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 191-200 of 600 questions.
What type of number is \( \sqrt{5}\times\sqrt{20} \)?
A. परिमेय वास्तविक संख्याRational real number
\( \sqrt{5}\times\sqrt{20}=\sqrt{100}=10 \) है। इसलिए परिणाम परिमेय वास्तविक संख्या है। / \( \sqrt{5}\times\sqrt{20}=\sqrt{100}=10 \). Therefore the result is a rational real number.
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What type of number is \( \sqrt{7}\times\sqrt{14} \)?
B. अपरिमेय वास्तविक संख्याIrrational real number
\( \sqrt{7}\times\sqrt{14}=\sqrt{98}=7\sqrt{2} \) है। यह अपरिमेय वास्तविक संख्या है। / \( \sqrt{7}\times\sqrt{14}=\sqrt{98}=7\sqrt{2} \). This is an irrational real number.
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What is the product of \(2+\sqrt{13}\) and \(2-\sqrt{13}\)?
B. ( -9 )
संयुग्मी गुणन से (22-\(\sqrt{13}\)2=4-13=-9) मिलता है। इस रूप में अंतर के वर्ग का नियम लगाएँ। / Conjugate multiplication gives (22-\(\sqrt{13}\)2=4-13=-9). Use the difference of squares rule here.
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What is the value of \( \frac{2+\sqrt{3}}{2-\sqrt{3}} \) after rationalising?
A. \(7+4\sqrt{3}\)
हर के संयुग्मी \(2+\sqrt{3}\) से गुणा करें। अंश (\(2+\sqrt{3}\)2=7+4\sqrt{3}) और हर (1) होगा। / Multiply by the conjugate \(2+\sqrt{3}\). The numerator becomes (\(2+\sqrt{3}\)2=7+4\sqrt{3}) and the denominator becomes (1).
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What will be the denominator after rationalising \( \frac{\sqrt{5}-1}{\sqrt{5}+1} \)?
A. (4)
हर के संयुग्मी \( \sqrt{5}-1 \) से गुणा करने पर हर (5-1=4) होगा। संयुग्मी विधि में अंतर के वर्ग का प्रयोग करें। / Multiplying by the conjugate \( \sqrt{5}-1 \) makes the denominator (5-1=4). Use difference of squares in the conjugate method.
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What is the value of \( |-\sqrt{49}+3| \)?
A. (4)
\( -\sqrt{49}+3=-7+3=-4 \) है और ( |-4|=4 )। निरपेक्ष मान दूरी देता है। / \( -\sqrt{49}+3=-7+3=-4 \) and ( |-4|=4 ). Absolute value gives distance.
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What is the value of \( |\sqrt{16}-\sqrt{81}| \)?
A. (5)
\( \sqrt{16}=4 \) और \( \sqrt{81}=9 \) है। ( |4-9|=5 ) होगा। / \( \sqrt{16}=4 \) and \( \sqrt{81}=9 \). So ( |4-9|=5 ).
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What is the value of \( \sqrt{a^2} \) in real numbers?
C. ( |a| )
वास्तविक संख्याओं में \( \sqrt{a^2}=|a| \) होता है क्योंकि वर्गमूल अमुख्य रूप से गैर-ऋणात्मक होता है। संकेत का ध्यान रखें। / In real numbers, \( \sqrt{a^2}=|a| \) because the principal square root is non-negative. Pay attention to the sign.
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If (x=-5), what is the value of \( \sqrt{x^2} \)?
B. (5)
\( \sqrt{x^2}=|x| \) होता है। (x=-5) होने पर ( |-5|=5 ) मिलेगा। / \( \sqrt{x^2}=|x| \). When (x=-5), ( |-5|=5 ).
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What is the rationalised form of \( \frac{1}{\sqrt{3}+\sqrt{2}} \)?
C. \( \sqrt{3}-\sqrt{2} \)
संयुग्मी \( \sqrt{3}-\sqrt{2} \) से गुणा करने पर हर (3-2=1) बनता है। इसलिए परिमेय हर वाला रूप \( \sqrt{3}-\sqrt{2} \) है। / Multiplying by the conjugate \( \sqrt{3}-\sqrt{2} \) makes the denominator (3-2=1). So the rationalised form is \( \sqrt{3}-\sqrt{2} \).
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