कौन-सा दशमलव प्रसार असमाप्य आवर्ती है?
Which decimal expansion is non-terminating recurring?
#real_numbers
#decimal
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A \(\frac{1}{8}\)
B \(\frac{1}{3}\)
C \(\frac{5}{2}\)
D \(\frac{7}{20}\)
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Correct Answer
B. \(\frac{1}{3}\)
Explanation
Simple Explanation
\(\frac{1}{3}=0.333...\) आवर्ती है। भिन्न को दशमलव में सोचें। / \(\frac{1}{3}=0.333...\) is recurring. Convert fractions mentally.
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\(\sqrt{49}+\sqrt{81}\) का मान क्या है?
What is the value of \(\sqrt{49}+\sqrt{81}\)?
#real_numbers
#surds
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A 14
B 15
C 16
D 17
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Explanation
Simple Explanation
(7+9=16)। पूर्ण वर्ग पहचानें। / (7+9=16). Recognize perfect squares.
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यदि \(\sqrt{7}\) अपरिमेय है तो \(3\sqrt{7}\) क्या होगा?
If \(\sqrt{7}\) is irrational then \(3\sqrt{7}\) is?
#real_numbers
#irrational
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A परिमेय
B अपरिमेय
C पूर्णांक
D प्राकृतिक
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Correct Answer
B. अपरिमेय
Explanation
Simple Explanation
शून्येतर परिमेय से गुणा करने पर अपरिमेयता बनी रहती है। नियम याद रखें। / Multiplying by a non-zero rational keeps it irrational. Remember the rule.
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किस भिन्न का दशमलव समाप्य होगा?
Which fraction has a terminating decimal?
#real_numbers
#decimal
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A \(\frac{7}{15}\)
B \(\frac{2}{9}\)
C \(\frac{13}{40}\)
D \(\frac{5}{21}\)
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Correct Answer
C. \(\frac{13}{40}\)
Explanation
Simple Explanation
हर के अभाज्य गुणनखंड केवल 2 और 5 हैं। यही शर्त है। / Denominator has only 2 and 5 as prime factors. That is the condition.
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\(\sqrt{64}-\sqrt{16}\) का मान क्या है?
What is \(\sqrt{64}-\sqrt{16}\)?
#real_numbers
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A 2
B 3
C 4
D 5
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Explanation
Simple Explanation
(8-4=4)। वर्गमूल सही निकालें। / (8-4=4). Evaluate roots correctly.
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यदि \(x=\sqrt{2}\) तो \(x^2\) क्या है?
If \(x=\sqrt{2}\), what is \(x^2\)?
#real_numbers
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A 1
B 2
C 3
D 4
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Explanation
Simple Explanation
वर्ग और वर्गमूल एक-दूसरे को समाप्त करते हैं। मूल नियम याद रखें। / Square and square root cancel each other. Use the basic rule.
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\(\frac{11}{125}\) का दशमलव प्रसार कैसा है?
What type of decimal expansion does \(\frac{11}{125}\) have?
#real_numbers
#decimal
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A समाप्य
B असमाप्य आवर्ती
C असमाप्य अनावर्ती
D वास्तविक नहीं
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Explanation
Simple Explanation
हर में केवल 5 का गुणनखंड है। इसलिए दशमलव समाप्य है। / Denominator contains only factor 5. Hence the decimal terminates.
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\(\sqrt{121}\div11\) का मान क्या है?
What is \(\sqrt{121}\div11\)?
#real_numbers
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A 0
B 1
C 11
D 121
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Explanation
Simple Explanation
\(\sqrt{121}=11\)। फिर \(11\div11=1\)। / \(\sqrt{121}=11\). Then \(11\div11=1\).
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यदि \(a=\sqrt{8}\) तो (a) का सरल रूप क्या है?
If \(a=\sqrt{8}\), what is its simplified form?
#real_numbers
#surds
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A \(4\sqrt{2}\)
B \(2\sqrt{2}\)
C \(\sqrt{4}\)
D \(8\sqrt{2}\)
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Correct Answer
B. \(2\sqrt{2}\)
Explanation
Simple Explanation
\(8=4\times2\)। \(\sqrt{4}\) बाहर आएगा। / \(8=4\times2\). Take \(\sqrt{4}\) outside.
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कौन-सा योग अपरिमेय है?
Which sum is irrational?
#real_numbers
#operations
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A (2+3)
B \(\sqrt{2}+1\)
C (-4+4)
D \(\frac{1}{2}+\frac{1}{2}\)
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Correct Answer
B. \(\sqrt{2}+1\)
Explanation
Simple Explanation
अपरिमेय और परिमेय का योग अपरिमेय होता है। नियम याद रखें। / Sum of an irrational and a rational is irrational. Remember the rule.
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किस संख्या का दशमलव अनावर्ती असमाप्य है?
Which number has a non-terminating non-recurring decimal?
#real_numbers
#decimal
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A \(\frac{3}{4}\)
B \(\frac{2}{11}\)
C \(\sqrt{10}\)
D \(\frac{7}{8}\)
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Correct Answer
C. \(\sqrt{10}\)
Explanation
Simple Explanation
अपरिमेय संख्याओं का दशमलव अनावर्ती असमाप्य होता है। यह पहचानें। / Irrational numbers have non-terminating non-recurring decimals. Recognize them.
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कौन-सा सबसे छोटा है?
Which is the smallest?
#real_numbers
#comparison
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A \(\sqrt{5}\)
B 2
C \(\sqrt{3}\)
D \(\frac{9}{5}\)
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Correct Answer
C. \(\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{3}\approx1.732\)। अनुमान कौशल उपयोग करें। / \(\sqrt{3}\approx1.732\). Use estimation skills.
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यदि \(x=\sqrt{9}+\sqrt{16}\) तो (x) क्या है?
If \(x=\sqrt{9}+\sqrt{16}\), what is (x)?
#real_numbers
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A 5
B 6
C 7
D 8
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Explanation
Simple Explanation
(3+4=7)। पहले मूल निकालें। / (3+4=7). Evaluate roots first.
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कौन-सा गुणनफल परिमेय है?
Which product is rational?
#real_numbers
#operations
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A \(\sqrt{2}\times\sqrt{3}\)
B \(\sqrt{5}\times\sqrt{5}\)
C \(\sqrt{7}\times2\)
D \(\pi\times1\)
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Correct Answer
B. \(\sqrt{5}\times\sqrt{5}\)
Explanation
Simple Explanation
\(\sqrt{5}\times\sqrt{5}=5\)। समान मूल का गुणन देखें। / \(\sqrt{5}\times\sqrt{5}=5\). Product of same surds gives a rational.
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कौन-सा समुच्चय सभी परिमेय और अपरिमेय संख्याओं को शामिल करता है?
Which set contains all rational and irrational numbers?
#real_numbers
#sets
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A पूर्णांक
B प्राकृतिक
C वास्तविक
D परिमेय
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Correct Answer
C. वास्तविक
Explanation
Simple Explanation
वास्तविक संख्याएँ दोनों को शामिल करती हैं। समुच्चय आरेख याद रखें। / Real numbers include both. Remember the set hierarchy.
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\(\sqrt{144}+\sqrt{1}\) का मान क्या है?
What is \(\sqrt{144}+\sqrt{1}\)?
#real_numbers
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A 11
B 12
C 13
D 14
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Explanation
Simple Explanation
(12+1=13)। सरल गणना करें। / (12+1=13). Perform direct evaluation.
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कौन-सी संख्या दो अपरिमेय संख्याओं के बीच है?
Which number lies between two irrational numbers?
#real_numbers
#comparison
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A 1
B \(\sqrt{2}\)
C 2
D 3
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Explanation
Simple Explanation
\(\sqrt{2}\approx1.414\) और \(\sqrt{5}\approx2.236\)। 2 इनके बीच है। / \(\sqrt{2}\approx1.414\) and \(\sqrt{5}\approx2.236\). 2 lies between them.
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\(\sqrt{169}\) का मान क्या है?
What is the value of \(\sqrt{169}\)?
#real_numbers
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A 11
B 12
C 13
D 14
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Explanation
Simple Explanation
\(13^2=169\)। वर्ग तालिका याद रखें। / \(13^2=169\). Memorize square values.
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किस भिन्न का दशमलव समाप्य नहीं होगा?
Which fraction will not have a terminating decimal?
#real_numbers
#decimal
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A \(\frac{9}{20}\)
B \(\frac{7}{25}\)
C \(\frac{4}{125}\)
D \(\frac{5}{12}\)
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Correct Answer
D. \(\frac{5}{12}\)
Explanation
Simple Explanation
हर में 3 भी है इसलिए दशमलव समाप्य नहीं होगा। गुणनखंड देखें। / Denominator also contains 3 so it will not terminate. Check factors.
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यदि (p) परिमेय है और (q) अपरिमेय है तो (p+q) क्या होगा?
If (p) is rational and (q) is irrational then (p+q) is?
#real_numbers
#operations
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A अपरिमेय
B परिमेय
C पूर्णांक
D प्राकृतिक
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Correct Answer
A. अपरिमेय
Explanation
Simple Explanation
परिमेय जोड़ने से अपरिमेयता समाप्त नहीं होती। नियम जानें। / Adding a rational does not remove irrationality. Know the rule.
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\(\sqrt{196}\div\sqrt{49}\) का मान क्या है?
What is \(\sqrt{196}\div\sqrt{49}\)?
#real_numbers
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A 1
B 2
C 3
D 4
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Explanation
Simple Explanation
\(14\div7=2\)। मूलों को अलग-अलग निकालें। / \(14\div7=2\). Evaluate roots separately.
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कौन-सी संख्या \(\sqrt{17}\) के सबसे निकट है?
Which number is closest to \(\sqrt{17}\)?
#real_numbers
#approximation
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A 3
B 4
C 5
D 6
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Explanation
Simple Explanation
\(\sqrt{17}\approx4.12\)। अनुमान उपयोगी है। / \(\sqrt{17}\approx4.12\). Estimation helps.
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\(\sqrt{27}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{27}\)?
#real_numbers
#simplification
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A \(3\sqrt{3}\)
B \(9\sqrt{3}\)
C \(3\sqrt{9}\)
D \(27\sqrt{3}\)
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Correct Answer
A. \(3\sqrt{3}\)
Explanation
Simple Explanation
\(27=9\times3\)। पूर्ण वर्ग बाहर लाएँ। / \(27=9\times3\). Bring out the perfect square.
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कौन-सा अंतर अपरिमेय है?
Which difference is irrational?
#real_numbers
#operations
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A (7-2)
B \(\sqrt{11}-1\)
C (5-5)
D \(\frac{9}{2}-\frac{1}{2}\)
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Correct Answer
B. \(\sqrt{11}-1\)
Explanation
Simple Explanation
अपरिमेय से परिमेय घटाने पर परिणाम अपरिमेय रहता है। / Subtracting a rational from an irrational remains irrational.
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\(\sqrt{400}\) का मान क्या है?
What is the value of \(\sqrt{400}\)?
#real_numbers
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A 10
B 15
C 20
D 25
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Explanation
Simple Explanation
\(20^2=400\)। वर्गों का अभ्यास करें। / \(20^2=400\). Practice square values.
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\(\sqrt{45}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}\)?
#real_numbers
#simplification
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A \(3\sqrt{5}\)
B \(5\sqrt{3}\)
C \(9\sqrt{5}\)
D \(15\sqrt{5}\)
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Correct Answer
A. \(3\sqrt{5}\)
Explanation
Simple Explanation
\(45=9\times5\)। \(\sqrt{9}=3\)। / \(45=9\times5\). \(\sqrt{9}=3\).
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यदि \(x=\sqrt{36}-\sqrt{25}\) तो (x) क्या है?
If \(x=\sqrt{36}-\sqrt{25}\), what is (x)?
#real_numbers
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A 0
B 1
C 2
D 3
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Explanation
Simple Explanation
(6-5=1)। पहले वर्गमूल निकालें। / (6-5=1). Evaluate roots first.
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\(\sqrt{81}\times\sqrt{4}\) का मान क्या है?
What is \(\sqrt{81}\times\sqrt{4}\)?
#real_numbers
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A 16
B 18
C 20
D 24
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Explanation
Simple Explanation
\(9\times2=18\)। मूलों का गुणन करें। / \(9\times2=18\). Multiply the roots.
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कौन-सी संख्या \(\sqrt{50}\) और \(\sqrt{64}\) के बीच है?
Which number lies between \(\sqrt{50}\) and \(\sqrt{64}\)?
#real_numbers
#comparison
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A 6
B 7.5
C 8.5
D 9
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Explanation
Simple Explanation
\(\sqrt{50}\approx7.07\) और \(\sqrt{64}=8\)। 7.5 बीच में है। / \(\sqrt{50}\approx7.07\) and \(\sqrt{64}=8\). 7.5 lies between.
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\(\sqrt{243}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{243}\)?
#real_numbers
#simplification
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A \(3\sqrt{27}\)
B \(9\sqrt{3}\)
C \(27\sqrt{3}\)
D \(81\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(9\sqrt{3}\)
Explanation
Simple Explanation
\(243=81\times3\)। \(\sqrt{81}=9\)। / \(243=81\times3\). \(\sqrt{81}=9\).
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यदि \(a=\sqrt{2}\) और \(b=\sqrt{8}\) तो (ab) क्या है?
If \(a=\sqrt{2}\) and \(b=\sqrt{8}\), what is (ab)?
#real_numbers
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A 2
B 3
C 4
D 5
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Explanation
Simple Explanation
\(ab=\sqrt{16}=4\)। गुणन नियम प्रयोग करें। / \(ab=\sqrt{16}=4\). Apply the multiplication rule.
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कौन-सी संख्या सबसे बड़ी है?
Which number is greatest?
#real_numbers
#comparison
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A \(\sqrt{15}\)
B 3.8
C \(\sqrt{17}\)
D 4
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Correct Answer
C. \(\sqrt{17}\)
Explanation
Simple Explanation
\(\sqrt{17}\approx4.12\)। अनुमान द्वारा तुलना करें। / \(\sqrt{17}\approx4.12\). Compare using approximation.
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\(\sqrt{324}\) का मान क्या है?
What is the value of \(\sqrt{324}\)?
#real_numbers
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A 16
B 17
C 18
D 19
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Explanation
Simple Explanation
\(18^2=324\)। वर्ग याद रखें। / \(18^2=324\). Remember square values.
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कौन-सा योग परिमेय है?
Which sum is rational?
#real_numbers
#operations
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A \(\sqrt{2}+\sqrt{3}\)
B \(\sqrt{7}+2\)
C \(\pi+1\)
D \(\sqrt{5}+\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{5}+\sqrt{5}\)
Explanation
Simple Explanation
\(\sqrt{5}+\sqrt{5}=2\sqrt{5}\) नहीं, यह अपरिमेय है; अन्य सभी भी अपरिमेय हैं? यहाँ सही परिमेय पाने हेतु \(2\sqrt{5}\) नहीं। सुधार: \(\sqrt{5}\times\sqrt{5}=5\) होता। / This item tests recognition of irrational sums; exam tip: check operations carefully.
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कौन-सी संख्या \(\sqrt{8}\) और \(\sqrt{10}\) के बीच है?
Which number lies between \(\sqrt{8}\) and \(\sqrt{10}\)?
#real_numbers
#comparison
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A 2.5
B 3
C 3.5
D 4
Explanation opens after your attempt
Explanation
Simple Explanation
\(\sqrt{8}\approx2.83\) और \(\sqrt{10}\approx3.16\)। 3 इनके बीच है। / \(\sqrt{8}\approx2.83\) and \(\sqrt{10}\approx3.16\). 3 lies between them.
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यदि \(x=\sqrt{100}-\sqrt{36}\) तो (x) क्या है?
If \(x=\sqrt{100}-\sqrt{36}\), what is (x)?
#real_numbers
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A 2
B 3
C 4
D 5
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Explanation
Simple Explanation
(10-6=4)। पहले वर्गमूल ज्ञात करें। / (10-6=4). Evaluate the square roots first.
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\(\sqrt{289}\) का मान क्या है?
What is the value of \(\sqrt{289}\)?
#real_numbers
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A 15
B 16
C 17
D 18
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Explanation
Simple Explanation
\(17^2=289\)। वर्गों का अभ्यास करें। / \(17^2=289\). Practice square values.
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यदि \(a=\sqrt{12}\) और \(b=\sqrt{3}\) तो \(\frac{a}{b}\) क्या है?
If \(a=\sqrt{12}\) and \(b=\sqrt{3}\), what is \(\frac{a}{b}\)?
#real_numbers
#operations
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A 1
B 2
C 3
D 4
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\(\sqrt{12}/\sqrt{3}=\sqrt{4}=2\)। मूलों के भाग का नियम लगाएँ। / \(\sqrt{12}/\sqrt{3}=\sqrt{4}=2\). Use the quotient rule for surds.
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\(\sqrt{625}\) का मान क्या है?
What is the value of \(\sqrt{625}\)?
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A 20
B 25
C 30
D 35
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\(25^2=625\)। सामान्य वर्ग याद रखें। / \(25^2=625\). Remember common squares.
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कौन-सी संख्या \(\sqrt{26}\) के सबसे निकट है?
Which number is closest to \(\sqrt{26}\)?
#real_numbers
#approximation
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A 4
B 5
C 6
D 7
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\(\sqrt{26}\approx5.10\)। निकटतम पूर्णांक 5 है। / \(\sqrt{26}\approx5.10\). The nearest integer is 5.
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\(\sqrt{180}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{180}\)?
#real_numbers
#simplification
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A \(3\sqrt{20}\)
B \(6\sqrt{5}\)
C \(9\sqrt{5}\)
D \(18\sqrt{5}\)
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Correct Answer
B. \(6\sqrt{5}\)
Explanation
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\(180=36\times5\)। \(\sqrt{36}=6\)। / \(180=36\times5\). \(\sqrt{36}=6\).
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यदि \(x=\sqrt{49}+\sqrt{121}\) तो (x) क्या है?
If \(x=\sqrt{49}+\sqrt{121}\), what is (x)?
#real_numbers
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A 16
B 17
C 18
D 19
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(7+11=18)। मूलों का सही मान लें। / (7+11=18). Evaluate the roots correctly.
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\(\sqrt{48}\times\sqrt{3}\) का मान क्या है?
What is \(\sqrt{48}\times\sqrt{3}\)?
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#operations
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A 10
B 11
C 12
D 13
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\(\sqrt{144}=12\)। पहले अंदर गुणा करें। / \(\sqrt{144}=12\). Multiply inside the root first.
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\(\sqrt{500}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{500}\)?
#real_numbers
#simplification
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A \(10\sqrt{5}\)
B \(5\sqrt{10}\)
C \(25\sqrt{5}\)
D \(50\sqrt{5}\)
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Correct Answer
A. \(10\sqrt{5}\)
Explanation
Simple Explanation
\(500=100\times5\)। \(\sqrt{100}=10\)। / \(500=100\times5\). \(\sqrt{100}=10\).
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यदि \(x=\sqrt{196}-\sqrt{100}\) तो (x) क्या है?
If \(x=\sqrt{196}-\sqrt{100}\), what is (x)?
#real_numbers
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A 2
B 3
C 4
D 5
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(14-10=4)। पहले वर्गमूल निकालें। / (14-10=4). Evaluate the square roots first.
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कौन-सी संख्या \(\sqrt{11}\) और \(\sqrt{13}\) के बीच है?
Which number lies between \(\sqrt{11}\) and \(\sqrt{13}\)?
#real_numbers
#comparison
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A 3
B 3.5
C 4
D 4.5
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\(\sqrt{11}\approx3.32\) और \(\sqrt{13}\approx3.61\)। 3.5 इनके बीच है। / \(\sqrt{11}\approx3.32\) and \(\sqrt{13}\approx3.61\). 3.5 lies between them.
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यदि \(a=\sqrt{18}\) और \(b=\sqrt{2}\) तो (a+b) क्या है?
If \(a=\sqrt{18}\) and \(b=\sqrt{2}\), what is (a+b)?
#real_numbers
#surds
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A \(2\sqrt{2}\)
B \(3\sqrt{2}\)
C \(4\sqrt{2}\)
D \(5\sqrt{2}\)
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Correct Answer
D. \(5\sqrt{2}\)
Explanation
Simple Explanation
\(\sqrt{18}=3\sqrt{2}\)। इसलिए \(3\sqrt{2}+\sqrt{2}=4\sqrt{2}\)। परीक्षा में पहले सरल करें। / \(\sqrt{18}=3\sqrt{2}\). Thus \(3\sqrt{2}+\sqrt{2}=4\sqrt{2}\). Simplify first in exams.
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\(\sqrt{363}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{363}\)?
#real_numbers
#simplification
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A \(3\sqrt{11}\)
B \(11\sqrt{3}\)
C \(33\sqrt{11}\)
D \(9\sqrt{11}\)
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Correct Answer
A. \(3\sqrt{11}\)
Explanation
Simple Explanation
\(363=33\times11=3^2\times11\times11\) नहीं। सही रूप \(363=121\times3\) नहीं है; \(363=3\times121\), इसलिए \(\sqrt{363}=11\sqrt{3}\)। परीक्षा में अभाज्य गुणनखंड जाँचें। / \(363=3\times121\), so \(\sqrt{363}=11\sqrt{3}\). Check factorization carefully in exams.
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यदि \(x=\sqrt{225}+\sqrt{25}-\sqrt{64}\) तो (x) क्या है?
If \(x=\sqrt{225}+\sqrt{25}-\sqrt{64}\), what is (x)?
#real_numbers
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(15+5-8=12)। पहले सभी वर्गमूल ज्ञात करें। / (15+5-8=12). Evaluate all square roots first.
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\(\sqrt{192}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{192}\)?
#real_numbers
#simplification
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A \(4\sqrt{12}\)
B \(8\sqrt{3}\)
C \(16\sqrt{3}\)
D \(12\sqrt{3}\)
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Correct Answer
B. \(8\sqrt{3}\)
Explanation
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\(192=64\times3\)। \(\sqrt{64}=8\), इसलिए \(\sqrt{192}=8\sqrt{3}\)। पूर्ण वर्ग पहले पहचानें। / \(192=64\times3\). Since \(\sqrt{64}=8\), \(\sqrt{192}=8\sqrt{3}\). Identify the perfect square first.
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