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 151-160 of 600 questions.
If \(x=2+\sqrt{3}\), what type of number is (x-2)?
B. अपरिमेयIrrational
\(x-2=\sqrt{3}\) है जो अपरिमेय है। प्रश्न में पहले समान परिमेय पद हटाएं। / \(x-2=\sqrt{3}\), which is irrational. First cancel matching rational terms in such questions.
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Which is the simplified form of \(\sqrt{18}+\sqrt{8}\)?
C. \(5\sqrt{2}\)
\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\), इसलिए योग \(5\sqrt{2}\) है। पहले मूलों को सरल करें। / \(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the sum is \(5\sqrt{2}\). Simplify radicals first.
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What type of number is the value of (\(\sqrt{7}\)2+3)?
A. परिमेयRational
(\(\sqrt{7}\)2+3=10) है जो परिमेय है। अपरिमेय का वर्ग परिमेय हो सकता है। / (\(\sqrt{7}\)2+3=10), which is rational. The square of an irrational can be rational.
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What is obtained after simplifying \(\frac{1}{2+\sqrt{3}}\)?
D. \(2-\sqrt{3}\)
हर का परिमेयकरण करने पर \(\frac{1}{2+\sqrt{3}}=2-\sqrt{3}\) मिलता है। संयुग्मी से गुणा करना याद रखें। / Rationalising the denominator gives \(\frac{1}{2+\sqrt{3}}=2-\sqrt{3}\). Remember to multiply by the conjugate.
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If \(a=\sqrt{5}+1\) and \(b=\sqrt{5}-1\), what is (a+b)?
B. \(2\sqrt{5}\)
\(a+b=2\sqrt{5}\) है जो अपरिमेय है। समान मूल वाले पदों को जोड़ें। / \(a+b=2\sqrt{5}\), which is irrational. Add like radical terms.
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Which is the simplified form of \(\sqrt{50}-\sqrt{2}\)?
C. \(4\sqrt{2}\)
\(\sqrt{50}=5\sqrt{2}\), इसलिए अंतर \(4\sqrt{2}\) है। समान मूलों को घटाना आसान तरीका है। / \(\sqrt{50}=5\sqrt{2}\), so the difference is \(4\sqrt{2}\). Subtracting like radicals is the easy method.
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What is the simplified form of \(\sqrt{3}+\sqrt{12}+\sqrt{27}\)?
D. \(6\sqrt{3}\)
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\), इसलिए कुल \(6\sqrt{3}\) है। सभी पदों को पहले समान मूल में बदलें। / \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\), so the total is \(6\sqrt{3}\). First convert all terms into like radicals.
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What type of number does decimal \(1.02002000200002\ldots\) represent?
B. अपरिमेयIrrational
इसमें निश्चित दोहराने वाला खंड नहीं है इसलिए यह अपरिमेय है। अनावर्ती दशमलव को आवर्ती समझने से बचें। / It has no fixed repeating block, so it is irrational. Avoid treating a non-repeating decimal as repeating.
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What is the value of \(\frac{\sqrt{27}}{\sqrt{3}}\)?
A. (3)
\(\frac{\sqrt{27}}{\sqrt{3}}=\sqrt{9}=3\) है। भाग में अंदर की संख्याओं का अनुपात लें। / \(\frac{\sqrt{27}}{\sqrt{3}}=\sqrt{9}=3\). In division take the ratio of the numbers inside roots.
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Which is the simplified form of \(\sqrt{45}+\sqrt{20}\)?
D. \(5\sqrt{5}\)
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\), इसलिए योग \(5\sqrt{5}\) है। पहले पूर्ण वर्ग गुणनखंड निकालें। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\), so the sum is \(5\sqrt{5}\). First take out perfect-square factors.
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