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 181-190 of 600 questions.
What is the sum of \(7+\sqrt{13}\) and \(7-\sqrt{13}\)?
A. (14)
अपरिमेय पद कट जाते हैं और योग (14) है। संयुग्मी संख्याओं का योग परिमेय हो सकता है। / The irrational terms cancel and the sum is (14). The sum of conjugate numbers can be rational.
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What is the product of \(7+\sqrt{13}\) and \(7-\sqrt{13}\)?
B. (36)
गुणनफल (72-\(\sqrt{13}\)2=49-13=36) है। संयुग्मी गुणन में \(a^2-b^2\) लगाएं। / The product is (72-\(\sqrt{13}\)2=49-13=36). Use \(a^2-b^2\) for conjugate multiplication.
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If \(p=4+\sqrt{5}\), what type of number is (p)?
D. अपरिमेयIrrational
परिमेय (4) में अपरिमेय \(\sqrt{5}\) जोड़ने से अपरिमेय संख्या मिलती है। अपरिमेय भाग बचा रहता है। / Adding irrational \(\sqrt{5}\) to rational (4) gives an irrational number. The irrational part remains.
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To construct \(\sqrt{2}\) on the number line, what hypotenuse length is used?
B. (1) और (1) भुजाओं वाला कर्णHypotenuse with legs (1) and (1)
समकोण त्रिभुज में (1) और (1) भुजाओं का कर्ण \(\sqrt{2}\) होता है। पाइथागोरस प्रमेय का उपयोग करें। / In a right triangle, legs (1) and (1) give hypotenuse \(\sqrt{2}\). Use Pythagoras theorem.
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What type of number is \(\sqrt{2}\times\sqrt{8}\)?
B. परिमेयRational
\(\sqrt{2}\times\sqrt{8}=\sqrt{16}=4\) है जो परिमेय है। दो अपरिमेयों का गुणनफल परिमेय हो सकता है। / \(\sqrt{2}\times\sqrt{8}=\sqrt{16}=4\), which is rational. The product of two irrationals can be rational.
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What is the value of \(\sqrt{20}\div\sqrt{2}\)?
B. \(\sqrt{10}\)
\(\sqrt{20}\div\sqrt{2}=\sqrt{10}\) है जो अपरिमेय है। भाग में मूलों को एक मूल में लिखें। / \(\sqrt{20}\div\sqrt{2}=\sqrt{10}\), which is irrational. Write the roots in division as one root.
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If the area of a square is (18) square units, what will be the simplified form of its side?
C. \(3\sqrt{2}\)
भुजा \(\sqrt{18}=3\sqrt{2}\) होगी। वर्ग में भुजा क्षेत्रफल के वर्गमूल के बराबर होती है। / The side will be \(\sqrt{18}=3\sqrt{2}\). In a square, side equals the square root of area.
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What is the rationalised form of \(\frac{1}{3-\sqrt{2}}\)?
A. \(\frac{3+\sqrt{2}}{7}\)
संयुग्मी से गुणा करने पर हर (9-2=7) बनता है। इसलिए रूप \(\frac{3+\sqrt{2}}{7}\) है। / Multiplying by the conjugate makes the denominator (9-2=7). So the form is \(\frac{3+\sqrt{2}}{7}\).
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Which statement is correct about \(\sqrt{3}+\sqrt{27}\) and \(\sqrt{48}\)?
C. दोनों बराबर हैंBoth are equal
\(\sqrt{3}+\sqrt{27}=4\sqrt{3}\) और \(\sqrt{48}=4\sqrt{3}\) हैं। सरल रूप तुलना को आसान बनाता है। / \(\sqrt{3}+\sqrt{27}=4\sqrt{3}\) and \(\sqrt{48}=4\sqrt{3}\). Simplified form makes comparison easy.
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What is the simplified form of \(2\sqrt{5}+3\sqrt{20}\)?
B. \(8\sqrt{5}\)
\(\sqrt{20}=2\sqrt{5}\), इसलिए \(2\sqrt{5}+6\sqrt{5}=8\sqrt{5}\) है। गुणांक और मूल दोनों ध्यान से देखें। / \(\sqrt{20}=2\sqrt{5}\), so \(2\sqrt{5}+6\sqrt{5}=8\sqrt{5}\). Watch both coefficients and radicals carefully.
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