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 591-600 of 600 questions.
If (p(x)=x-2+5x+6) and (r(x)=p(-x)), what are the zeroes of (r(x))?
A. (2,3)
(p(x)) के शून्यक (-2) और (-3) हैं। (p(-x)=0) के लिए (-x=-2) या (-x=-3), इसलिए (x=2,3)। / The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).
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If (p(x)=x-2-7x+12), at which points will the graph of (p(x)) cut the (x)-axis?
A. ((3,0),(4,0))
(x-2-7x+12=(x-3)(x-4)), इसलिए शून्यक (3) और (4) हैं। (x)-अक्ष पर बिंदु ((3,0)) और ((4,0)) होंगे। / (x-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).
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If (p(x)=x-2+2x+c) has no real zero, which condition on (c) is correct?
A. (c>1)
कोई वास्तविक शून्यक नहीं होने के लिए विविक्तकर (4-4c<0) चाहिए। इससे (c>1) मिलता है। / For no real zero, the discriminant must satisfy (4-4c<0). This gives (c>1).
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If (p(x)=x-2-6x+8), which monic polynomial has the squares of its zeroes as zeroes?
A. \(x^2-20x+64\)
मूल शून्यक (2) और (4) हैं, इसलिए नए शून्यक (4) और (16) हैं। नया बहुपद \(x^2-20x+64\) है। / The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).
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If (p(x)=2x-2+x-6), what is the value of (2p(1)-p(-2))?
A. -(6)
(p(1)=2+1-6=-3) और (p(-2)=8-2-6=0)। इसलिए (2p(1)-p(-2)=-6)। / (p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).
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If (p(x)=x-2+px+q) and (p(1)=0,\ p(2)=0), what is (p+q)?
A. -(1)
शून्यक (1) और (2) हैं, इसलिए बहुपद \(x^2-3x+2\) है। अतः (p=-3,\ q=2) और (p+q=-1)। / The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).
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If the zeroes of (p(x)=x-2-ax+b) are (a) and (b), which relation is correct?
A. (a+b=a) और (ab=b)(a+b=a) and (ab=b)
शून्यकों का योग बहुपद से (a) और गुणनफल (b) है। इसलिए यदि शून्यक (a,b) हैं, तो (a+b=a) और (ab=b) होना चाहिए। / The sum of zeroes from the polynomial is (a) and the product is (b). Hence if the zeroes are (a,b), then (a+b=a) and (ab=b).
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If (p(x)=x-3-1), which of the following is a linear factor?
A. (x-1)
(x-3-1=(x-1)\(x^2+x+1\)) है। इसलिए (x-1) रैखिक गुणनखंड है। / (x-3-1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.
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If (p(x)=x-2-8x+16), what is the value of (p(4+t))?
A. \(t^2\)
(p(x)=(x-4)2), इसलिए (p(4+t)=t-2)। ऐसे प्रश्नों में पहले पूर्ण वर्ग बनाना आसान होता है। / (p(x)=(x-4)2), so (p(4+t)=t-2). In such questions, first form a perfect square.
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If (p(x)=x-2-4x+6), what is the value of (p(x+1)-p(x))?
A. (2x-3)
(p(x+1)=x-2-2x+3) और (p(x+1)-p(x)=2x-3) है। ऐसे प्रश्नों में पहले (x+1) को सावधानी से प्रतिस्थापित करें। / (p(x+1)=x-2-2x+3) and (p(x+1)-p(x)=2x-3). In such questions, substitute (x+1) carefully first.
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