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 461-470 of 649 questions.
Which polynomial has zeroes \(\sqrt{7}\) and \(-\sqrt{7}\)?
A. \(x^2-7\)
शून्यकों का योग (0) और गुणनफल (-7) है। इसलिए बहुपद \(x^2-7\) होगा। / The sum of zeroes is (0) and the product is (-7). Hence the polynomial is \(x^2-7\).
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If \(2+\sqrt{3}\) and \(2-\sqrt{3}\) are zeroes of a quadratic polynomial, what is the polynomial?
A. \(x^2-4x+1\)
योग (4) और गुणनफल (1) है। अतः बहुपद \(x^2-4x+1\) है। / The sum is (4) and the product is (1). Therefore the polynomial is \(x^2-4x+1\).
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If (p(x)=x-2-5x+6), what type of number is (p\(\sqrt{2}\))?
B. अपरिमेयIrrational
(p\(\sqrt{2}\)=2-5\sqrt{2}+6=8-5\sqrt{2}), जो अपरिमेय है। परीक्षा में पहले प्रतिस्थापन करें फिर वर्गमूल को सरल करें। / (p\(\sqrt{2}\)=2-5\sqrt{2}+6=8-5\sqrt{2}), which is irrational. In exams substitute first and then simplify the radical.
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If \(a=7+4\sqrt{3}\) and \(b=7-4\sqrt{3}\), then what type of number is (ab)?
A. (1), परिमेय(1), rational
(ab=(7)2-\(4\sqrt{3}\)2=49-48=1), इसलिए यह परिमेय है। परीक्षा में संयुग्मी युग्म पर \(a^2-b^2\) लगाएं। / (ab=(7)2-\(4\sqrt{3}\)2=49-48=1), so it is rational. In exams apply \(a^2-b^2\) for conjugate pairs.
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If the zeroes of (p(x)=x-2-kx+1) are \(2+\sqrt{3}\) and \(2-\sqrt{3}\), what is the value of (k)?
B. (4)
शून्यकों का योग (4) है और \(x^2-kx+1\) में योग (k) होता है। इसलिए (k=4) है। / The sum of zeroes is (4), and in \(x^2-kx+1\), the sum is (k). Hence (k=4).
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If \(2+\sqrt{3}\) is a zero of the polynomial \(x^2-4x+1\), what is the other zero?
A. \(2-\sqrt{3}\)
परिमेय गुणांकों वाले द्विघात में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी मूल का नियम उपयोगी है। / For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
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A. \(3+\sqrt{5}\)
परिमेय गुणांकों में अपरिमेय शून्यक सामान्यतः संयुग्मी रूप में आते हैं। इसलिए \(3-\sqrt{5}\) का साथी शून्यक \(3+\sqrt{5}\) होगा। / For rational coefficients, irrational zeroes usually occur in conjugate pairs. Hence the companion zero of \(3-\sqrt{5}\) is \(3+\sqrt{5}\).
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If (p(x)=x-2-2\sqrt{5}x+5), which statement about its zeroes is correct?
A. दोनों शून्यक \(\sqrt{5}\) हैंBoth zeroes are \(\sqrt{5}\)
यह बहुपद (\(x-\sqrt{5}\)2) के बराबर है। अतः \(\sqrt{5}\) दोहरा शून्यक है। / This polynomial equals (\(x-\sqrt{5}\)2). Hence \(\sqrt{5}\) is a repeated zero.
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If the zeroes of a quadratic polynomial are \(3+\sqrt{5}\) and \(3-\sqrt{5}\), what is their sum?
B. (6)
योग (\(3+\sqrt{5}\)+\(3-\sqrt{5}\)=6) है। संयुग्मी अपरिमेयों में वर्गमूल भाग कट जाता है। / The sum is (\(3+\sqrt{5}\)+\(3-\sqrt{5}\)=6). In conjugate irrationals the radical parts cancel.
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For which value of (k) will (p(x)=x-2-10x+k) have zeroes \(5+\sqrt{2}\) and \(5-\sqrt{2}\)?
A. (23)
गुणनफल (\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23) है। इसलिए (k=23) होगा। / The product is (\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23). So (k=23).
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