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 221-230 of 600 questions.
What is the value of \(\sqrt{18}\times\sqrt{32}\)?
A. (24)
\(\sqrt{18}\times\sqrt{32}=\sqrt{576}=24\) है। दो अपरिमेयों का गुणनफल परिमेय हो सकता है। / \(\sqrt{18}\times\sqrt{32}=\sqrt{576}=24\). The product of two irrationals can be rational.
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Which statement is correct about \(\sqrt{5}+\sqrt{7}\)?
C. यह अपरिमेय हैIt is irrational
\(\sqrt{5}\) और \(\sqrt{7}\) अलग अपरिमेय मूल हैं और उनका योग अपरिमेय है। अलग मूलों को सीधे जोड़कर \(\sqrt{12}\) नहीं बनाते। / \(\sqrt{5}\) and \(\sqrt{7}\) are different irrational radicals and their sum is irrational. Different radicals are not added directly as \(\sqrt{12}\).
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What is the simplified value of \(\frac{\sqrt{112}}{\sqrt{7}}\)?
B. (4)
\(\frac{\sqrt{112}}{\sqrt{7}}=\sqrt{16}=4\) है। मूलों के भाग में अंदर का भागफल लें। / \(\frac{\sqrt{112}}{\sqrt{7}}=\sqrt{16}=4\). In division of roots take the quotient inside.
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What is the result of \(8\sqrt{2}-5\sqrt{2}\)?
B. \(3\sqrt{2}\)
समान मूलों के गुणांक घटाने पर \(3\sqrt{2}\) मिलता है। यह अपरिमेय है क्योंकि \(\sqrt{2}\) बचता है। / Subtracting coefficients of like radicals gives \(3\sqrt{2}\). It is irrational because \(\sqrt{2}\) remains.
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What is the value of (\sqrt{2}\(\sqrt{8}+\sqrt{18}\))?
A. (10)
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\), इसलिए कोष्ठक \(5\sqrt{2}\) और गुणनफल (10) है। पहले कोष्ठक सरल करें। / \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\), so the bracket is \(5\sqrt{2}\) and the product is (10). Simplify the bracket first.
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Which statement is correct when comparing \(\sqrt{29}\) and \(\sqrt{31}\)?
C. \(\sqrt{29}<\sqrt{31}\)
क्योंकि (29<31), इसलिए \(\sqrt{29}<\sqrt{31}\)। धनात्मक मूलों में अंदर की संख्याओं की तुलना करें। / Since (29<31), \(\sqrt{29}<\sqrt{31}\). For positive roots compare the numbers inside.
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What is the simplified form of (\sqrt{3}\times\(2\sqrt{3}+5\))?
A. \(6+5\sqrt{3}\)
वितरण करने पर \(2\times3+5\sqrt{3}=6+5\sqrt{3}\) मिलता है। मूल वाले पद और परिमेय पद अलग रखें। / Distributing gives \(2\times3+5\sqrt{3}=6+5\sqrt{3}\). Keep radical and rational terms separate.
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Which is the rationalised form of \(\frac{2}{\sqrt{3}+1}\)?
B. \(\sqrt{3}-1\)
संयुग्मी से गुणा करने पर (\frac{2\(\sqrt{3}-1\)}{3-1}=\sqrt{3}-1) मिलता है। हर को परिमेय बनाएं। / Multiplying by the conjugate gives (\frac{2\(\sqrt{3}-1\)}{3-1}=\sqrt{3}-1). Make the denominator rational.
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What is the sum of \(8+\sqrt{17}\) and \(8-\sqrt{17}\)?
A. (16)
अपरिमेय पद कट जाते हैं और योग (16) है। संयुग्मी संख्याओं का योग परिमेय होता है। / The irrational terms cancel and the sum is (16). The sum of conjugate numbers is rational.
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What is the product of \(8+\sqrt{17}\) and \(8-\sqrt{17}\)?
B. (47)
गुणनफल (82-\(\sqrt{17}\)2=64-17=47) है। संयुग्मी गुणन में \(a^2-b^2\) लगाएं। / The product is (82-\(\sqrt{17}\)2=64-17=47). Use \(a^2-b^2\) in conjugate multiplication.
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