Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 161-170 of 600 questions.
Which number lies between \(\sqrt{2}\) and \(\sqrt{8}\)?
C. \(\sqrt{5}\)
क्योंकि (2<5<8), इसलिए \(\sqrt{5}\) इनके बीच है। वर्गमूल की तुलना अंदर की संख्याओं से करें। / Since (2<5<8), \(\sqrt{5}\) lies between them. Compare square roots using the numbers inside.
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If \(x=\sqrt{11}\), what is the value of \(x^2-1\)?
B. (10)
\(x^2=11\) इसलिए \(x^2-1=10\) है। पहले दिए गए मूल का वर्ग निकालें। / \(x^2=11\), so \(x^2-1=10\). First square the given radical.
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Which option is an irrational number?
A. \(0.101001000100001\ldots\)
पहला दशमलव असांत और अनावर्ती है इसलिए अपरिमेय है। आवर्ती दशमलव परिमेय होते हैं। / The first decimal is non-terminating and non-repeating, so it is irrational. Repeating decimals are rational.
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What is the rationalised form of \(\frac{2}{\sqrt{5}}\)?
A. \(\frac{2\sqrt{5}}{5}\)
हर को परिमेय बनाने के लिए \(\sqrt{5}\) से गुणा करें। परिणाम \(\frac{2\sqrt{5}}{5}\) है। / Multiply by \(\sqrt{5}\) to make the denominator rational. The result is \(\frac{2\sqrt{5}}{5}\).
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Which is the expansion of (\(\sqrt{10}+\sqrt{2}\)2)?
B. \(12+4\sqrt{5}\)
विस्तार \(10+2+2\sqrt{20}=12+4\sqrt{5}\) है। मध्य पद को सरल करना न भूलें। / The expansion is \(10+2+2\sqrt{20}=12+4\sqrt{5}\). Do not forget to simplify the middle term.
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Which option has a rational value?
C. (\(\sqrt{13}\)2)
(\(\sqrt{13}\)2=13) है जो परिमेय है। वर्ग करने से मूल हट सकता है। / (\(\sqrt{13}\)2=13), which is rational. Squaring can remove the radical.
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What is the irrational part of \(4+\sqrt{6}\)?
D. \(\sqrt{6}\)
(4) परिमेय है और \(\sqrt{6}\) अपरिमेय है। मिश्रित रूप में मूल वाला पद अपरिमेय भाग होता है। / (4) is rational and \(\sqrt{6}\) is irrational. In a mixed form the radical term is the irrational part.
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What is the simplified form of \(\sqrt{28}+\sqrt{63}-\sqrt{7}\)?
C. \(4\sqrt{7}\)
\(\sqrt{28}=2\sqrt{7}\) और \(\sqrt{63}=3\sqrt{7}\), इसलिए \(2\sqrt{7}+3\sqrt{7}-\sqrt{7}=4\sqrt{7}\) है। समान मूलों को जोड़ें और घटाएं। / \(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{63}=3\sqrt{7}\), so \(2\sqrt{7}+3\sqrt{7}-\sqrt{7}=4\sqrt{7}\). Add and subtract like radicals.
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If \(\sqrt{m}=6\), what is the value of (m)?
A. (36)
दोनों पक्षों का वर्ग करने पर (m=36) मिलता है। पूर्ण वर्ग पहचानना आवश्यक है। / Squaring both sides gives (m=36). Identifying perfect squares is essential.
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If (n) is not a perfect square and (n>0), what type of number will \(\sqrt{n}\) generally be?
D. अपरिमेयIrrational
धनात्मक पूर्ण संख्या का वर्गमूल अपरिमेय होता है जब वह पूर्ण वर्ग नहीं होती। यही वर्गमूल पहचान का मुख्य नियम है। / The square root of a positive integer is irrational when it is not a perfect square. This is the main rule for identifying square roots.
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