Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 231-240 of 600 questions.
If \(q=5-\sqrt{2}\), what type of number is (q)?
C. अपरिमेयIrrational
परिमेय (5) में से अपरिमेय \(\sqrt{2}\) घटाने पर अपरिमेय संख्या मिलती है। अपरिमेय भाग बचा रहता है। / Subtracting irrational \(\sqrt{2}\) from rational (5) gives an irrational number. The irrational part remains.
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To construct \(\sqrt{5}\) on the number line, which right triangle hypotenuse can be used?
B. भुजाएँ (1) और (2)Legs (1) and (2)
समकोण त्रिभुज में कर्ण \(\sqrt{1^2+2^2}=\sqrt{5}\) होगा। निर्माण में पाइथागोरस प्रमेय लगती है। / In a right triangle, the hypotenuse is \(\sqrt{1^2+2^2}=\sqrt{5}\). Pythagoras theorem is used in construction.
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What is the value of \(\sqrt{54}\div\sqrt{6}\)?
B. (3)
\(\sqrt{54}\div\sqrt{6}=\sqrt{9}=3\) है। मूलों के भाग में अंदर का भागफल लें। / \(\sqrt{54}\div\sqrt{6}=\sqrt{9}=3\). In division of roots take the quotient inside.
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If the area of a square is (50) square units, what will be the simplified form of its side?
C. \(5\sqrt{2}\)
भुजा \(\sqrt{50}=5\sqrt{2}\) होगी। वर्ग में भुजा क्षेत्रफल के वर्गमूल के बराबर होती है। / The side will be \(\sqrt{50}=5\sqrt{2}\). In a square, side equals the square root of area.
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What is the rationalised form of \(\frac{1}{4-\sqrt{7}}\)?
A. \(\frac{4+\sqrt{7}}{9}\)
संयुग्मी से गुणा करने पर हर (16-7=9) बनता है। इसलिए उत्तर \(\frac{4+\sqrt{7}}{9}\) है। / Multiplying by the conjugate makes the denominator (16-7=9). So the answer is \(\frac{4+\sqrt{7}}{9}\).
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Which statement is correct about \(\sqrt{2}+\sqrt{50}\) and \(6\sqrt{2}\)?
C. दोनों बराबर हैंBoth are equal
\(\sqrt{50}=5\sqrt{2}\), इसलिए \(\sqrt{2}+\sqrt{50}=6\sqrt{2}\) है। तुलना से पहले सरल करें। / \(\sqrt{50}=5\sqrt{2}\), so \(\sqrt{2}+\sqrt{50}=6\sqrt{2}\). Simplify before comparing.
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What is the simplified form of \(3\sqrt{7}+2\sqrt{28}\)?
B. \(7\sqrt{7}\)
\(\sqrt{28}=2\sqrt{7}\), इसलिए \(3\sqrt{7}+4\sqrt{7}=7\sqrt{7}\) है। गुणांक और मूल दोनों ध्यान से देखें। / \(\sqrt{28}=2\sqrt{7}\), so \(3\sqrt{7}+4\sqrt{7}=7\sqrt{7}\). Watch both coefficients and radicals carefully.
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Which option will have a non-terminating non-repeating decimal expansion?
C. \(\sqrt{37}\)
\(\sqrt{37}\) अपरिमेय है क्योंकि (37) पूर्ण वर्ग नहीं है। अपरिमेय का दशमलव असांत अनावर्ती होता है। / \(\sqrt{37}\) is irrational because (37) is not a perfect square. An irrational number has a non-terminating non-repeating decimal.
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If \(a=\sqrt{3}+2\) and \(b=\sqrt{3}-2\), what is (ab)?
A. (-1)
(ab=\(\sqrt{3}\)2-22=3-4=-1) है। संयुग्मी गुणनफल परिमेय हो सकता है। / (ab=\(\sqrt{3}\)2-22=3-4=-1). A conjugate product can be rational.
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Which is the simplified form of \(\sqrt{7}+\sqrt{112}\)?
B. \(5\sqrt{7}\)
\(\sqrt{112}=4\sqrt{7}\), इसलिए योग \(5\sqrt{7}\) है। समान मूल जोड़ने से पहले सरल करें। / \(\sqrt{112}=4\sqrt{7}\), so the sum is \(5\sqrt{7}\). Simplify before adding like radicals.
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