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 471-480 of 649 questions.
A. (9)
गुणनफल (\(4+\sqrt{7}\)\(4-\sqrt{7}\)=16-7=9) है। परीक्षा में ((a+b)(a-b)=a-2-b-2) लगाएं। / The product is (\(4+\sqrt{7}\)\(4-\sqrt{7}\)=16-7=9). Use ((a+b)(a-b)=a-2-b-2) in exams.
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If one zero of (p(x)=x-2+ax+6) is \(-\sqrt{6}\) and the other is \(\sqrt{6}\), what is (a)?
A. (0)
शून्यकों का योग (0) है और \(x^2+ax+6\) में योग (-a) होता है। अतः (a=0)। / The sum of the zeroes is (0), and in \(x^2+ax+6\), the sum is (-a). Thus (a=0).
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Which monic quadratic polynomial has zeroes \(2+\sqrt{6}\) and \(2-\sqrt{6}\)?
A. \(x^2-4x-2\)
योग (4) और गुणनफल (4-6=-2) है, इसलिए बहुपद \(x^2-4x-2\) है। परीक्षा में \(x^2-Sx+P\) सूत्र याद रखें। / The sum is (4) and the product is (4-6=-2), so the polynomial is \(x^2-4x-2\). Remember the formula \(x^2-Sx+P\).
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Which polynomial has zeroes \(1+\sqrt{2}\) and \(1-\sqrt{2}\)?
A. \(x^2-2x-1\)
योग (2) और गुणनफल (-1) है। इसलिए बहुपद \(x^2-2x-1\) है। / The sum is (2) and the product is (-1). So the polynomial is \(x^2-2x-1\).
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If \(x=\sqrt{3}\), what is the value of \(x^2-3\)?
B. (0)
क्योंकि (\(\sqrt{3}\)2=3), इसलिए \(x^2-3=0\) है। परीक्षा में वर्गमूल का वर्ग मूलांक देता है। / Since (\(\sqrt{3}\)2=3), \(x^2-3=0\). In exams the square of a square root gives the radicand.
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If (p(x)=x-2-8x+10), what are its zeroes?
A. \(4+\sqrt{6}\) और \(4-\sqrt{6}\)\(4+\sqrt{6}\) and \(4-\sqrt{6}\)
सूत्र से शून्यक \(\frac{8\pm\sqrt{64-40}}{2}=4\pm\sqrt{6}\) हैं। पहले विविक्तकर सरल करें। / By the formula, the zeroes are \(\frac{8\pm\sqrt{64-40}}{2}=4\pm\sqrt{6}\). Simplify the discriminant first.
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If (p(x)=x-2-7), what is the form of (p\(\sqrt{7}+1\))?
A. \(1+2\sqrt{7}\)
(\(\sqrt{7}+1\)2-7=8+2\sqrt{7}-7=1+2\sqrt{7}) है। परीक्षा में ((a+b)2) सावधानी से लगाएं। / (\(\sqrt{7}+1\)2-7=8+2\sqrt{7}-7=1+2\sqrt{7}). Use ((a+b)2) carefully in exams.
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If (p(x)=3x-2-12x+6), what is the nature of its zeroes?
C. दो भिन्न अपरिमेय शून्यकTwo distinct irrational zeroes
सरल रूप \(x^2-4x+2\) है और (D=16-8=8) है। (8) पूर्ण वर्ग नहीं है, इसलिए शून्यक अपरिमेय हैं। / The simplified form is \(x^2-4x+2\), and (D=16-8=8). Since (8) is not a perfect square, the zeroes are irrational.
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For which (k) will \(x=\sqrt{2}\) be a zero of the polynomial \(x^2+kx-2\)?
A. (0)
रखने पर \(2+k\sqrt{2}-2=k\sqrt{2}=0\), इसलिए (k=0) है। परीक्षा में शून्यक होने पर (p\(\alpha\)=0) लिखें। / Substitution gives \(2+k\sqrt{2}-2=k\sqrt{2}=0\), so (k=0). In exams write (p\(\alpha\)=0) for a zero.
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If \(\alpha=\sqrt{3}+1\) and \(\beta=\sqrt{3}-1\), what is \(\alpha\beta\)?
A. (2)
(\alpha\beta=\(\sqrt{3}+1\)\(\sqrt{3}-1\)=3-1=2) है। संयुग्मी गुणनफल से अपरिमेय भाग कट जाता है। / (\alpha\beta=\(\sqrt{3}+1\)\(\sqrt{3}-1\)=3-1=2). The irrational part cancels in conjugate multiplication.
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