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 601-610 of 649 questions.
Which quadratic polynomial has zeroes \(2+\sqrt{10}\) and \(2-\sqrt{10}\)?
A. \(x^2-4x-6\)
योग (4) और गुणनफल (4-10=-6) है। इसलिए बहुपद \(x^2-4x-6\) होगा। / The sum is (4) and the product is (4-10=-6). Hence the polynomial is \(x^2-4x-6\).
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If \(x=\sqrt{7}+\sqrt{5}\), what is the correct value of \(x^2\)?
A. \(12+2\sqrt{35}\)
\(x^2=7+5+2\sqrt{35}=12+2\sqrt{35}\) है। परीक्षा में ((a+b)2) में (2ab) न छोड़ें। / \(x^2=7+5+2\sqrt{35}=12+2\sqrt{35}\). In exams do not miss (2ab) in ((a+b)2).
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Which expression is a rational number?
A. (\(\sqrt{28}\)\(\sqrt{7}\))
(\(\sqrt{28}\)\(\sqrt{7}\)=\sqrt{196}=14) है जो परिमेय है। परीक्षा में गुणन और जोड़ के नियम अलग रखें। / (\(\sqrt{28}\)\(\sqrt{7}\)=\sqrt{196}=14) which is rational. In exams keep multiplication and addition rules separate.
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A. अनवसानी आवर्तीNon-terminating recurring
हर में (11) है इसलिए दशमलव समाप्त नहीं होगा। परिमेय संख्या होने के कारण यह आवर्ती होगा। / The denominator contains (11) so the decimal will not terminate. Since it is rational it will be recurring.
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If (p) and (q) are non-zero rational numbers and \(p+q\sqrt{3}=0\), which conclusion is correct?
A. \(\sqrt{3}=-\frac{p}{q}\) होगा जो असंभव है\(\sqrt{3}=-\frac{p}{q}\) would be true which is impossible
\(-\frac{p}{q}\) परिमेय है इसलिए इससे \(\sqrt{3}\) परिमेय हो जाएगा जो गलत है। परीक्षा में विरोधाभास विधि पहचानें। / \(-\frac{p}{q}\) is rational so it would make \(\sqrt{3}\) rational which is false. In exams recognize the contradiction method.
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If \(a=\sqrt{13}+\sqrt{6}\) and \(b=\sqrt{13}-\sqrt{6}\), what is the value of (ab)?
A. (7)
(ab=13-6=7) है। परीक्षा में संयुग्मी गुणन से मूल हट जाते हैं। / (ab=13-6=7). In exams conjugate multiplication removes radicals.
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What is the rationalized form of \(\frac{3}{\sqrt{13}-2}\)?
A. \(\frac{\sqrt{13}+2}{3}\)
हर का संयुग्मी \(\sqrt{13}+2\) है और हर (13-4=9) बनता है। इसलिए मान (\frac{3\(\sqrt{13}+2\)}{9}=\frac{\sqrt{13}+2}{3}) है। / The conjugate of the denominator is \(\sqrt{13}+2\) and the denominator becomes (13-4=9). Hence the value is (\frac{3\(\sqrt{13}+2\)}{9}=\frac{\sqrt{13}+2}{3}).
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If \(x=4-\sqrt{15}\), then \(\frac{1}{x}\) is equal to which expression?
A. \(4+\sqrt{15}\)
(\(4-\sqrt{15}\)\(4+\sqrt{15}\)=1) है। इसलिए व्युत्क्रम \(4+\sqrt{15}\) होगा। / (\(4-\sqrt{15}\)\(4+\sqrt{15}\)=1). Therefore the reciprocal is \(4+\sqrt{15}\).
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If the zeroes are \(6+\sqrt{5}\) and \(6-\sqrt{5}\), what are their sum and product respectively?
A. (12) और (31)(12) and (31)
योग (12) और गुणनफल (36-5=31) है। परीक्षा में संयुग्मी जोड़े का योग और गुणनफल अलग निकालें। / The sum is (12) and the product is (36-5=31). In exams find the sum and product of conjugate pairs separately.
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In which option is the product of two irrational numbers rational?
A. (\(2+\sqrt{3}\)\(2-\sqrt{3}\))
(\(2+\sqrt{3}\)\(2-\sqrt{3}\)=4-3=1) है जो परिमेय है। परीक्षा में संयुग्मी गुणन को प्रतिउदाहरण के रूप में याद रखें। / (\(2+\sqrt{3}\)\(2-\sqrt{3}\)=4-3=1) which is rational. In exams remember conjugate multiplication as a counterexample.
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