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 241-250 of 600 questions.
What type of number is \( \sqrt{3}\times\sqrt{21} \)?
B. अपरिमेय वास्तविक संख्याIrrational real number
\( \sqrt{3}\times\sqrt{21}=\sqrt{63}=3\sqrt{7} \) है। यह अपरिमेय वास्तविक संख्या है। / \( \sqrt{3}\times\sqrt{21}=\sqrt{63}=3\sqrt{7} \). This is an irrational real number.
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What is the product of \(3+\sqrt{14}\) and \(3-\sqrt{14}\)?
B. ( -5 )
संयुग्मी गुणन से (32-\(\sqrt{14}\)2=9-14=-5) मिलता है। अंतर के वर्ग का नियम लगाएँ। / Conjugate multiplication gives (32-\(\sqrt{14}\)2=9-14=-5). Use the difference of squares rule.
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What is the value of \( \frac{3+\sqrt{2}}{3-\sqrt{2}} \) after rationalising?
A. \( \frac{11+6\sqrt{2}}{7} \)
हर के संयुग्मी \(3+\sqrt{2}\) से गुणा करें। अंश (\(3+\sqrt{2}\)2=11+6\sqrt{2}) और हर (7) होगा। / Multiply by the conjugate \(3+\sqrt{2}\). The numerator is (\(3+\sqrt{2}\)2=11+6\sqrt{2}) and the denominator is (7).
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What will be the denominator after rationalising \( \frac{\sqrt{7}+2}{\sqrt{7}-2} \)?
A. (3)
हर के संयुग्मी \( \sqrt{7}+2 \) से गुणा करने पर हर (7-4=3) होगा। संयुग्मी विधि में अंतर के वर्ग का प्रयोग करें। / Multiplying by the conjugate \( \sqrt{7}+2 \) makes the denominator (7-4=3). Use difference of squares in the conjugate method.
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What is the value of \( |-\sqrt{64}+5| \)?
A. (3)
\( -\sqrt{64}+5=-8+5=-3 \) है और ( |-3|=3 )। निरपेक्ष मान दूरी देता है। / \( -\sqrt{64}+5=-8+5=-3 \) and ( |-3|=3 ). Absolute value gives distance.
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What is the value of \( |\sqrt{25}-\sqrt{100}| \)?
A. (5)
\( \sqrt{25}=5 \) और \( \sqrt{100}=10 \) है। ( |5-10|=5 ) होगा। / \( \sqrt{25}=5 \) and \( \sqrt{100}=10 \). So ( |5-10|=5 ).
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What is the value of ( \sqrt{( -9)2} )?
B. (9)
वास्तविक संख्याओं में \( \sqrt{a^2}=|a| \) होता है। इसलिए ( \sqrt{( -9)2}=9 )। / In real numbers, \( \sqrt{a^2}=|a| \). Therefore ( \sqrt{( -9)2}=9 ).
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If (x=-8), what is the value of \( \sqrt{x^2}+x \)?
A. (0)
\( \sqrt{x^2}=|x| \) होता है। (x=-8) होने पर (8+(-8)=0) मिलेगा। / \( \sqrt{x^2}=|x| \). When (x=-8), we get (8+(-8)=0).
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What is the rationalised form of \( \frac{1}{5+2\sqrt{6}} \)?
D. \(5-2\sqrt{6}\)
संयुग्मी \(5-2\sqrt{6}\) से गुणा करने पर हर (25-24=1) बनता है। इसलिए परिमेय हर वाला रूप \(5-2\sqrt{6}\) है। / Multiplying by the conjugate \(5-2\sqrt{6}\) makes the denominator (25-24=1). So the rationalised form is \(5-2\sqrt{6}\).
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What is the simplified form of \( \sqrt{242}-\sqrt{128} \)?
C. \(3\sqrt{2}\)
\( \sqrt{242}=11\sqrt{2} \) और \( \sqrt{128}=8\sqrt{2} \) है। इसलिए अंतर \(3\sqrt{2}\) मिलता है। / \( \sqrt{242}=11\sqrt{2} \) and \( \sqrt{128}=8\sqrt{2} \). Therefore the difference is \(3\sqrt{2}\).
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