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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In ((x+a)2), the coefficient of (x) is (14). What is the value of (a)?
B. (7)
((x+a)2=x-2+2ax+a-2) है इसलिए (2a=14) और (a=7)। परीक्षा में मध्य गुणांक को (2a) मानें। / ((x+a)2=x-2+2ax+a-2), so (2a=14) and (a=7). Exam tip: treat the middle coefficient as (2a).
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In ((x-a)2), the constant term is (36) and (a>0). What will be the coefficient of (x)?
C. (-12)
\(a^2=36\) से (a=6) और मध्य पद (-2ax=-12x) होगा। परीक्षा में घटाव वाले वर्ग का मध्य पद ऋण होता है। / From \(a^2=36\), (a=6), and the middle term is (-2ax=-12x). Exam tip: the middle term is negative in a subtraction square.
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If \(x-\frac{1}{x}=4\), what is the value of \(x^2+\frac{1}{x^2}\)?
B. (18)
वर्ग करने पर \(x^2-2+\frac{1}{x^2}=16\) है इसलिए \(x^2+\frac{1}{x^2}=18\)। परीक्षा में घटाव पहचान में (2) जोड़ें। / Squaring gives \(x^2-2+\frac{1}{x^2}=16\), so \(x^2+\frac{1}{x^2}=18\). Exam tip: add (2) in the subtraction identity.
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How can \(x^2+4x+7\) be written as a perfect square plus a constant?
A. ((x+2)2+3)
(x-2+4x+7=x-2+4x+4+3=(x+2)2+3) है। परीक्षा में पूर्ण वर्ग बनाने के लिए (4) जोड़कर संतुलन करें। / Here (x-2+4x+7=x-2+4x+4+3=(x+2)2+3). Exam tip: add (4) to make a square and balance it.
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How will you write \(x^2-6x+11\) in completed square form?
B. ((x-3)2+2)
(x-2-6x+11=x-2-6x+9+2=(x-3)2+2) है। परीक्षा में मध्य गुणांक का आधा (-3) लें। / Here (x-2-6x+11=x-2-6x+9+2=(x-3)2+2). Exam tip: take half of the middle coefficient as (-3).
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Write (2(x+3)2-5) in simplified quadratic form.
B. \(2x^2+12x+13\)
((x+3)2=x-2+6x+9) है और (2) से गुणा करके (5) घटाएं। परीक्षा में बाहरी गुणन पूरे कोष्ठक पर लगाएं। / Since ((x+3)2=x-2+6x+9), multiply by (2) and subtract (5). Exam tip: apply the outside multiplier to the whole bracket.
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Which is the simplified form of (3(x-2)2+4x)?
A. \(3x^2-8x+12\)
((x-2)2=x-2-4x+4) है इसलिए \(3x^2-12x+12+4x=3x^2-8x+12\)। परीक्षा में समान पद जोड़ें। / ((x-2)2=x-2-4x+4), so \(3x^2-12x+12+4x=3x^2-8x+12\). Exam tip: combine like terms.
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For \(x^2-9x+20\), at which two values of (x) will the expression be zero?
B. (4) और (5)(4) and (5)
(x-2-9x+20=(x-4)(x-5)) है इसलिए (x=4) या (x=5)। परीक्षा में गुणनखंडों से शून्य मान निकालें। / Since (x-2-9x+20=(x-4)(x-5)), (x=4) or (x=5). Exam tip: find zero values from factors.
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Which values make \(x^2+x-12\) equal to zero?
A. (3) और (-4)(3) and (-4)
(x-2+x-12=(x+4)(x-3)) है इसलिए मान (-4) और (3) हैं। परीक्षा में विकल्पों में क्रम से भ्रमित न हों। / Since (x-2+x-12=(x+4)(x-3)), the values are (-4) and (3). Exam tip: do not get confused by the order in options.
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What is the difference between \(x^2+2x+1\) and \(x^2-2x+1\)?
B. (4x)
घटाने पर \(x^2\) और (1) कट जाते हैं और (4x) बचता है। परीक्षा में समान पदों को अलग अलग घटाएं। / On subtracting, \(x^2\) and (1) cancel, leaving (4x). Exam tip: subtract like terms separately.
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