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 371-380 of 649 questions.
If (p(x)=x-3-3x), what is (p\(\sqrt{3}\))?
A. (0)
(\(\sqrt{3}\)3=3\sqrt{3}), इसलिए \(3\sqrt{3}-3\sqrt{3}=0\) है। परीक्षा में ऐसे प्रश्नों में घात को सरल करना मुख्य कदम है। / (\(\sqrt{3}\)3=3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.
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Which polynomial has zeroes with sum \(5\sqrt{2}\) and product (12)?
A. \(x^2-5\sqrt{2}x+12\)
बहुपद \(x^2-Sx+P\) होता है। यहाँ \(S=5\sqrt{2}\) और (P=12) हैं। / The polynomial is \(x^2-Sx+P\). Here \(S=5\sqrt{2}\) and (P=12).
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C. सिर्फ \(\sqrt{2}\) ही अकेला अपरिमेय शून्यक हो और गुणांक परिमेय रहेंOnly \(\sqrt{2}\) is the sole irrational zero while coefficients stay rational
परिमेय गुणांकों वाले द्विघात में अपरिमेय शून्यक अपने संयुग्मी के साथ आता है। परीक्षा में अकेले अपरिमेय मूल पर संदेह करें। / In a quadratic with rational coefficients an irrational zero comes with its conjugate. In exams be suspicious of a lone irrational root.
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If (p(x)=x-2-3x+\sqrt{2}), what is the product of its zeroes?
A. \(\sqrt{2}\)
गुणनफल \(\frac{c}{a}\) होता है। यहाँ \(c=\sqrt{2}\) और (a=1), इसलिए गुणनफल \(\sqrt{2}\) है। / The product is \(\frac{c}{a}\). Here \(c=\sqrt{2}\) and (a=1), so the product is \(\sqrt{2}\).
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Which polynomial has rational coefficients and zeroes \(1+\sqrt{2}\) and \(1-\sqrt{2}\)?
A. \(x^2-2x-1\)
योग (2) और गुणनफल (1-2=-1), इसलिए बहुपद \(x^2-2x-1\) है। परीक्षा में चिन्हों को ठीक रखें। / The sum is (2) and the product is (1-2=-1), so the polynomial is \(x^2-2x-1\). Keep signs correct in exams.
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If (p(x)=\sqrt{2}x-2-4x+\sqrt{2}), what is the sum of its zeroes?
A. \(2\sqrt{2}\)
योग \(-\frac{b}{a}=\frac{4}{\sqrt{2}}=2\sqrt{2}\) है। हर का परिमेयकरण करने से उत्तर सरल होता है। / The sum is \(-\frac{b}{a}=\frac{4}{\sqrt{2}}=2\sqrt{2}\). Rationalising the denominator simplifies the answer.
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If \(\sqrt{m}\) is rational and (m) is a positive integer, what is true about (m)?
B. (m) पूर्ण वर्ग है(m) is a perfect square
धनात्मक पूर्णांक (m) के लिए \(\sqrt{m}\) परिमेय तभी होगा जब (m) पूर्ण वर्ग हो। परीक्षा में पूर्ण वर्ग पहचानना जरूरी है। / For a positive integer (m), \(\sqrt{m}\) is rational only when (m) is a perfect square. Identifying perfect squares is important in exams.
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If (p(x)=\sqrt{3}x-2-6x+2\sqrt{3}), what is the product of its zeroes?
A. (2)
गुणनफल \(\frac{c}{a}=\frac{2\sqrt{3}}{\sqrt{3}}=2\) है। समान करणी कट सकती है। / The product is \(\frac{c}{a}=\frac{2\sqrt{3}}{\sqrt{3}}=2\). Like radicals can cancel.
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For which value of (n) is \(\sqrt{n}\) irrational?
C. (n=98)
(98) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{98}=7\sqrt{2}\) अपरिमेय है। परीक्षा में पूर्ण वर्ग गुणनखंड निकालें। / (98) is not a perfect square, so \(\sqrt{98}=7\sqrt{2}\) is irrational. In exams extract perfect-square factors.
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If (p(x)=x-2-\(\sqrt{2}+\sqrt{3}\)x+\sqrt{6}), what can its zeroes be?
A. \(\sqrt{2}\) और \(\sqrt{3}\)\(\sqrt{2}\) and \(\sqrt{3}\)
योग \(\sqrt{2}+\sqrt{3}\) और गुणनफल \(\sqrt{6}\) विकल्प \(\sqrt{2}\), \(\sqrt{3}\) से मिलते हैं। इसलिए वही शून्यक हैं। / The sum \(\sqrt{2}+\sqrt{3}\) and product \(\sqrt{6}\) match the option \(\sqrt{2}\), \(\sqrt{3}\). Hence those are the zeroes.
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