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 411-420 of 600 questions.
If (p(x)=x-2+ax+b), (p(2)=0), and (p(4)=0), what is (a+b)?
C. (2)
शून्य (2) और (4) हैं, इसलिए बहुपद ((x-2)(x-4)=x-2-6x+8) है। अतः (a+b=-6+8=2)। / The zeros are (2) and (4), so the polynomial is ((x-2)(x-4)=x-2-6x+8). Hence (a+b=-6+8=2).
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If (p(x)=x-2+ax+b), (p(-1)=0), and (p(5)=0), what is the value of (b)?
A. (-5)
शून्य (-1) और (5) होने पर बहुपद ((x+1)(x-5)=x-2-4x-5) है। इसलिए (b=-5)। / With zeros (-1) and (5), the polynomial is ((x+1)(x-5)=x-2-4x-5). Hence (b=-5).
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If (a=0), (b=0), and \(c\ne0\) in (p(x)=ax-4+bx-3+cx-2+d), what will be the degree of (p(x))?
C. (2)
\(x^4\) और \(x^3\) के पद हट जाते हैं, लेकिन \(c\ne0\) से \(x^2\) पद बचता है। इसलिए घात (2) है। / The \(x^4\)- and \(x^3\)-terms vanish, but \(c\ne0\) keeps the \(x^2\)-term. So the degree is (2).
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What is the sum of all coefficients in (p(x)=7x-3-4x-2-2x-1)?
A. (0)
सभी गुणांकों का योग (7-4-2-1=0) है। यह (p(1)) के बराबर भी होता है। / The sum of all coefficients is (7-4-2-1=0). It is also equal to (p(1)).
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If the sum of all coefficients of (p(x)=3x-3+kx-2-7x+2) is (5), what is (k)?
C. (7)
गुणांकों का योग (3+k-7+2=k-2) है, इसलिए (k-2=5) और (k=7)। गुणांकों का योग (p(1)) होता है। / The sum of coefficients is (3+k-7+2=k-2), so (k-2=5) and (k=7). The sum of coefficients is (p(1)).
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What is the sum of coefficients of odd-power terms in (p(x)=5x-5-3x-4+2x-3-x+6)?
C. (6)
विषम घातों \(x^5\), \(x^3\) और (x) के गुणांक (5), (2) और (-1) हैं। उनका योग (6) है। / The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (5), (2), and (-1). Their sum is (6).
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What is the constant term in ((3x-2)\(x^2+5x-1\))?
C. (2)
अचर पद केवल ((-2)(-1)=2) से आता है। अचर पद के लिए अचर भागों का गुणन देखें। / The constant term comes only from ((-2)(-1)=2). For the constant term, multiply the constant parts.
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What is the simplified polynomial form of ((x+6)2-(x-2)2)?
B. (16x+32)
((x+6)2-(x-2)2=((x+6)-(x-2))((x+6)+(x-2))=8(2x+4)=16x+32)। अंतर के वर्ग की पहचान लगाएं। / ((x+6)2-(x-2)2=((x+6)-(x-2))((x+6)+(x-2))=8(2x+4)=16x+32). Use the difference of squares identity.
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If (p(x)=x-3+ax+b), (p(1)=6), and (p(-1)=-4), what is the value of (a)?
C. (4)
शर्तों से (1+a+b=6) और (-1-a+b=-4) मिलते हैं। इन्हें हल करने पर (a=4) मिलता है। / The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).
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If (p(x)=2x-3+rx-2+s), (p(0)=-3), and (p(1)=4), what is (r)?
C. (5)
(p(0)=s=-3) और (p(1)=2+r-3=4), इसलिए (r=5)। पहले (x=0) से अचर पद निकालें। / (p(0)=s=-3) and (p(1)=2+r-3=4), so (r=5). First use (x=0) to find the constant term.
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