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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If (p(x)=x-3+ax+b), (p(1)=6), and (p(-2)=-9), what is the value of (a)?
C. (3)
शर्तों से (a+b=5) और (-2a+b=-1) मिलते हैं। घटाने पर (3a=6) नहीं बल्कि (3a=6), इसलिए (a=2)। / The conditions give (a+b=5) and (-2a+b=-1). Subtracting gives (3a=6), so (a=2).
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For what value of (r) can ((r+4)x-3+(r-1)x-2+9) become a constant polynomial?
D. ऐसा कोई मान नहींNo such value
अचर बहुपद के लिए (r+4=0) और (r-1=0) दोनों चाहिए, जो साथ संभव नहीं हैं। सभी चर वाले पद हटने चाहिए। / For a constant polynomial, both (r+4=0) and (r-1=0) are needed, which is impossible together. All variable terms must vanish.
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If (p(x)=x-2-4x-12), what is the value of (p(6)-p(-2))?
A. (0)
(p(6)=0) और (p(-2)=0), इसलिए अंतर (0) है। दोनों मान अलग निकालकर ही घटाएं। / (p(6)=0) and (p(-2)=0), so the difference is (0). Find both values separately before subtracting.
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Which option correctly proves (p(4)=0) for (p(x)=x-3-64)?
A. \(4^3-64=0\)
(p(4)=43-64=64-64=0)। शून्य सिद्ध करने के लिए सही मान को सही जगह रखें। / (p(4)=43-64=64-64=0). To prove a zero, substitute the correct value in the correct place.
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What is (p(1)) for (p(x)=x-4-x-3+x-2-x+1)?
B. (1)
(p(1)=1-1+1-1+1=1)। वैकल्पिक संकेतों को क्रम से जोड़ें। / (p(1)=1-1+1-1+1=1). Add alternating signs in order.
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If (p(x)=5x-2+bx+c), (p(0)=-4), and (p(1)=3), what is (b)?
B. (2)
(p(0)=c=-4) और (p(1)=5+b-4=3), इसलिए (b=2)। पहले (x=0) से अचर पद निकालें। / (p(0)=c=-4) and (p(1)=5+b-4=3), so (b=2). First use (x=0) to find the constant term.
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What is the value of (p(4)+p(5)) for (p(x)=x-2-9x+20)?
A. (0)
(p(4)=0) और (p(5)=0), इसलिए योग (0) है। दोनों मान इस बहुपद के शून्य हैं। / (p(4)=0) and (p(5)=0), so the sum is (0). Both values are zeros of this polynomial.
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If (p(x)=x-2-49), which value is correct for (p(a)=0)?
C. (a=7)
(p(7)=49-49=0)। \(x^2-49\) के शून्य (7) और (-7) हैं। / (p(7)=49-49=0). The zeros of \(x^2-49\) are (7) and (-7).
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Which value is a zero of (p(x)=16x-2-24x+9)?
A. \(\frac{3}{4}\)
(16x-2-24x+9=(4x-3)2), इसलिए शून्य \(x=\frac{3}{4}\) है। पूर्ण वर्ग पहचानें। / (16x-2-24x+9=(4x-3)2), so the zero is \(x=\frac{3}{4}\). Recognize the perfect square.
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If (x=1) and (x=-2) are both zeros of (p(x)=x-3+ax-2+bx+18), what is (a+b)?
A. (-19)
(p(1)=0) से (1+a+b+18=0), इसलिए (a+b=-19)। पूछे गए योग के लिए यह शर्त सीधे पर्याप्त है। / From (p(1)=0), (1+a+b+18=0), so (a+b=-19). This condition is directly enough for the asked sum.
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