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For a real number x let `[x]` denote the largest integer less than or equal to x and `{x}=x-[x]`. The possible integer value of n for which `int_(1)^(n)[x]{x}dx` exceeds 2013 is

A

63

B

64

C

90

D

91

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The correct Answer is:
D
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KVPY PREVIOUS YEAR-QUESTION PAPER 2013-PART-I ( MATHEMATICS)
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  2. Let n be a positive integer such that log2 log 2 log2 log2 log2 (n) lt...

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  3. Let omega be a cube root of unity not equal to 1. Then the maximum pos...

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  4. If a, b are positive real numbers such that the lines ax + 9y = 5 and ...

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  5. Two line segments AB and CD are constrained to move along the x and y ...

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  6. Consider a triangle ABC in the xy -plane with vertices A = (0,0), B = ...

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  7. Let ABC be an acute-angled triangle and let D be the midpoint of BC. I...

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  8. The angles alpha , beta , gamma of a triangle satisfy the equations 2...

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  9. Let f : R to R be a function such that lim(x to oo) f(x) = M gt 0. T...

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  10. For x , t in R let p(t) (x)= ( sin t) x^(2) - (2 cost ) x + sin ...

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  11. Let f(x) = sqrt(2-x-x^(2)) and g(x) = cos x . Which of the following ...

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  12. For real x with -10 le x le 10 define f(x) = int(-10)^(x) 2^([t]) dt...

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  13. For a real number x let [x] denote the largest integer less than or eq...

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  14. The area bounded by the curve y = cos x, the line joining (-pi //4 , c...

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  15. A box contains coupons labeled 1, 2, 3....n. A coupon is picked at ran...

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  16. Let n ge 3. A list of numbers 0 le x1 le x2 le … le xn has mean mu a...

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  17. Let vec(v1) , vec(v2) , vec(v3), vec(v4) be unit vectors in the xy-pl...

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  18. The number of integers n with 100 le n le 999 and containing at most t...

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  19. For an integer n let Sn = {n + 1, n + 2, ....., n + 18}. Which of the ...

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  20. Let P be a closed polygon with 10 sides and 10 vertices (assume that t...

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