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Let xn = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^...

Let `x_n = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^2 ...... (1 - 1/((n(n + 1))/2))^2, n ge 2` Then the value of `underset(nrarrinfty)(lim) x_n` is

A

10

B

12

C

8

D

16

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. Let F:RrarrR be a thrice differentiable function. Suppose that F(1)=0,...

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  2. The integral int2^4 (logx^2)/((logx^2)+log(36-12x+x^2)) dx is equal to...

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  3. Let xn = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^2 ...... (1 - 1/((n(n + 1))/2)...

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  4. underset(nrarrinfty)lim (sqrt1+sqrt2+.......+sqrt(n-1))/(nsqrtn) = ?

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  5. Let f : Rrarr R be a continuous function which satisfies f(x) = int0^x...

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  6. Let xn = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^2 ...... (1 - 1/((n(n + 1))/2)...

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  7. Let f(x) denote the fractional part of a real number x. Then the value...

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  8. Let f : (0,infty) rarr R be given by f(x) = int(1/x)^(x) e^-(t + 1/t...

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  9. Let f : [a , b]rarr [1, infty] be a continuous function and let g : R ...

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  10. The value of int0^1 4x^3 {d^2/(dx^2) (1 - x^2)^5 } dx is

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  11. The following integral int(pi/4)^(pi/2) (2 cosec x)^17 dx is equal to

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  12. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

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  13. Given that for each a in (0,1), underset(h rarr 0)(lim) inth^(1 - h)...

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  14. Given that for each a in (0,1), underset(h rarr 0)(lim) inth^(1 - h)...

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  15. Match List - I with List - II

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  16. The integral int0^pi sqrt(1 + 4 sin^2(x/2) - 4 sin (x/2)) dx equals :

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  17. If I = int0^2 (e^x)^4 (x - alpha) dx = 0, then alpha lies in the inter...

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  18. Suppose M = int0^(pi/2) cosx/(x+2) dx , N = int0^(pi/4) sinxcosx/(x+1)...

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  19. Let f(x) = max{x + absx, x - [x]}, where [x] de notes the greatest int...

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  20. Let f(x) = {(int0^x abs(1 - t) dt , x gt 1),(x - 1/2 , x le 1):} Then

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