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Lt(xto0)(x^(2))/(int(0)^(x)Tan^(-1)tdt)...

`Lt_(xto0)(x^(2))/(int_(0)^(x)Tan^(-1)tdt)`

A

2

B

`1/2`

C

`-2`

D

4

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. If I(n)=int(0)^(pi//4) tan^(n) x dx then {:(" " Lt),(n rarr oo):}n(I(n...

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  2. I(m, n)= int(0)^(1) x^(m) (ln x)^(n) dx=

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  3. Lt(xto0)(x^(2))/(int(0)^(x)Tan^(-1)tdt)

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  4. {:(" " Lt),(x rarr 0):} (int(0)^(x^(2))sec^(2) t dt)/(x sin x) =

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  5. Let f:RtoR be a differentiable function having f(2)=6,f'(2)=(1)/(48).T...

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  6. Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in...

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  7. If I(1) = int(1)^(2)(dx)/(sqrt(1+x^(2))) and I(2)= int(1)^(2) (dx)/(x)...

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  8. If I(1)= int(0)^(3pi) f( sin^(2) x)dx and I(2)= int(0)^(pi) f(sin^(2)x...

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  9. I= int(0)^(1)e^(x^(2))dx rArr

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  10. If I(1) = int(0)^(1) 2^(x^(2))dx, I(2) = int(0)^(1) 2^(x^(3))dx, I(3) ...

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  11. If [x] denotes the greatest integer less than or equal to x then int(1...

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  12. int(0)^(oo)[(2)/(e^(x))]dx=

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  13. Let I = int(0)^(1) (sin x)/(sqrt(x)) dx and J= int(0)^(1) (cos x)/(sqr...

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  14. Which of the following is true Statement-I : int(0)^(2pi) sqrt((1-cos2...

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  15. Which of the following are false : Statement-I : (int(0)^(pi//2) (sq...

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  16. Which of the following are true: I : int(0)^(4) sqrt(x^(2)-4x +4)dx=...

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  17. Arrange the following according to their values in ascending order A...

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  18. If 2 int(0)^(1) tan^(-1) x dx = int(0)^(1) cot^(-1) (1- x+x^(2))dx, th...

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  19. Arrange the following according to their values in ascending order A...

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  20. Match the following : {:(" LIST - I","LIST - II"),("I)" int(0)^(2)|...

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