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.
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Why is \(a\neq0\) necessary in \(ax^2+bx+c\)?
D. ताकि व्यंजक द्विघात रहेSo that the expression remains quadratic
यदि (a=0) हो तो \(x^2\) पद नहीं रहेगा। तब व्यंजक द्विघात नहीं रहेगा। / If (a=0), the \(x^2\) term will not remain. Then the expression will not be quadratic.
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How will \(7-3x+2x^2\) be written in standard form?
D. \(2x^2-3x+7\)
मानक रूप में घातों को घटते क्रम में लिखते हैं। इसलिए \(2x^2-3x+7\) सही है। / In standard form, powers are written in decreasing order. So \(2x^2-3x+7\) is correct.
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What is the value of \(3x^2+2x-1\) when (x=1)?
C. (4)
(3(1)2+2(1)-1=4) है। परीक्षा में ऋण स्थिर पद को अंत में जोड़ें। / (3(1)2+2(1)-1=4). Exam tip: handle the negative constant term at the end.
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What is the value of \(x^2-4x+7\) when (x=3)?
B. (4)
\(3^2-4\cdot3+7=9-12+7=4\) है। परीक्षा में संकेतों पर ध्यान दें। / \(3^2-4\cdot3+7=9-12+7=4\). Exam tip: pay attention to signs.
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Which is the expansion of ((2x+3)(x-2))?
D. \(2x^2-x-6\)
गुणा करने पर \(2x^2-4x+3x-6=2x^2-x-6\) मिलता है। परीक्षा में समान पद जोड़ें। / Multiplying gives \(2x^2-4x+3x-6=2x^2-x-6\). Exam tip: combine like terms.
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What is the expansion of ((3x-1)(x+4))?
D. \(3x^2+11x-4\)
((3x-1)(x+4)=3x-2+12x-x-4) है। इसलिए \(3x^2+11x-4\) मिलेगा। / ((3x-1)(x+4)=3x-2+12x-x-4). So \(3x^2+11x-4\) is obtained.
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Which expression is a perfect square between \(x^2+2x+1\) and \(x^2-1\)?
D. \(x^2+2x+1\)
(x-2+2x+1=(x+1)2) है। जबकि \(x^2-1\) वर्गों का अंतर है। / (x-2+2x+1=(x+1)2). But \(x^2-1\) is a difference of squares.
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If \(x^2+px+16\) is a perfect square and (p) is positive, what is the value of (p)?
B. (8)
\(16=4^2\) है इसलिए मध्य पद \(2\cdot4x=8x\) होगा। अतः (p=8) है। / \(16=4^2\), so the middle term is \(2\cdot4x=8x\). Hence (p=8).
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If \(x^2-10x+k\) is a perfect square, what is the value of (k)?
C. (25)
(-10x) में आधा गुणांक (-5) है और उसका वर्ग (25) है। परीक्षा में आधे गुणांक का वर्ग लें। / Half the coefficient in (-10x) is (-5), and its square is (25). Exam tip: square half of the coefficient.
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If \(9x^2+mx+25\) is a perfect square and the middle term is positive, what is the value of (m)?
B. (30)
(9x-2=(3x)2) और \(25=5^2\) है इसलिए मध्य पद \(2\cdot3x\cdot5=30x\) होगा। परीक्षा में दोनों वर्ग पदों की जड़ें लेकर दुगुना गुणन करें। / (9x-2=(3x)2) and \(25=5^2\), so the middle term will be \(2\cdot3x\cdot5=30x\). Exam tip: take the roots of both square terms and multiply twice.
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