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If varphi(x) is a polynomial function an...

If `varphi(x)` is a polynomial function and `varphi^(prime)(x)>varphi(x)AAxgeq1a n dvarphi(1)=0,` then `varphi(x)geq0AAxgeq1` `varphi(x)

A

`phi(x)ge 0 AA x ge1`

B

`phi(x)lt 0 AA x ge1`

C

`phi(x)=0 AA x ge1`

D

None of these

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KVPY PREVIOUS YEAR-MOCK TEST 8-EXERCISE
  1. if A(z1),B(z2),C(z3),D(z4) lies on |z|=4 (taken in order) , where z1...

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  2. If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)A...

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  3. Let (a1, a2, a3, a4, a5) denote a re-arrangement of (1, -4, 6, 7, -10)...

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  4. The period of the function f(x)=cos2pi{2x}+ sin2 pi {2x}, is ( ...

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  5. Prove that sin theta = x + p/x is possible for real x if p le 1/4

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  6. If |vec a + vecb| = |vec a - vecb| , then which one of the following i...

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  7. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y ...

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  8. Given that the sum of two non-negative quantities is 200, the probabil...

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  9. If x^2+ax+b^2=0 has real roots then which of these is a possible order...

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  10. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1, then (gof)(x...

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  11. The area of the region enclosed by the curve |y|=-(1-|x|)^2+5, is

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  12. If (mi , 1/mi), i= 1, 2, 3, 4 are four distinct points on a circle, sh...

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  13. The line passing through the extremity A of the major exis and extremi...

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  14. Number of integral points (integral points means both the co-ordinates...

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  15. The domain of the funciton f(x) given by 3^(x) + 3^(f) = "min" (2t^(3...

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  16. The sum of the square of the length of the chord intercepted by the li...

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  17. The value of int0^1lim(n->oo)sum(k=0)^n(x^(k+2)2^k)/(k!)dx is:

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  18. If X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N} , wh...

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  19. The domain of f(x)=(log(2)(x+3))/(x^(2)+3x+2) is

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  20. The least possible value of a for which (x^3-6x^2+11 x-6)/(x^3+x^2-10 ...

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