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int(-4)^(4) (sin^(-1)( sinx)+ cos^(-1)(c...

`int_(-4)^(4) (sin^(-1)( sinx)+ cos^(-1)(cos x))/((1+x^(2))(1+[(x^(2))/(17)])) dx= log (((1+pi^(2)))/sqrt(a)) `
`bpi" tan"^(-1)((c-pi)/(1+c pi))` (where, [.] denotes greatest inteher function), then the number of ways in which `a-(2b+c)` distinct object can distributed among `(a-5)/(c)` persons equally , is

A

`(9!)/((3!)^(3))`

B

`(12!)/((140^(3))`

C

`(15!)/((5!)^(3))`

D

`(10!)/((6!)^(3))`

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The correct Answer is:
A
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. Let f(x)=x^(2) +ax + b and the only solution of the equation f(x)= mi...

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  2. Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^ycostdt=0,then evaluate (dy)/(...

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  3. int(-4)^(4) (sin^(-1)( sinx)+ cos^(-1)(cos x))/((1+x^(2))(1+[(x^(2))/(...

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  4. The value of the definite integral int (0)^(infty) (dx)/((1+x^(a))(1...

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  5. The value of the definite integral overset(3pi//4)underset(0)int(1+x)s...

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  6. Let C(n)= int(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then ...

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  7. If [int0^1(dt)/(t^2+2tcosalpha+1)]x^2-[int- 3^3(t^2sin2t)/(t^2+1)dt]x-...

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  8. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

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  9. If a, b and c are real numbers, then the value of underset(trarr0)(lim...

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  10. The value of ("lim")(nvecoo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+s...

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  11. Let f(x) =int-1^x e^(t^2) dt and h(x)=f(1+g(x)), where g (x) is define...

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  12. If f be a function satisfying f(x+y)=f(x)+f(y),AAx,yinR. If f(1) = k, ...

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  13. Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4)) and g be the inverse of f. ...

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  14. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

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  15. Let f be a positive function. Let I(1)=int(1-k)^(k)x f[x(1-x)]dx , I(...

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  16. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

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  17. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx where a is positive r...

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  18. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

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  19. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

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  20. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

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