must be expanded carefully. Always verify the middle term before solving the interval.
Step 3
Exam Tip
यहाँ (D=4(v+2)2 -4(4v+11)=4\(v^2-7\)) नहीं, सही रूप (4\(v^2-7\)) नहीं है। परीक्षा में विस्तार सावधानी से करें।
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समीकरण (x-2 -2(3t+1)x+\(5t^2+2t+4\)=0) के कोई वास्तविक मूल नहीं हैं। (t) के लिए सही अंतराल क्या है?
The equation (x-2 -2(3t+1)x+\(5t^2+2t+4\)=0) has no real roots. What is the correct interval for (t)?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-2<t<1)
B (t<-2) या (t>1) / (t<-2) or (t>1)
C (t=-2) या (t=1) / (t=-2) or (t=1)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. (-2<t<1)
Step 1
Concept
Here (D=4(3t+1)2 -4\(5t^2+2t+4\)=16(t-1)(t+2)). From (D<0), (-2<t<1).
Step 2
Why this answer is correct
The correct answer is A. (-2<t<1). Here (D=4(3t+1)2 -4\(5t^2+2t+4\)=16(t-1)(t+2)). From (D<0), (-2<t<1).
Step 3
Exam Tip
यहाँ (D=4(3t+1)2 -4\(5t^2+2t+4\)=16(t-1)(t+2)) है। (D<0) से (-2<t<1)।
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यदि (x-2 +2(t+1)x+(3t+7)=0) के कोई वास्तविक मूल नहीं हों, तो (t) किस अंतराल में होगा?
If (x-2 +2(t+1)x+(3t+7)=0) has no real roots, in which interval will (t) lie?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-4<t<1)
B (t<-4) या (t>1) / (t<-4) or (t>1)
C (t=-4) या (t=1) / (t=-4) or (t=1)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. (-4<t<1)
Step 1
Concept
Here (D=4(t+1)2 -4(3t+7)=4\(t^2-t-6\)). For (D<0), factor again carefully before selecting the interval.
Step 2
Why this answer is correct
The correct answer is A. (-4<t<1). Here (D=4(t+1)2 -4(3t+7)=4\(t^2-t-6\)). For (D<0), factor again carefully before selecting the interval.
Step 3
Exam Tip
यहाँ (D=4(t+1)2 -4(3t+7)=4\(t^2-t-6\)) है। (D<0) से (-2<t<3) नहीं, गुणनखंड फिर से जाँचें।
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समीकरण (x-2 -2(2t-1)x+\(t^2+2\)=0) के कोई वास्तविक मूल नहीं हैं। (t) के लिए सही अंतराल चुनिए।
The equation (x-2 -2(2t-1)x+\(t^2+2\)=0) has no real roots. Choose the correct interval for (t).
#quadratic-equations
#no-real-roots
#parameter-interval
A \(\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3}\)
B \(t<\frac{4-2\sqrt{6}}{3}\) या \(t>\frac{4+2\sqrt{6}}{3}\) / \(t<\frac{4-2\sqrt{6}}{3}\) or \(t>\frac{4+2\sqrt{6}}{3}\)
C (t=1) मात्र / Only (t=1)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. \(\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3}\)
Step 1
Concept
Here (D=4(2t-1)2 -4\(t^2+2\)=4\(3t^2-4t-1\)). From (D<0), the interval between the two boundary roots is obtained.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3}\). Here (D=4(2t-1)2 -4\(t^2+2\)=4\(3t^2-4t-1\)). From (D<0), the interval between the two boundary roots is obtained.
Step 3
Exam Tip
यहाँ (D=4(2t-1)2 -4\(t^2+2\)=4\(3t^2-4t-1\)) है। (D<0) से दिए गए दोनों मूलों के बीच का अंतराल मिलता है।
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यदि (x-2 +2(k-1)x+(k+5)=0) के कोई वास्तविक मूल नहीं हैं, तो (k) किस अंतराल में होगा?
If (x-2 +2(k-1)x+(k+5)=0) has no real roots, in which interval will (k) lie?
#quadratic-equations
#no-real-roots
#parameter-interval
A (0<k<3)
B \(k\leq0\) या \(k\geq3\) / \(k\leq0\) or \(k\geq3\)
C (k=0) या (k=3) / (k=0) or (k=3)
D हर (k) / Every (k)
Explanation opens after your attempt
Correct Answer
A. (0<k<3)
Step 1
Concept
Here (D=4(k-1)2 -4(k+5)=4\(k^2-3k-4\)). Use (D<0) and factor carefully before choosing the interval.
Step 2
Why this answer is correct
The correct answer is A. (0<k<3). Here (D=4(k-1)2 -4(k+5)=4\(k^2-3k-4\)). Use (D<0) and factor carefully before choosing the interval.
Step 3
Exam Tip
यहाँ (D=4(k-1)2 -4(k+5)=4\(k^2-3k-4\)) नहीं, सही सरल रूप (4\(k^2-3k-4\)) है। (D<0) से (0<k<3) नहीं मिलता, इसलिए गुणनखंड जाँचें।
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समीकरण (x-2 +(k+2)x+9=0) में कोई वास्तविक मूल न होने के लिए (k) का अंतराल क्या है?
What is the interval of (k) for no real roots in (x-2 +(k+2)x+9=0)?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-8<k<4)
B (k<-8) या (k>4) / (k<-8) or (k>4)
C (k=-8) या (k=4) / (k=-8) or (k=4)
D (k=2) मात्र / Only (k=2)
Explanation opens after your attempt
Correct Answer
A. (-8<k<4)
Step 1
Concept
Here (D=(k+2)2 -36). From (D<0), we get (-8<k<4).
Step 2
Why this answer is correct
The correct answer is A. (-8<k<4). Here (D=(k+2)2 -36). From (D<0), we get (-8<k<4).
Step 3
Exam Tip
यहाँ (D=(k+2)2 -36) है। (D<0) से (-8<k<4) मिलता है।
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समीकरण (3x-2 -2(2a+1)x+\(a^2+a+1\)=0) के वास्तविक मूल न होने का अंतराल कौन सा है?
Which interval gives no real roots for (3x-2 -2(2a+1)x+\(a^2+a+1\)=0)?
#quadratic equations
#no real roots
#interval
A (-2<a<1)
B (a<-2) या (a>1) / (a<-2) or (a>1)
C (a=-2) या (a=1) / (a=-2) or (a=1)
D \(a\le -2\) या \(a\ge1\) / \(a\le -2\) or \(a\ge1\)
Explanation opens after your attempt
Correct Answer
A. (-2<a<1)
Step 1
Concept
For no real roots, (D<0) is required. From \(a^2+a-2<0\), we get (-2<a<1).
Step 2
Why this answer is correct
The correct answer is A. (-2<a<1). For no real roots, (D<0) is required. From \(a^2+a-2<0\), we get (-2<a<1).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। \(a^2+a-2<0\) से (-2<a<1) मिलता है।
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यदि विविक्तकर (D=(z+1)2 -9) है, तो वास्तविक मूल न होने के लिए (z) किस अंतराल में होगा?
If the discriminant is (D=(z+1)2 -9), in which interval will (z) lie for no real roots?
#quadratic equations
#D negative
#interval
A (-4<z<2)
B (z<-4) या (z>2) / (z<-4) or (z>2)
C (z=-4) या (z=2) / (z=-4) or (z=2)
D सभी वास्तविक (z) / All real (z)
Explanation opens after your attempt
Correct Answer
A. (-4<z<2)
Step 1
Concept
For no real roots, (D<0) is needed. From ((z+1)2 <9), we get (-4<z<2).
Step 2
Why this answer is correct
The correct answer is A. (-4<z<2). For no real roots, (D<0) is needed. From ((z+1)2 <9), we get (-4<z<2).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। ((z+1)2 <9) से (-4<z<2) मिलता है।
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समीकरण (x-2 +(k-3)x+4=0) में कोई वास्तविक मूल न होने के लिए (k) का अंतराल क्या है?
What is the interval of (k) for no real roots in (x-2 +(k-3)x+4=0)?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-1<k<7)
B (k<-1) या (k>7) / (k<-1) or (k>7)
C (k=-1) या (k=7) / (k=-1) or (k=7)
D (k=3) मात्र / Only (k=3)
Explanation opens after your attempt
Correct Answer
A. (-1<k<7)
Step 1
Concept
Here (D=(k-3)2 -16). From (D<0), we get (-1<k<7).
Step 2
Why this answer is correct
The correct answer is A. (-1<k<7). Here (D=(k-3)2 -16). From (D<0), we get (-1<k<7).
Step 3
Exam Tip
यहाँ (D=(k-3)2 -16) है। (D<0) से (-1<k<7) मिलता है।
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समीकरण (x-2 +2(a-2)x+2a+5=0) के वास्तविक मूल न होने के लिए (a) किस अंतराल में होगा?
In which interval will (a) lie for (x-2 +2(a-2)x+2a+5=0) to have no real roots?
#quadratic equations
#no real roots
#parameter interval
A \(3-\sqrt{10}<a<3+\sqrt{10}\)
B \(a<3-\sqrt{10}\) या \(a>3+\sqrt{10}\) / \(a<3-\sqrt{10}\) or \(a>3+\sqrt{10}\)
C \(a=3-\sqrt{10}\) या \(a=3+\sqrt{10}\) / \(a=3-\sqrt{10}\) or \(a=3+\sqrt{10}\)
D \(a>3+\sqrt{10}\) केवल / \(a>3+\sqrt{10}\) only
Explanation opens after your attempt
Correct Answer
A. \(3-\sqrt{10}<a<3+\sqrt{10}\)
Step 1
Concept
For no real roots, (D<0) is required. Here (D=4\(a^2-6a-1\)), so \(3-\sqrt{10}<a<3+\sqrt{10}\).
Step 2
Why this answer is correct
The correct answer is A. \(3-\sqrt{10}<a<3+\sqrt{10}\). For no real roots, (D<0) is required. Here (D=4\(a^2-6a-1\)), so \(3-\sqrt{10}<a<3+\sqrt{10}\).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4\(a^2-6a-1\)), इसलिए \(3-\sqrt{10}<a<3+\sqrt{10}\)।
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समीकरण \(x^2-2mx+3m=0\) के वास्तविक मूल न होने के लिए सही अंतराल कौन सा है?
Which interval is correct for \(x^2-2mx+3m=0\) to have no real roots?
#quadratic equations
#no real roots
#interval
A (0<m<3)
B (m<0)
C (m>3)
D (m=0) या (m=3) / (m=0) or (m=3)
Explanation opens after your attempt
Correct Answer
A. (0<m<3)
Step 1
Concept
For no real roots, (D<0) is needed. From (D=4m(m-3 )<0), we get (0<m<3).
Step 2
Why this answer is correct
The correct answer is A. (0<m<3). For no real roots, (D<0) is needed. From (D=4m(m-3 )<0), we get (0<m<3).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। (D=4m(m-3 )<0) से (0<m<3) मिलता है।
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समीकरण \(x^2+2tx+t+4=0\) के वास्तविक मूल न होने के लिए (t) किस अंतराल में होगा?
In which interval will (t) lie for \(x^2+2tx+t+4=0\) to have no real roots?
#quadratic equations
#no real roots
#interval
A \(-\frac{3}{2}<t<2\)
B \(t<-\frac{3}{2}\) या (t>2) / \(t<-\frac{3}{2}\) or (t>2)
C \(t=-\frac{3}{2}\) या (t=2) / \(t=-\frac{3}{2}\) or (t=2)
D (t>0)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{3}{2}<t<2\)
Step 1
Concept
For no real roots, (D<0) is required. Here (D=4(t-2)(2t+3)), so \(-\frac{3}{2}<t<2\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}<t<2\). For no real roots, (D<0) is required. Here (D=4(t-2)(2t+3)), so \(-\frac{3}{2}<t<2\).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4(t-2)(2t+3)), इसलिए \(-\frac{3}{2}<t<2\)।
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समीकरण (x-2 -(k+1)x+4=0) में वास्तविक मूल न होने के लिए (k) किस अंतराल में होगा?
For (x-2 -(k+1)x+4=0), in which interval will (k) lie for no real roots?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-5<k<3)
B (k<-5) या (k>3) / (k<-5) or (k>3)
C (k=3) मात्र / Only (k=3)
D (k=-5) या (k=3) / (k=-5) or (k=3)
Explanation opens after your attempt
Correct Answer
A. (-5<k<3)
Step 1
Concept
Here (D=(k+1)2 -16), and no real roots need (D<0). This gives (-5<k<3).
Step 2
Why this answer is correct
The correct answer is A. (-5<k<3). Here (D=(k+1)2 -16), and no real roots need (D<0). This gives (-5<k<3).
Step 3
Exam Tip
यहाँ (D=(k+1)2 -16) है और वास्तविक मूल न होने के लिए (D<0) चाहिए। इससे (-5<k<3) मिलता है।
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यदि \( \frac{a}{10} \) संख्या रेखा पर \( \sqrt{2} \) और (1.5) के बीच है, तो (a) का कौन सा पूर्णांक मान संभव है?
If \( \frac{a}{10} \) lies between \( \sqrt{2} \) and (1.5) on the number line, which integer value of (a) is possible?
#number-line
#parameter
#between-values
A (14.5)
B (13)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{2}\approx1.414 \), so \( \frac{a}{10} \) must be between (1.414) and (1.5). (a=14.5) gives (1.45).
Step 2
Why this answer is correct
The correct answer is A. (14.5). \( \sqrt{2}\approx1.414 \), so \( \frac{a}{10} \) must be between (1.414) and (1.5). (a=14.5) gives (1.45).
Step 3
Exam Tip
\( \sqrt{2}\approx1.414 \), इसलिए \( \frac{a}{10} \) को (1.414) और (1.5) के बीच होना चाहिए। (a=14.5) से (1.45) मिलता है।
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संख्या रेखा पर \( \sqrt{20} \) और \( \sqrt{27} \) के बीच कौन सा पूर्णांक आता है?
Which integer lies between \( \sqrt{20} \) and \( \sqrt{27} \) on the number line?
#number-line
#integers-between-roots
#estimation
A (5)
B (4)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{20}\approx4.47\) and \( \sqrt{27}\approx5.19\), so (5) lies between them. Use perfect squares to identify bounds.
Step 2
Why this answer is correct
The correct answer is A. (5). \( \sqrt{20}\approx4.47\) and \( \sqrt{27}\approx5.19\), so (5) lies between them. Use perfect squares to identify bounds.
Step 3
Exam Tip
\( \sqrt{20}\approx4.47\) और \( \sqrt{27}\approx5.19\), इसलिए (5) बीच में है। पूर्ण वर्गों से सीमा पहचानें।
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संख्या रेखा पर \( \frac{8}{4}\) किस पूर्णांक के बराबर है?
On the number line, \(\frac{8}{4}\) is equal to which integer?
#fractions
#integers
#number-line
A (2)
B (4)
C (8)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(\frac{8}{4}=2\), so it is located at (2). Convert a simple fraction into an integer to identify the point.
Step 2
Why this answer is correct
The correct answer is A. (2). \(\frac{8}{4}=2\), so it is located at (2). Convert a simple fraction into an integer to identify the point.
Step 3
Exam Tip
\(\frac{8}{4}=2\), इसलिए यह (2) पर स्थित है। सरल भिन्न को पूर्णांक में बदलकर बिंदु पहचानें।
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संख्या रेखा पर \(\frac{7}{5}\) को दिखाते समय यह किस पूर्णांक के बाद आएगा?
While showing \(\frac{7}{5}\) on the number line, after which integer will it appear?
#improper-fractions
#number-line
#representation
A (1)
B (0)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(\frac{7}{5}=1.4\), so it comes after (1) and before (2). Think of an improper fraction in mixed form.
Step 2
Why this answer is correct
The correct answer is A. (1). \(\frac{7}{5}=1.4\), so it comes after (1) and before (2). Think of an improper fraction in mixed form.
Step 3
Exam Tip
\(\frac{7}{5}=1.4\) है, इसलिए यह (1) के बाद और (2) से पहले आता है। अपूर्ण भिन्न को मिश्रित रूप में सोचें।
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दो क्रमागत विषम धनात्मक पूर्णांकों का गुणनफल (483) है। बड़ी संख्या क्या है?
The product of two consecutive positive odd integers is (483). What is the larger integer?
#quadratic equations
#consecutive odd integers
#product
A (21)
B (23)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).
Step 2
Why this answer is correct
The correct answer is B. (23). The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).
Step 3
Exam Tip
संख्याएँ (x) और (x+2) हैं। (x(x+2)=483) से (x=21) मिलता है इसलिए बड़ी संख्या (23) है।
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दो क्रमागत सम धनात्मक पूर्णांकों का गुणनफल (360) है। छोटी संख्या क्या है?
The product of two consecutive positive even integers is (360). What is the smaller integer?
#quadratic equations
#consecutive even integers
#product
A (16)
B (18)
C (20)
D (22)
Explanation opens after your attempt
Step 1
Concept
Let the integers be (x) and (x+2). From (x(x+2)=360), \(x^2+2x-360=0\), so (x=18).
Step 2
Why this answer is correct
The correct answer is B. (18). Let the integers be (x) and (x+2). From (x(x+2)=360), \(x^2+2x-360=0\), so (x=18).
Step 3
Exam Tip
संख्याएँ (x) और (x+2) मानें। (x(x+2)=360) से \(x^2+2x-360=0\) और (x=18) मिलता है।
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दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (841) है। छोटा पूर्णांक क्या है?
The sum of squares of two consecutive positive integers is (841). What is the smaller integer?
#quadratic equations
#word problems
#sum of squares
A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x-2 +(x+1)2 =841), giving (x=20). Write consecutive numbers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is C. (20). If the smaller integer is (x), then (x-2 +(x+1)2 =841), giving (x=20). Write consecutive numbers as (x) and (x+1).
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x-2 +(x+1)2 =841), जिससे (x=20) मिलता है। लगातार संख्याओं को (x) और (x+1) लिखें।
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दो लगातार धनात्मक सम पूर्णांकों का गुणनफल (288) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive even integers is (288). What is the larger integer?
#quadratic-equations
#word-problems
#even-integers
A (18)
B (16)
C (20)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the smaller even integer is (x), then (x(x+2)=288). Since (x=16), the larger integer is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the smaller even integer is (x), then (x(x+2)=288). Since (x=16), the larger integer is (18).
Step 3
Exam Tip
यदि छोटा सम पूर्णांक (x) है, तो (x(x+2)=288)। (x=16) होने से बड़ा पूर्णांक (18) है।
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दो लगातार धनात्मक विषम पूर्णांकों का गुणनफल (399) है। छोटा पूर्णांक क्या है?
The product of two consecutive positive odd integers is (399). What is the smaller integer?
#quadratic-equations
#word-problems
#odd-integers
A (19)
B (21)
C (17)
D (23)
Explanation opens after your attempt
Step 1
Concept
If the smaller odd integer is (x), then (x(x+2)=399). Since \(19\times21=399\), the smaller integer is (19).
Step 2
Why this answer is correct
The correct answer is A. (19). If the smaller odd integer is (x), then (x(x+2)=399). Since \(19\times21=399\), the smaller integer is (19).
Step 3
Exam Tip
यदि छोटा विषम पूर्णांक (x) है, तो (x(x+2)=399)। \(19\times21=399\), इसलिए छोटा पूर्णांक (19) है।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (306) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive integers is (306). What is the larger integer?
#quadratic-equations
#word-problems
#consecutive-integers
A (18)
B (17)
C (19)
D (16)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x(x+1)=306). When (x=17), the larger integer is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the smaller integer is (x), then (x(x+1)=306). When (x=17), the larger integer is (18).
Step 3
Exam Tip
यदि छोटा पूर्णांक (x) है, तो (x(x+1)=306)। (x=17) होने पर बड़ा पूर्णांक (18) है।
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दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (365) है। छोटा पूर्णांक क्या है?
The sum of squares of two consecutive positive integers is (365). What is the smaller integer?
#quadratic equations
#word problems
#sum of squares
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x-2 +(x+1)2 =365), giving (x=13). Write consecutive integers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is C. (13). If the smaller integer is (x), then (x-2 +(x+1)2 =365), giving (x=13). Write consecutive integers as (x) and (x+1).
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x-2 +(x+1)2 =365), जिससे (x=13) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।
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दो लगातार धनात्मक सम पूर्णांकों का गुणनफल (168) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive even integers is (168). What is the larger integer?
#quadratic-equations
#word-problems
#even-integers
A (14)
B (12)
C (16)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the smaller even integer is (x), then (x(x+2)=168). Since (x=12), the larger integer is (14).
Step 2
Why this answer is correct
The correct answer is A. (14). If the smaller even integer is (x), then (x(x+2)=168). Since (x=12), the larger integer is (14).
Step 3
Exam Tip
यदि छोटा सम पूर्णांक (x) है, तो (x(x+2)=168)। (x=12) होने से बड़ा पूर्णांक (14) है।
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दो लगातार धनात्मक विषम पूर्णांकों का गुणनफल (195) है। छोटा पूर्णांक क्या है?
The product of two consecutive positive odd integers is (195). What is the smaller integer?
#quadratic-equations
#word-problems
#odd-integers
A (13)
B (15)
C (11)
D (17)
Explanation opens after your attempt
Step 1
Concept
If the smaller odd integer is (x), then (x(x+2)=195). (x=13) is correct because \(13\times15=195\).
Step 2
Why this answer is correct
The correct answer is A. (13). If the smaller odd integer is (x), then (x(x+2)=195). (x=13) is correct because \(13\times15=195\).
Step 3
Exam Tip
यदि छोटा विषम पूर्णांक (x) है, तो (x(x+2)=195)। (x=13) सही है क्योंकि \(13\times15=195\)।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (156) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive integers is (156). What is the larger integer?
#quadratic-equations
#word-problems
#consecutive-integers
A (13)
B (12)
C (14)
D (11)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x(x+1)=156). When (x=12), the larger integer is (13).
Step 2
Why this answer is correct
The correct answer is A. (13). If the smaller integer is (x), then (x(x+1)=156). When (x=12), the larger integer is (13).
Step 3
Exam Tip
यदि छोटा पूर्णांक (x) है, तो (x(x+1)=156)। (x=12) मिलने पर बड़ा पूर्णांक (13) है।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (380) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive integers is (380). What is the larger integer?
#quadratic equations
#consecutive integers
#application
A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
The numbers are (x) and (x+1). From (x(x+1)=380), (x=19), so the larger integer is (20).
Step 2
Why this answer is correct
The correct answer is C. (20). The numbers are (x) and (x+1). From (x(x+1)=380), (x=19), so the larger integer is (20).
Step 3
Exam Tip
संख्याएँ (x) और (x+1) होंगी। (x(x+1)=380) से (x=19), इसलिए बड़ा पूर्णांक (20) है।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (306) है। छोटा पूर्णांक क्या है?
The product of two consecutive positive integers is (306). What is the smaller integer?
#quadratic equations
#word problems
#consecutive integers
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x(x+1)=306), giving (x=17). Write consecutive integers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is B. (17). If the smaller integer is (x), then (x(x+1)=306), giving (x=17). Write consecutive integers as (x) and (x+1).
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x(x+1)=306), जिससे (x=17) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (210) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive integers is (210). What is the larger integer?
#quadratic equations
#consecutive integers
#application
A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
Let the numbers be (x) and (x+1), then (x(x+1)=210) gives (x=14). So the larger integer is (15).
Step 2
Why this answer is correct
The correct answer is C. (15). Let the numbers be (x) and (x+1), then (x(x+1)=210) gives (x=14). So the larger integer is (15).
Step 3
Exam Tip
संख्याएँ (x) और (x+1) मानें, तब (x(x+1)=210) से (x=14) है। इसलिए बड़ा पूर्णांक (15) है।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (182) है। छोटा पूर्णांक क्या है?
The product of two consecutive positive integers is (182). What is the smaller integer?
#quadratic equations
#word problems
#consecutive integers
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x(x+1)=182), which gives (x=13). Writing consecutive integers as (x) and (x+1) is the correct method.
Step 2
Why this answer is correct
The correct answer is B. (13). If the smaller integer is (x), then (x(x+1)=182), which gives (x=13). Writing consecutive integers as (x) and (x+1) is the correct method.
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x(x+1)=182), जिससे (x=13) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखना सही तरीका है।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (132) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive integers is (132). What is the larger integer?
#quadratic equations
#word problems
#consecutive integers
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let the numbers be (x) and (x+1), then (x(x+1)=132) gives (x=11). So the larger integer is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). Let the numbers be (x) and (x+1), then (x(x+1)=132) gives (x=11). So the larger integer is (12).
Step 3
Exam Tip
मान लें संख्याएँ (x) और (x+1) हैं, तब (x(x+1)=132) से (x=11) है। इसलिए बड़ा पूर्णांक (12) है।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (72) है। छोटा पूर्णांक क्या है?
The product of two consecutive positive integers is (72). What is the smaller integer?
#quadratic equations
#word problems
#consecutive integers
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
Let the smaller integer be (x), then (x(x+1)=72) gives (x=8). In exams, write consecutive numbers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is B. (8). Let the smaller integer be (x), then (x(x+1)=72) gives (x=8). In exams, write consecutive numbers as (x) and (x+1).
Step 3
Exam Tip
मान लें छोटा पूर्णांक (x) है, तब (x(x+1)=72) से (x=8) मिलता है। परीक्षा में लगातार संख्याओं को (x) और (x+1) लिखें।
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यदि (x-2 -(2a+7)x+(a+3)(a+4)=0) की जड़ें लगातार पूर्णांक रूप में हैं, तो वे कौन-सी हैं?
If the roots of (x-2 -(2a+7)x+(a+3)(a+4)=0) are in consecutive integer form, which are they?
#quadratic-roots
#consecutive-roots
#parametric
A (a+2) और (a+5) / (a+2) and (a+5)
B (a+3) और (a+4) / (a+3) and (a+4)
C (a) और (a+7) / (a) and (a+7)
D (2a+3) और (4) / (2a+3) and (4)
Explanation opens after your attempt
Correct Answer
B. (a+3) और (a+4) / (a+3) and (a+4)
Step 1
Concept
The sum of roots is (2a+7) and the product is ((a+3)(a+4)). These match (a+3) and (a+4).
Step 2
Why this answer is correct
The correct answer is B. (a+3) और (a+4) / (a+3) and (a+4). The sum of roots is (2a+7) and the product is ((a+3)(a+4)). These match (a+3) and (a+4).
Step 3
Exam Tip
जड़ों का योग (2a+7) और गुणनफल ((a+3)(a+4)) है। ये (a+3) और (a+4) से मिलते हैं।
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समीकरण \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(16x^2+5x-74=0\)
B \(16x^2-5x-74=0\)
C \(4x^2+5x-74=0\)
D \(16x^2+5x+74=0\)
Explanation opens after your attempt
Correct Answer
A. \(16x^2+5x-74=0\)
Step 1
Concept
Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).
Step 2
Why this answer is correct
The correct answer is A. \(16x^2+5x-74=0\). Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).
Step 3
Exam Tip
पूरे समीकरण को (20) से गुणा करने पर \(16x^2-12+5x-10=60\) मिलता है। इसलिए \(16x^2+5x-82=0\) नहीं बल्कि \(16x^2+5x-82=0\) मिलेगा।
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समीकरण \(\frac{3x^2+2}{4}-\frac{x-5}{3}=6\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of \(\frac{3x^2+2}{4}-\frac{x-5}{3}=6\)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(9x^2-4x-42=0\)
B \(9x^2+4x-42=0\)
C \(3x^2-4x-42=0\)
D \(9x^2-4x+42=0\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2-4x-42=0\)
Step 1
Concept
Multiplying the whole equation by (12) gives \(9x^2+6-4x+20=72\). Therefore the standard form is \(9x^2-4x-46=0\).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2-4x-42=0\). Multiplying the whole equation by (12) gives \(9x^2+6-4x+20=72\). Therefore the standard form is \(9x^2-4x-46=0\).
Step 3
Exam Tip
पूरे समीकरण को (12) से गुणा करने पर \(9x^2+6-4x+20=72\) मिलता है। इसलिए मानक रूप \(9x^2-4x-46=0\) नहीं बल्कि \(9x^2-4x-46=0\) होगा।
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समीकरण (\frac{(x+1)2 }{2}+\frac{(x-3)2 }{3}=10) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of (\frac{(x+1)2 }{2}+\frac{(x-3)2 }{3}=10)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(5x^2-6x-39=0\)
B \(5x^2+6x-39=0\)
C \(6x^2-5x-39=0\)
D \(5x^2-6x+39=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2-6x-39=0\)
Step 1
Concept
Multiplying the whole equation by (6) gives (3(x+1)2 +2(x-3)2 =60). Simplifying gives the correct form \(5x^2-6x-39=0\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2-6x-39=0\). Multiplying the whole equation by (6) gives (3(x+1)2 +2(x-3)2 =60). Simplifying gives the correct form \(5x^2-6x-39=0\).
Step 3
Exam Tip
पूरे समीकरण को (6) से गुणा करने पर (3(x+1)2 +2(x-3)2 =60) मिलता है। सरल करने पर \(5x^2-6x-39=0\) सही रूप है।
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समीकरण \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(4x^2+5x-59=0\)
B \(4x^2+5x+59=0\)
C \(2x^2+5x-59=0\)
D \(4x^2-5x-59=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+5x-59=0\)
Step 1
Concept
Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+5x-59=0\). Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).
Step 3
Exam Tip
पूरे समीकरण को (10) से गुणा करने पर \(4x^2-2+5x+15=70\) मिलता है। इसलिए \(4x^2+5x-57=0\) नहीं बल्कि \(4x^2+5x-57=0\) मिलेगा।
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समीकरण \(\frac{x^2+1}{3}-\frac{x-2}{2}=5\) को पूर्णांक गुणांकों वाले मानक रूप में लिखिए।
Write \(\frac{x^2+1}{3}-\frac{x-2}{2}=5\) in standard form with integer coefficients.
#quadratic-equations
#fractions
#standard-form
#hard
A \(2x^2-3x-22=0\)
B \(2x^2-3x+22=0\)
C \(3x^2-2x-22=0\)
D \(2x^2+3x-22=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-3x-22=0\)
Step 1
Concept
Multiplying the whole equation by (6) gives \(2x^2+2-3x+6=30\). Therefore the standard form is \(2x^2-3x-22=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-3x-22=0\). Multiplying the whole equation by (6) gives \(2x^2+2-3x+6=30\). Therefore the standard form is \(2x^2-3x-22=0\).
Step 3
Exam Tip
पूरे समीकरण को (6) से गुणा करने पर \(2x^2+2-3x+6=30\) मिलता है। इसलिए मानक रूप \(2x^2-3x-22=0\) है।
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समीकरण \(\frac{x^2-3}{2}+\frac{x-1}{3}=4\) को पूर्णांक गुणांकों वाले मानक रूप में लिखिए।
Write \(\frac{x^2-3}{2}+\frac{x-1}{3}=4\) in standard form with integer coefficients.
#quadratic-equations
#fractions
#standard-form
#hard
A \(3x^2+2x-29=0\)
B \(3x^2+2x-35=0\)
C \(x^2+2x-29=0\)
D \(3x^2-2x-29=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+2x-29=0\)
Step 1
Concept
Multiplying the whole equation by (6) gives \(3x^2-9+2x-2=24\). Thus the standard form is \(3x^2+2x-35=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+2x-29=0\). Multiplying the whole equation by (6) gives \(3x^2-9+2x-2=24\). Thus the standard form is \(3x^2+2x-35=0\).
Step 3
Exam Tip
पूरे समीकरण को (6) से गुणा करने पर \(3x^2-9+2x-2=24\) मिलता है। इसलिए \(3x^2+2x-35=0\) नहीं बल्कि सही रूप \(3x^2+2x-35=0\) होगा।
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समीकरण \(\frac{3}{4}x^2-\frac{1}{2}x+2=0\) का पूर्णांक गुणांकों वाला रूप कौन-सा है?
What is the form with integer coefficients for \(\frac{3}{4}x^2-\frac{1}{2}x+2=0\)?
#quadratic-equations
#fractional-coefficients
#medium
A \(3x^2-2x+8=0\)
B \(3x^2-2x+2=0\)
C \(4x^2-2x+8=0\)
D \(3x^2+2x+8=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-2x+8=0\)
Step 1
Concept
Multiply the whole equation by (4) to remove the denominators. This gives \(3x^2-2x+8=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-2x+8=0\). Multiply the whole equation by (4) to remove the denominators. This gives \(3x^2-2x+8=0\).
Step 3
Exam Tip
हर हटाने के लिए पूरे समीकरण को (4) से गुणा करें। इससे \(3x^2-2x+8=0\) मिलता है।
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दो क्रमागत धनात्मक पूर्णांकों के वर्गों का योग (145) है। यदि छोटा पूर्णांक (x) है, तो समीकरण कौन-सा है?
The sum of squares of two consecutive positive integers is (145). If the smaller integer is (x), which equation is correct?
#quadratic-equations
#consecutive-integers
#word-problem
#medium
A \(2x^2+2x-144=0\)
B \(2x^2+2x-145=0\)
C \(x^2+x-145=0\)
D \(2x^2-x-145=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+2x-144=0\)
Step 1
Concept
The integers are (x) and (x+1), so (x-2 +(x+1)2 =145). Simplifying gives \(2x^2+2x-144=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+2x-144=0\). The integers are (x) and (x+1), so (x-2 +(x+1)2 =145). Simplifying gives \(2x^2+2x-144=0\).
Step 3
Exam Tip
पूर्णांक (x) और (x+1) होंगे, इसलिए (x-2 +(x+1)2 =145)। सरल करने पर \(2x^2+2x-144=0\) मिलता है।
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समीकरण \(\frac{2}{5}x^2+\frac{1}{5}x-2=0\) का पूर्णांक गुणांकों वाला रूप कौन-सा है?
What is the form with integer coefficients for \(\frac{2}{5}x^2+\frac{1}{5}x-2=0\)?
#quadratic-equations
#fractional-coefficients
#medium
A \(2x^2+x-10=0\)
B \(2x^2+x-2=0\)
C \(5x^2+x-2=0\)
D \(2x^2+5x-10=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+x-10=0\)
Step 1
Concept
Multiply the whole equation by (5) to remove denominator (5). This gives \(2x^2+x-10=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+x-10=0\). Multiply the whole equation by (5) to remove denominator (5). This gives \(2x^2+x-10=0\).
Step 3
Exam Tip
हर (5) हटाने के लिए पूरे समीकरण को (5) से गुणा करें। इससे \(2x^2+x-10=0\) मिलता है।
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दो क्रमागत पूर्णांकों के वर्गों का योग (85) है। यदि छोटा पूर्णांक (x) है, तो समीकरण कौन-सा है?
The sum of squares of two consecutive integers is (85). If the smaller integer is (x), which equation is correct?
#quadratic-equations
#consecutive-integers
#word-problem
#medium
A \(2x^2+2x-84=0\)
B \(2x^2+2x-85=0\)
C \(x^2+x-85=0\)
D \(2x^2-x-85=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+2x-84=0\)
Step 1
Concept
The integers are (x) and (x+1), so (x-2 +(x+1)2 =85). Simplifying gives \(2x^2+2x-84=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+2x-84=0\). The integers are (x) and (x+1), so (x-2 +(x+1)2 =85). Simplifying gives \(2x^2+2x-84=0\).
Step 3
Exam Tip
पूर्णांक (x) और (x+1) होंगे, इसलिए (x-2 +(x+1)2 =85)। सरल करने पर \(2x^2+2x-84=0\) मिलता है।
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समीकरण \(\frac{1}{3}x^2-\frac{2}{3}x+1=0\) का पूर्णांक गुणांकों वाला रूप कौन-सा है?
What is the form with integer coefficients for \(\frac{1}{3}x^2-\frac{2}{3}x+1=0\)?
#quadratic-equations
#fractional-coefficients
#medium
A \(x^2-2x+3=0\)
B \(x^2+2x+3=0\)
C \(3x^2-2x+1=0\)
D \(x^2-2x+1=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2x+3=0\)
Step 1
Concept
Multiply the whole equation by (3) to remove the denominator (3). This gives \(x^2-2x+3=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2x+3=0\). Multiply the whole equation by (3) to remove the denominator (3). This gives \(x^2-2x+3=0\).
Step 3
Exam Tip
हर (3) हटाने के लिए पूरे समीकरण को (3) से गुणा करें। इससे \(x^2-2x+3=0\) मिलता है।
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दो लगातार धन पूर्णांकों का गुणनफल (30) है। यदि छोटा पूर्णांक (x) है तो समीकरण क्या होगा?
The product of two consecutive positive integers is (30). If the smaller integer is (x), what is the equation?
#quadratic equations
#word problem
#consecutive integers
A (x(x+1)=30)
B (x+x+1=30)
C (x(x-1)=30)
D (2x=30)
Explanation opens after your attempt
Correct Answer
A. (x(x+1)=30)
Step 1
Concept
The next consecutive integer is (x+1). Since the product is (30), the equation is (x(x+1)=30).
Step 2
Why this answer is correct
The correct answer is A. (x(x+1)=30). The next consecutive integer is (x+1). Since the product is (30), the equation is (x(x+1)=30).
Step 3
Exam Tip
लगातार अगला पूर्णांक (x+1) होगा। गुणनफल (30) है इसलिए (x(x+1)=30) बनेगा।
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यदि (m) धनात्मक पूर्णांक है और \(\sqrt{m}\) परिमेय है, तो (m) के बारे में कौन सा निष्कर्ष सही है?
If (m) is a positive integer and \(\sqrt{m}\) is rational, which conclusion about (m) is correct?
#perfect-square
#rational-square-root
#real-numbers
A (m) पूर्ण वर्ग है / (m) is a perfect square
B (m) अभाज्य है / (m) is prime
C (m) अपरिमेय है / (m) is irrational
D (m) ऋणात्मक है / (m) is negative
Explanation opens after your attempt
Correct Answer
A. (m) पूर्ण वर्ग है / (m) is a perfect square
Step 1
Concept
The rational square root of a positive integer is an integer only when it is a perfect square. In exams identifying perfect squares is important.
Step 2
Why this answer is correct
The correct answer is A. (m) पूर्ण वर्ग है / (m) is a perfect square. The rational square root of a positive integer is an integer only when it is a perfect square. In exams identifying perfect squares is important.
Step 3
Exam Tip
धनात्मक पूर्णांक का परिमेय वर्गमूल तभी पूर्णांक होता है जब वह पूर्ण वर्ग हो। परीक्षा में पूर्ण वर्ग पहचानना जरूरी है।
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यदि \(\sqrt{m}\) अपरिमेय है और (m) धनात्मक पूर्णांक है, तो (m) के बारे में सही निष्कर्ष कौन सा है?
If \(\sqrt{m}\) is irrational and (m) is a positive integer, which conclusion about (m) is correct?
#irrational-square-root
#perfect-square
#real-numbers
A (m) पूर्ण वर्ग नहीं है / (m) is not a perfect square
B (m) हमेशा अभाज्य है / (m) is always prime
C (m) सम संख्या है / (m) is even
D (m) विषम संख्या है / (m) is odd
Explanation opens after your attempt
Correct Answer
A. (m) पूर्ण वर्ग नहीं है / (m) is not a perfect square
Step 1
Concept
The square root of a perfect square is an integer, so for an irrational square root (m) is not a perfect square. In exams identifying perfect squares is important.
Step 2
Why this answer is correct
The correct answer is A. (m) पूर्ण वर्ग नहीं है / (m) is not a perfect square. The square root of a perfect square is an integer, so for an irrational square root (m) is not a perfect square. In exams identifying perfect squares is important.
Step 3
Exam Tip
पूर्ण वर्ग का वर्गमूल पूर्णांक होता है, इसलिए अपरिमेय वर्गमूल के लिए (m) पूर्ण वर्ग नहीं होगा। परीक्षा में पूर्ण वर्ग पहचानना जरूरी है।
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यदि \(\sqrt{m}\) परिमेय है और (m) धनात्मक पूर्णांक है, तो (m) के बारे में सही कथन क्या है?
If \(\sqrt{m}\) is rational and (m) is a positive integer, what is true about (m)?
#perfect square
#rational root
#real numbers
A (m) अभाज्य है / (m) is prime
B (m) पूर्ण वर्ग है / (m) is a perfect square
C (m) विषम है / (m) is odd
D (m) हमेशा (2) का गुणज है / (m) is always a multiple of (2)
Explanation opens after your attempt
Correct Answer
B. (m) पूर्ण वर्ग है / (m) is a perfect square
Step 1
Concept
For a positive integer (m), \(\sqrt{m}\) is rational only when (m) is a perfect square. Identifying perfect squares is important in exams.
Step 2
Why this answer is correct
The correct answer is B. (m) पूर्ण वर्ग है / (m) is a perfect square. For a positive integer (m), \(\sqrt{m}\) is rational only when (m) is a perfect square. Identifying perfect squares is important in exams.
Step 3
Exam Tip
धनात्मक पूर्णांक (m) के लिए \(\sqrt{m}\) परिमेय तभी होगा जब (m) पूर्ण वर्ग हो। परीक्षा में पूर्ण वर्ग पहचानना जरूरी है।
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यदि \(\sqrt{m}=a\) जहाँ (a) परिमेय है और (m) धनात्मक पूर्णांक है, तो (m) के लिए क्या आवश्यक है?
If \(\sqrt{m}=a\), where (a) is rational and (m) is a positive integer, what is necessary for (m)?
#perfect-square
#rational-root
#reasoning
A (m) पूर्ण वर्ग होना चाहिए / (m) must be a perfect square
B (m) अभाज्य होना चाहिए / (m) must be prime
C (m) सम होना चाहिए / (m) must be even
D (m) पूर्ण वर्ग नहीं होना चाहिए / (m) must not be a perfect square
Explanation opens after your attempt
Correct Answer
A. (m) पूर्ण वर्ग होना चाहिए / (m) must be a perfect square
Step 1
Concept
The square root of a positive integer is rational only when it is a perfect square. This is the key rule for roots.
Step 2
Why this answer is correct
The correct answer is A. (m) पूर्ण वर्ग होना चाहिए / (m) must be a perfect square. The square root of a positive integer is rational only when it is a perfect square. This is the key rule for roots.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब वह पूर्ण वर्ग हो। यह जड़ों की प्रकृति का मुख्य नियम है।
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यदि (n) धनात्मक पूर्णांक है और \(\sqrt{n}\) अपरिमेय है, तो \(\sqrt{4n}\) कब परिमेय होगी?
If (n) is a positive integer and \(\sqrt{n}\) is irrational, when will \(\sqrt{4n}\) be rational?
#irrational-root
#reasoning
#properties
A कभी नहीं / Never
B हमेशा / Always
C केवल जब (n) सम हो / Only when (n) is even
D केवल जब (n) अभाज्य हो / Only when (n) is prime
Explanation opens after your attempt
Correct Answer
A. कभी नहीं / Never
Step 1
Concept
\(\sqrt{4n}=2\sqrt{n}\). Multiplying an irrational number by a non zero rational keeps it irrational.
Step 2
Why this answer is correct
The correct answer is A. कभी नहीं / Never. \(\sqrt{4n}=2\sqrt{n}\). Multiplying an irrational number by a non zero rational keeps it irrational.
Step 3
Exam Tip
\(\sqrt{4n}=2\sqrt{n}\) है। गैर शून्य परिमेय से अपरिमेय को गुणा करने पर संख्या अपरिमेय रहती है।
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यदि \(\sqrt{k}\) अपरिमेय है और (k) धनात्मक पूर्णांक है तो कौन सा (k) हो सकता है?
If \(\sqrt{k}\) is irrational and (k) is a positive integer, which (k) can be correct?
#perfect-square
#irrational-root
#reasoning
A (k=123)
B (k=121)
C (k=144)
D (k=169)
Explanation opens after your attempt
Correct Answer
A. (k=123)
Step 1
Concept
(123) is not a perfect square so \(\sqrt{123}\) is irrational. Roots of perfect squares are rational.
Step 2
Why this answer is correct
The correct answer is A. (k=123). (123) is not a perfect square so \(\sqrt{123}\) is irrational. Roots of perfect squares are rational.
Step 3
Exam Tip
(123) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{123}\) अपरिमेय है। पूर्ण वर्गों की जड़ परिमेय होती है।
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यदि \(\sqrt{m}\) परिमेय है और (m) धनात्मक पूर्णांक है तो कौन सा (m) हो सकता है?
If \(\sqrt{m}\) is rational and (m) is a positive integer, which (m) can be correct?
#perfect-square
#rational-root
#reasoning
A (m=400)
B (m=401)
C (m=402)
D (m=403)
Explanation opens after your attempt
Correct Answer
A. (m=400)
Step 1
Concept
\(400=20^2\) is a perfect square so \(\sqrt{400}\) is rational. The other options are not perfect squares.
Step 2
Why this answer is correct
The correct answer is A. (m=400). \(400=20^2\) is a perfect square so \(\sqrt{400}\) is rational. The other options are not perfect squares.
Step 3
Exam Tip
\(400=20^2\) पूर्ण वर्ग है इसलिए \(\sqrt{400}\) परिमेय है। बाकी विकल्प पूर्ण वर्ग नहीं हैं।
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कौन सा कथन \(\sqrt{a}\) के लिए सही है जब (a) धनात्मक पूर्णांक है?
Which statement is correct for \(\sqrt{a}\) when (a) is a positive integer?
#perfect-square
#irrational-root
#exam-rule
A यदि (a) पूर्ण वर्ग नहीं है तो \(\sqrt{a}\) अपरिमेय है / If (a) is not a perfect square then \(\sqrt{a}\) is irrational
B यदि (a) सम है तो \(\sqrt{a}\) हमेशा परिमेय है / If (a) is even then \(\sqrt{a}\) is always rational
C यदि (a) विषम है तो \(\sqrt{a}\) हमेशा पूर्णांक है / If (a) is odd then \(\sqrt{a}\) is always an integer
D हर (a) के लिए \(\sqrt{a}\) पूर्ण संख्या है / For every (a), \(\sqrt{a}\) is a whole number
Explanation opens after your attempt
Correct Answer
A. यदि (a) पूर्ण वर्ग नहीं है तो \(\sqrt{a}\) अपरिमेय है / If (a) is not a perfect square then \(\sqrt{a}\) is irrational
Step 1
Concept
The square root of a positive integer is rational only when the number is a perfect square. So a non perfect square gives an irrational root.
Step 2
Why this answer is correct
The correct answer is A. यदि (a) पूर्ण वर्ग नहीं है तो \(\sqrt{a}\) अपरिमेय है / If (a) is not a perfect square then \(\sqrt{a}\) is irrational. The square root of a positive integer is rational only when the number is a perfect square. So a non perfect square gives an irrational root.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब संख्या पूर्ण वर्ग हो। इसलिए पूर्ण वर्ग न हो तो जड़ अपरिमेय होगी।
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यदि \(\sqrt{k}\) अपरिमेय है और (k) धनात्मक पूर्णांक है तो (k) के बारे में सही कथन क्या है?
If \(\sqrt{k}\) is irrational and (k) is a positive integer, what is correct about (k)?
#perfect-square
#irrational-root
#reasoning
A (k) पूर्ण वर्ग नहीं है / (k) is not a perfect square
B (k) हमेशा पूर्ण वर्ग है / (k) is always a perfect square
C (k=0) है / (k=0)
D (k) हमेशा ऋणात्मक है / (k) is always negative
Explanation opens after your attempt
Correct Answer
A. (k) पूर्ण वर्ग नहीं है / (k) is not a perfect square
Step 1
Concept
If a positive integer is not a perfect square its square root is irrational. So (k) is not a perfect square.
Step 2
Why this answer is correct
The correct answer is A. (k) पूर्ण वर्ग नहीं है / (k) is not a perfect square. If a positive integer is not a perfect square its square root is irrational. So (k) is not a perfect square.
Step 3
Exam Tip
धनात्मक पूर्णांक पूर्ण वर्ग न हो तो उसकी वर्गमूल अपरिमेय होती है। इसलिए (k) पूर्ण वर्ग नहीं होगा।
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यदि (m) धनात्मक पूर्णांक है और \(\sqrt{m}\) परिमेय है तो (m) क्या होना चाहिए?
If (m) is a positive integer and \(\sqrt{m}\) is rational, what must (m) be?
#perfect-square
#rational-root
#exam-rule
A पूर्ण वर्ग / Perfect square
B हमेशा अभाज्य / Always prime
C हमेशा सम / Always even
D पूर्ण वर्ग नहीं / Not a perfect square
Explanation opens after your attempt
Correct Answer
A. पूर्ण वर्ग / Perfect square
Step 1
Concept
The square root of a positive integer is rational only when it is a perfect square. Apply this rule directly.
Step 2
Why this answer is correct
The correct answer is A. पूर्ण वर्ग / Perfect square. The square root of a positive integer is rational only when it is a perfect square. Apply this rule directly.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब वह पूर्ण वर्ग हो। इस नियम को सीधे लागू करें।
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यदि \(2+\sqrt{m}\) अपरिमेय है और (m) धनात्मक पूर्णांक है तो कौन सा (m) हो सकता है?
If \(2+\sqrt{m}\) is irrational and (m) is a positive integer, which (m) can be correct?
#perfect-square
#irrational-expression
#reasoning
A (18)
B (16)
C (25)
D (36)
Explanation opens after your attempt
Step 1
Concept
(18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.
Step 2
Why this answer is correct
The correct answer is A. (18). (18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.
Step 3
Exam Tip
(18) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{18}\) अपरिमेय है। बाकी विकल्पों की जड़ परिमेय है।
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यदि \(\sqrt{n}\) परिमेय है और (n) धनात्मक पूर्णांक है तो (n) के बारे में सही कथन क्या है?
If \(\sqrt{n}\) is rational and (n) is a positive integer, what is correct about (n)?
#perfect-square
#rational-root
#exam-rule
A (n) पूर्ण वर्ग है / (n) is a perfect square
B (n) हमेशा अभाज्य है / (n) is always prime
C (n) हमेशा विषम है / (n) is always odd
D (n) पूर्ण वर्ग नहीं है / (n) is not a perfect square
Explanation opens after your attempt
Correct Answer
A. (n) पूर्ण वर्ग है / (n) is a perfect square
Step 1
Concept
The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.
Step 2
Why this answer is correct
The correct answer is A. (n) पूर्ण वर्ग है / (n) is a perfect square. The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब संख्या पूर्ण वर्ग हो। यह सीधा परीक्षा नियम है।
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यदि (n) एक धनात्मक पूर्णांक है और \(\sqrt{n}\) अपरिमेय है तो (n) के बारे में क्या कहा जा सकता है?
If (n) is a positive integer and \(\sqrt{n}\) is irrational then what can be said about (n)?
#perfect-square
#irrational-root
#exam-rule
A (n) पूर्ण वर्ग नहीं है / (n) is not a perfect square
B (n) हमेशा सम है / (n) is always even
C (n) हमेशा अभाज्य है / (n) is always prime
D (n=0) है / (n=0)
Explanation opens after your attempt
Correct Answer
A. (n) पूर्ण वर्ग नहीं है / (n) is not a perfect square
Step 1
Concept
The square root of a positive integer is irrational when it is not a perfect square. Remember this simple rule.
Step 2
Why this answer is correct
The correct answer is A. (n) पूर्ण वर्ग नहीं है / (n) is not a perfect square. The square root of a positive integer is irrational when it is not a perfect square. Remember this simple rule.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल अपरिमेय तब होती है जब वह पूर्ण वर्ग नहीं होता। यह सरल नियम याद रखें।
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किसी धनात्मक पूर्णांक (n) के लिए यदि \(\sqrt{n}\) परिमेय है तो (n) के बारे में क्या कहा जा सकता है?
For a positive integer (n), if \(\sqrt{n}\) is rational then what can be said about (n)?
#perfect-square
#rational-root
#exam-rule
A (n) पूर्ण वर्ग है / (n) is a perfect square
B (n) हमेशा अभाज्य है / (n) is always prime
C (n) शून्य है / (n) is zero
D (n) हमेशा विषम है / (n) is always odd
Explanation opens after your attempt
Correct Answer
A. (n) पूर्ण वर्ग है / (n) is a perfect square
Step 1
Concept
The square root of a positive integer is rational only when the number is a perfect square. This is a direct MCQ rule.
Step 2
Why this answer is correct
The correct answer is A. (n) पूर्ण वर्ग है / (n) is a perfect square. The square root of a positive integer is rational only when the number is a perfect square. This is a direct MCQ rule.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब संख्या पूर्ण वर्ग हो। यह MCQ में सीधा नियम है।
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यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^4\cdot 5\cdot 7^3\cdot 11}\) का दशमलव सांत हो तो (n) क्या होगा?
If (n) is the smallest positive integer for which \(\frac{n}{2^4\cdot 5\cdot 7^3\cdot 11}\) has a terminating decimal, what is (n)?
#minimum-factor
#terminating-condition
#prime-factorisation
#expert
A (3773)
B (343)
C (539)
D (7546)
Explanation opens after your attempt
Step 1
Concept
The factors \(7^3\) and (11) must be removed from the reduced denominator, so \(n=7^3\cdot 11=3773\). For the least value, do not cancel (2) and (5).
Step 2
Why this answer is correct
The correct answer is A. (3773). The factors \(7^3\) and (11) must be removed from the reduced denominator, so \(n=7^3\cdot 11=3773\). For the least value, do not cancel (2) and (5).
Step 3
Exam Tip
सरलतम हर से \(7^3\) और (11) हटने चाहिए इसलिए \(n=7^3\cdot 11=3773\) होगा। न्यूनतम मान में (2) और (5) को काटना जरूरी नहीं है।
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यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^3\cdot 3^2\cdot 5^4\cdot 17^2}\) का दशमलव सांत हो तो (n) क्या होगा?
If (n) is the smallest positive integer for which \(\frac{n}{2^3\cdot 3^2\cdot 5^4\cdot 17^2}\) has a terminating decimal, what is (n)?
#minimum-factor
#terminating-condition
#prime-factorisation
#real-numbers
A (153)
B (289)
C (2601)
D (13005)
Explanation opens after your attempt
Step 1
Concept
For termination, \(3^2\) and \(17^2\) must cancel completely, so (n=2601). For the least value, cancel only the factors other than (2) and (5).
Step 2
Why this answer is correct
The correct answer is C. (2601). For termination, \(3^2\) and \(17^2\) must cancel completely, so (n=2601). For the least value, cancel only the factors other than (2) and (5).
Step 3
Exam Tip
सांत दशमलव के लिए \(3^2\) और \(17^2\) पूरी तरह कटने चाहिए इसलिए (n=2601) होगा। न्यूनतम मान में केवल (2) और (5) के अलावा गुणनखंड काटें।
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यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^5\cdot 3^2\cdot 5^3\cdot 7^2}\) का दशमलव सांत हो तो (n) क्या होगा?
If (n) is the smallest positive integer for which \(\frac{n}{2^5\cdot 3^2\cdot 5^3\cdot 7^2}\) has a terminating decimal, what is (n)?
#minimum-factor
#terminating-condition
#prime-factorisation
#real-numbers
A (63)
B (147)
C (441)
D (2205)
Explanation opens after your attempt
Step 1
Concept
For termination, \(3^2\) and \(7^2\) must cancel completely, so (n=441). For the least value, cancel only the factors other than (2) and (5).
Step 2
Why this answer is correct
The correct answer is C. (441). For termination, \(3^2\) and \(7^2\) must cancel completely, so (n=441). For the least value, cancel only the factors other than (2) and (5).
Step 3
Exam Tip
सांत दशमलव के लिए \(3^2\) और \(7^2\) पूरी तरह कटने चाहिए इसलिए (n=441) होगा। न्यूनतम मान में केवल (2) और (5) के अलावा गुणनखंड काटें।
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यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^2\cdot 3^4\cdot 5\cdot 13}\) का दशमलव सांत हो, तो (n) क्या होगा?
If (n) is the smallest positive integer for which \(\frac{n}{2^2\cdot 3^4\cdot 5\cdot 13}\) has a terminating decimal, what is (n)?
#minimum-factor
#terminating-condition
#expert-mcq
#real-numbers
A (81)
B (156)
C (1053)
D (4212)
Explanation opens after your attempt
Step 1
Concept
For a terminating decimal, \(3^4\) and (13) must cancel completely, so \(n=3^4\cdot 13=1053\). For the least value, cancel only the unwanted prime factors.
Step 2
Why this answer is correct
The correct answer is C. (1053). For a terminating decimal, \(3^4\) and (13) must cancel completely, so \(n=3^4\cdot 13=1053\). For the least value, cancel only the unwanted prime factors.
Step 3
Exam Tip
सांत दशमलव के लिए \(3^4\) और (13) पूरी तरह कटने चाहिए, इसलिए \(n=3^4\cdot 13=1053\)। न्यूनतम मान में केवल अनचाहे अभाज्य गुणनखंड काटें।
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यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^4\cdot 3^3\cdot 5^2\cdot 11}\) का दशमलव प्रसार सांत हो, तो (n) क्या होगा?
If (n) is the smallest positive integer for which \(\frac{n}{2^4\cdot 3^3\cdot 5^2\cdot 11}\) has a terminating decimal expansion, what is (n)?
#minimum-factor
#terminating-condition
#real-numbers
#hard
A (33)
B (81)
C (297)
D (1188)
Explanation opens after your attempt
Step 1
Concept
For a terminating decimal, the reduced denominator must contain only (2) and (5).
Step 2
Why this answer is correct
The factors \(3^3\) and (11) must be cancelled, so the least (n) is \(3^3\cdot 11=297\).
Step 3
Exam Tip
For the smallest value, cancel only the unwanted prime factors. चरण 1: सांत दशमलव के लिए सरलतम हर में केवल (2) और (5) रहने चाहिए। चरण 2: हर में \(3^3\) और (11) हटाने होंगे, इसलिए \(n=3^3\cdot 11=297\) न्यूनतम है। चरण 3: सबसे छोटा मान पूछे तो केवल अनचाहे अभाज्य गुणनखंड काटिए।
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यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिसके लिए \(\frac{n}{2^3\cdot 3^2\cdot 5\cdot 7}\) का दशमलव प्रसार सांत हो जाता है, तो (n) का मान क्या होगा?
If (n) is the smallest positive integer for which the decimal expansion of \(\frac{n}{2^3\cdot 3^2\cdot 5\cdot 7}\) becomes terminating, what is the value of (n)?
#minimum-factor
#terminating-decimal
#prime-factorisation
#real-numbers
A (21)
B (45)
C (63)
D (315)
Explanation opens after your attempt
Step 1
Concept
For a terminating decimal, the reduced denominator must contain only (2) and (5).
Step 2
Why this answer is correct
The denominator has extra prime factors \(3^2\) and (7), so (n) must contain \(3^2\cdot 7=63\).
Step 3
Exam Tip
When the smallest value is asked, cancel only the unwanted prime factors. चरण 1: सांत दशमलव के लिए सरलतम हर में केवल (2) और (5) बचने चाहिए। चरण 2: हर में \(3^2\) और (7) अतिरिक्त अभाज्य गुणनखंड हैं, इसलिए (n) में \(3^2\cdot 7=63\) अवश्य होना चाहिए। चरण 3: सबसे छोटा मान पूछे जाने पर केवल अनचाहे अभाज्य गुणनखंडों को काटिए।
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\(\frac{1}{2^r5^s}\) को किसी पूर्णांक अंश के साथ \(10^8\) हर वाली भिन्न के रूप में लिखना हो, तो कौन-सी शर्त आवश्यक है?
To write \(\frac{1}{2^r5^s}\) as a fraction with denominator \(10^8\) and an integer numerator, which condition is necessary?
#powers-of-10
#terminating-decimal
#exponents
#advanced
A \(r\leq 8\) और \(s\leq 8\) / \(r\leq 8\) and \(s\leq 8\)
B (r+s=8)
C (r=s=8)
D (r>8) या (s>8) / (r>8) or (s>8)
Explanation opens after your attempt
Correct Answer
A. \(r\leq 8\) और \(s\leq 8\) / \(r\leq 8\) and \(s\leq 8\)
Step 1
Concept
\(10^8=2^8\cdot 5^8\).
Step 2
Why this answer is correct
The denominator \(2^r5^s\) must divide \(10^8\), so \(r\leq 8\) and \(s\leq 8\).
Step 3
Exam Tip
When converting to denominator \(10^k\), remember the divisor condition. चरण 1: \(10^8=2^8\cdot 5^8\) है। चरण 2: हर \(2^r5^s\) को \(10^8\) का भाजक होना चाहिए, इसलिए \(r\leq 8\) और \(s\leq 8\)। चरण 3: हर को \(10^k\) में बदलते समय भाजक की शर्त याद रखें।
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