Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Which is an irrational number between (1) and (2)?
B. \( \sqrt{2} \)
\(1<\sqrt{2}<2\) और \( \sqrt{2} \) अपरिमेय है। वर्गों की तुलना से इसका स्थान पता चलता है।
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Which is an irrational number between (2) and (3)?
A. \( \sqrt{6} \)
\(2^2<6<3^2\) इसलिए \( \sqrt{6} \) (2) और (3) के बीच है। (6) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है। / Since \(2^2<6<3^2\), \( \sqrt{6} \) lies between (2) and (3). Since (6) is not a perfect square, it is irrational.
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What is the value of \( \sqrt{0.04} \)?
B. (0.2)
\(0.2^2=0.04\) इसलिए \( \sqrt{0.04}=0.2 \)। दशमलव के वर्गमूल में स्थान मान ध्यान रखें। / \(0.2^2=0.04\), so \( \sqrt{0.04}=0.2 \). Be careful with place value in decimal square roots.
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What is the value of \( \sqrt{0.25} \)?
A. (0.5)
\(0.5^2=0.25\) इसलिए \( \sqrt{0.25}=0.5 \)। वर्गमूल के लिए वर्ग करके जाँच सकते हैं। / \(0.5^2=0.25\), so \( \sqrt{0.25}=0.5 \). You can check a square root by squaring it.
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What is the value of \( \sqrt{\frac{49}{64}} \)?
A. \( \frac{7}{8} \)
अंश और हर के अलग-अलग वर्गमूल लें। \( \sqrt{\frac{49}{64}}=\frac{7}{8} \)। / Take square roots of numerator and denominator separately. \( \sqrt{\frac{49}{64}}=\frac{7}{8} \).
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What is \( \sqrt{\frac{16}{81}} \) equal to?
A. \( \frac{4}{9} \)
\( \sqrt{16}=4 \) और \( \sqrt{81}=9 \) है। इसलिए उत्तर \( \frac{4}{9} \) है। / \( \sqrt{16}=4 \) and \( \sqrt{81}=9 \). Therefore the answer is \( \frac{4}{9} \).
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What type of number is ( \(2+\sqrt{3}\) )?
B. अपरिमेय वास्तविक संख्याIrrational real number
परिमेय (2) में अपरिमेय \( \sqrt{3} \) जोड़ने पर अपरिमेय संख्या मिलती है। यह वास्तविक संख्या भी है। / Adding irrational \( \sqrt{3} \) to rational (2) gives an irrational number. It is also a real number.
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What type of number is ( \(5-\sqrt{2}\) )?
A. अपरिमेय वास्तविक संख्याIrrational real number
परिमेय संख्या में अपरिमेय संख्या घटाने पर परिणाम अपरिमेय होता है। इसलिए \(5-\sqrt{2}\) अपरिमेय वास्तविक संख्या है। / Subtracting an irrational number from a rational number gives an irrational result. Thus \(5-\sqrt{2}\) is an irrational real number.
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What is the value of \( \sqrt{7}\times\sqrt{7} \)?
C. (7)
एक ही वर्गमूल को स्वयं से गुणा करने पर अंदर की संख्या मिलती है। इसलिए \( \sqrt{7}\times\sqrt{7}=7 \)। / Multiplying the same square root by itself gives the number inside. Therefore \( \sqrt{7}\times\sqrt{7}=7 \).
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In which simplified surd form will \( \sqrt{40} \) be written?
A. \(2\sqrt{10}\)
\(40=4\times10\) इसलिए \( \sqrt{40}=2\sqrt{10} \)। पूर्ण वर्ग (4) को बाहर निकालें। / Since \(40=4\times10\), \( \sqrt{40}=2\sqrt{10} \). Take the perfect square (4) outside.
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