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 111-120 of 600 questions.
What is the simplified form of \( \sqrt{48}+\sqrt{27} \)?
B. \(7\sqrt{3}\)
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \) हैं। इसलिए योग \(7\sqrt{3}\) है। / \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \). Therefore the sum is \(7\sqrt{3}\).
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What is the simplified form of \( \sqrt{75}-\sqrt{12} \)?
A. \(3\sqrt{3}\)
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) हैं। अंतर \(3\sqrt{3}\) है। / \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \). The difference is \(3\sqrt{3}\).
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What is the form of \( \frac{3}{\sqrt{2}} \) with rational denominator?
B. \( \frac{3\sqrt{2}}{2} \)
अंश और हर को \( \sqrt{2} \) से गुणा करें। इससे हर (2) हो जाता है। / Multiply numerator and denominator by \( \sqrt{2} \). This makes the denominator (2).
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What is obtained by rationalising the denominator of \( \frac{5}{\sqrt{7}} \)?
C. \( \frac{5\sqrt{7}}{7} \)
अंश और हर को \( \sqrt{7} \) से गुणा करने पर \( \frac{5\sqrt{7}}{7} \) मिलता है। हर को परिमेय करना परीक्षा में सामान्य प्रश्न है। / Multiplying numerator and denominator by \( \sqrt{7} \) gives \( \frac{5\sqrt{7}}{7} \). Rationalising the denominator is a common exam question.
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What is obtained by rationalising the denominator of \( \frac{1}{2+\sqrt{3}} \)?
D. \(2-\sqrt{3}\)
संयुग्मी \(2-\sqrt{3}\) से गुणा करें और हर (4-3=1) बनेगा। इसलिए उत्तर \(2-\sqrt{3}\) है। / Multiply by the conjugate \(2-\sqrt{3}\) and the denominator becomes (4-3=1). Hence the answer is \(2-\sqrt{3}\).
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What will come in the numerator after rationalising \( \frac{1}{3-\sqrt{5}} \)?
A. \(3+\sqrt{5}\)
हर के संयुग्मी \(3+\sqrt{5}\) से गुणा किया जाता है। इसलिए नए अंश में \(3+\sqrt{5}\) आएगा। / We multiply by the conjugate \(3+\sqrt{5}\). So the new numerator will contain \(3+\sqrt{5}\).
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What is the value of ( \(2+\sqrt{5}\)\(2-\sqrt{5}\) )?
B. ( -1 )
यह अंतर के वर्ग का रूप है (22-\(\sqrt{5}\)2=4-5=-1)। संयुग्मी गुणा में मध्य पद कट जाते हैं। / It is a difference of squares (22-\(\sqrt{5}\)2=4-5=-1). Middle terms cancel in conjugate multiplication.
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What is the value of ( \(3+\sqrt{2}\)\(3-\sqrt{2}\) )?
A. (7)
(32-\(\sqrt{2}\)2=9-2=7) होता है। संयुग्मी का गुणन अक्सर परिमेय उत्तर देता है। / (32-\(\sqrt{2}\)2=9-2=7). Multiplying conjugates often gives a rational answer.
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Which is greater between \( \sqrt{3} \) and \( \sqrt{12} \)?
C. \( \sqrt{12} \)
क्योंकि (12>3) है इसलिए \( \sqrt{12}>\sqrt{3} \)। धनात्मक संख्याओं में बड़ा आधार बड़ा वर्गमूल देता है। / Since (12>3), \( \sqrt{12}>\sqrt{3} \). For positive numbers, a larger radicand gives a larger square root.
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Which is smaller between \( \sqrt{35} \) and (6)?
B. \( \sqrt{35} \)
\( \sqrt{35}<\sqrt{36}=6 \) है। इसलिए \( \sqrt{35} \) छोटी है।
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