Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 81-90 of 600 questions.
Which option contains only rational real numbers?
B. ( -5 ) और (0.4)( -5 ) and (0.4)
( -5 ) पूर्णांक है और (0.4) समाप्त दशमलव है। इसलिए दोनों परिमेय वास्तविक संख्याएँ हैं। / ( -5 ) is an integer and (0.4) is a terminating decimal. So both are rational real numbers.
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What is the simplified form of \( \sqrt{2}+\sqrt{8} \)?
A. \(3\sqrt{2}\)
\( \sqrt{8}=2\sqrt{2} \) इसलिए \( \sqrt{2}+2\sqrt{2}=3\sqrt{2} \)। पहले करणी को सरल करें। / \( \sqrt{8}=2\sqrt{2} \), so \( \sqrt{2}+2\sqrt{2}=3\sqrt{2} \). Simplify surds first.
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What is the simplified form of \( \sqrt{50}-\sqrt{18} \)?
A. \(2\sqrt{2}\)
\( \sqrt{50}=5\sqrt{2} \) और \( \sqrt{18}=3\sqrt{2} \) हैं। अंतर \(2\sqrt{2}\) है। / \( \sqrt{50}=5\sqrt{2} \) and \( \sqrt{18}=3\sqrt{2} \). The difference is \(2\sqrt{2}\).
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What is obtained by rationalising the denominator of \( \frac{1}{\sqrt{5}} \)?
A. \( \frac{\sqrt{5}}{5} \)
अंश और हर को \( \sqrt{5} \) से गुणा करें। इससे \( \frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5} \) मिलता है। / Multiply numerator and denominator by \( \sqrt{5} \). This gives \( \frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5} \).
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What is the form of \( \frac{2}{\sqrt{3}} \) with rational denominator?
A. \( \frac{2\sqrt{3}}{3} \)
हर को परिमेय करने के लिए अंश और हर को \( \sqrt{3} \) से गुणा करें। उत्तर \( \frac{2\sqrt{3}}{3} \) है। / To rationalise the denominator, multiply numerator and denominator by \( \sqrt{3} \). The answer is \( \frac{2\sqrt{3}}{3} \).
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Which is greater between \( \sqrt{2} \) and \( \sqrt{3} \)?
B. \( \sqrt{3} \)
धनात्मक संख्याओं में बड़ी संख्या का वर्गमूल बड़ा होता है। (3>2) इसलिए \( \sqrt{3}>\sqrt{2} \)। / For positive numbers, the square root of the greater number is greater. Since (3>2), \( \sqrt{3}>\sqrt{2} \).
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Which is smaller between \( \sqrt{23} \) and (5)?
C. \( \sqrt{23} \)
\( \sqrt{23}<\sqrt{25}=5 \) है। इसलिए \( \sqrt{23} \) छोटी है।
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Which is greater between \( -\sqrt{5} \) and ( -2 )?
B. ( -2 )
\( \sqrt{5}\approx2.236 \) इसलिए \( -\sqrt{5}\approx -2.236 \) है। ( -2 ) शून्य के अधिक निकट है इसलिए बड़ी है। / \( \sqrt{5}\approx2.236 \), so \( -\sqrt{5}\approx -2.236 \). ( -2 ) is closer to zero, so it is greater.
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Which is greater between \( \frac{3}{4} \) and \( \sqrt{1} \)?
B. \( \sqrt{1} \)
\( \sqrt{1}=1 \) और \( \frac{3}{4}=0.75 \) है। इसलिए \( \sqrt{1} \) बड़ी है। / \( \sqrt{1}=1 \) and \( \frac{3}{4}=0.75 \). Therefore \( \sqrt{1} \) is greater.
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How many rational numbers are there between any two distinct real numbers?
C. अनंतInfinitely many
दो अलग-अलग वास्तविक संख्याओं के बीच अनंत परिमेय संख्याएँ होती हैं। यह घनत्व गुण का सरल रूप है। / There are infinitely many rational numbers between two distinct real numbers. This is a simple form of the density property.
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