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 201-210 of 600 questions.
If \(x=\sqrt{7}+3\), what type of number is (x-3)?
B. अपरिमेयIrrational
\(x-3=\sqrt{7}\) है जो अपरिमेय है। पहले परिमेय पदों को अलग करें। / \(x-3=\sqrt{7}\), which is irrational. First separate the rational terms.
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Which is the simplified form of \(\sqrt{32}+\sqrt{18}\)?
B. \(7\sqrt{2}\)
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\), इसलिए योग \(7\sqrt{2}\) है। पहले मूलों को समान रूप में बदलें। / \(\sqrt{32}=4\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\), so the sum is \(7\sqrt{2}\). First convert radicals into like form.
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What is the value of (\(\sqrt{11}\)2-4)?
A. (7)
(\(\sqrt{11}\)2=11) इसलिए मान (7) है। वर्ग करने पर वर्गमूल हट सकता है। / (\(\sqrt{11}\)2=11), so the value is (7). Squaring can remove the square root.
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What is obtained after simplifying \(\frac{1}{\sqrt{5}-2}\)?
C. \(\sqrt{5}+2\)
संयुग्मी से गुणा करने पर हर (5-4=1) बनता है। इसलिए उत्तर \(\sqrt{5}+2\) है। / Multiplying by the conjugate makes the denominator (5-4=1). So the answer is \(\sqrt{5}+2\).
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If \(a=2\sqrt{3}+1\) and \(b=2\sqrt{3}-1\), what is (a+b)?
B. \(4\sqrt{3}\)
स्थिर पद कट जाते हैं और \(2\sqrt{3}+2\sqrt{3}=4\sqrt{3}\) मिलता है। समान मूलों को जोड़ें। / The constant terms cancel and \(2\sqrt{3}+2\sqrt{3}=4\sqrt{3}\). Add like radicals.
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What is the value of (\(4+\sqrt{7}\)\(4-\sqrt{7}\))?
B. (9)
यह \(a^2-b^2\) है इसलिए मान (16-7=9) है। संयुग्मी गुणन से मूल हट जाता है। / This is \(a^2-b^2\), so the value is (16-7=9). Conjugate multiplication removes the radical.
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Which is the simplified form of \(\sqrt{75}-\sqrt{12}\)?
A. \(3\sqrt{3}\)
\(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\), इसलिए अंतर \(3\sqrt{3}\) है। पहले पूर्ण वर्ग गुणनखंड निकालें। / \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\), so the difference is \(3\sqrt{3}\). First take out perfect-square factors.
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What type of number is the decimal \(2.303003000300003\ldots\)?
B. अपरिमेयIrrational
इसमें निश्चित दोहराने वाला खंड नहीं है इसलिए यह अपरिमेय है। असांत अनावर्ती दशमलव अपरिमेय होता है। / It has no fixed repeating block, so it is irrational. A non-terminating non-repeating decimal is irrational.
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What is the value of \(\frac{\sqrt{75}}{\sqrt{3}}\)?
A. (5)
\(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{25}=5\) है। भाग में मूलों को एक साथ लिखकर सरल करें। / \(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{25}=5\). Combine radicals in division and simplify.
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Which is the simplified form of \(\sqrt{80}+\sqrt{125}\)?
A. \(9\sqrt{5}\)
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{125}=5\sqrt{5}\), इसलिए योग \(9\sqrt{5}\) है। समान मूलों को जोड़ना चाहिए। / \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{125}=5\sqrt{5}\), so the sum is \(9\sqrt{5}\). Like radicals should be added.
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