Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 511-520 of 600 questions.
If (p(x)=x-2+ax+b), (p(-2)=0), and (p(5)=0), what is (a+b)?
A. (-13)
शून्य (-2) और (5) हैं, इसलिए बहुपद ((x+2)(x-5)=x-2-3x-10) है। अतः (a+b=-3-10=-13)। / The zeros are (-2) and (5), so the polynomial is ((x+2)(x-5)=x-2-3x-10). Hence (a+b=-3-10=-13).
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If (p(x)=x-2+ax+b), (p(-4)=0), and (p(1)=0), what is the value of (b)?
A. (-4)
शून्य (-4) और (1) होने पर बहुपद ((x+4)(x-1)=x-2+3x-4) है। इसलिए (b=-4)। / With zeros (-4) and (1), the polynomial is ((x+4)(x-1)=x-2+3x-4). Hence (b=-4).
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Which expression is not a polynomial because the variable has a fractional power?
C. \(x^{\frac{3}{2}}+x+1\)
\(x^{\frac{3}{2}}\) में चर की घात भिन्न है, इसलिए यह बहुपद नहीं है। बहुपद में घातें अऋणात्मक पूर्णांक होती हैं। / In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.
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If (a=0), \(b\ne0\), and \(c\ne0\) in (p(x)=ax-5+bx-4+cx-3+d), what will be the degree of (p(x))?
B. (4)
(a=0) से \(x^5\) पद हट जाता है और \(b\ne0\) से \(x^4\) पद बचता है। इसलिए घात (4) है। / Since (a=0), the \(x^5\)-term vanishes, and since \(b\ne0\), the \(x^4\)-term remains. So the degree is (4).
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What is the sum of all coefficients in (p(x)=8x-4-3x-3-4x+2)?
C. (3)
सभी गुणांकों का योग (8-3+0-4+2=3) है। यह (p(1)) के बराबर भी होता है। / The sum of all coefficients is (8-3+0-4+2=3). It is also equal to (p(1)).
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If the sum of all coefficients of (p(x)=4x-4+kx-3-6x+1) is (5), what is (k)?
C. (6)
गुणांकों का योग (4+k+0-6+1=k-1) है, इसलिए (k-1=5) और (k=6)। गुणांकों का योग (p(1)) से मिलता है। / The sum of coefficients is (4+k+0-6+1=k-1), so (k-1=5) and (k=6). The sum of coefficients is found by (p(1)).
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What is the sum of coefficients of odd-power terms in (p(x)=6x-6-5x-5+4x-3-2x-2+x-7)?
B. (0)
विषम घातों \(x^5\), \(x^3\) और (x) के गुणांक (-5), (4) और (1) हैं। उनका योग (0) है। / The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (-5), (4), and (1). Their sum is (0).
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What is the constant term in ((4x+3)\(x^2-2x+5\))?
D. (15)
अचर पद केवल \(3\cdot5=15\) से आता है। अचर पद के लिए अचर भागों का गुणन देखें। / The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
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What is the simplified polynomial form of ((2x+5)2-(2x-1)2)?
B. (24x+24)
अंतर के वर्ग से ((6)(4x+4)=24x+24) मिलता है। पहचान (a-2-b-2=(a-b)(a+b)) तेज तरीका है। / By difference of squares, ((6)(4x+4)=24x+24). The identity (a-2-b-2=(a-b)(a+b)) is a quick method.
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If (p(x)=x-3+ax+b), (p(2)=13), and (p(-1)=-7), what is the value of (a+b)?
B. (2)
शर्तों से (2a+b=5) और (-a+b=-6) मिलते हैं, इसलिए \(a=\frac{11}{3}\) और \(b=-\frac{7}{3}\)। अतः \(a+b=\frac{4}{3}\) नहीं बल्कि विकल्पों में कोई सही नहीं होता। / The conditions give (2a+b=5) and (-a+b=-6), so \(a=\frac{11}{3}\) and \(b=-\frac{7}{3}\). Hence \(a+b=\frac{4}{3}\), so none of the listed choices is correct.
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