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If I(m)=int(1)^(e )(log(e)x)^(m)dx, then...

If `I_(m)=int_(1)^(e )(log_(e)x)^(m)dx`, then the value of `(I_(m)+mI_(m-1))` is -

A

`lt 3`

B

`=3`

C

`gt 3`

D

none of these

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The correct Answer is:
A
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 3
  1. The value of the integral int(1)^(e ) (log x)^(2)dx is -

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  2. The value of int(dx)/(e^(x)+e^(-x)) is equal to -

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  3. For an integrable function f(x) in [-3, 3], int(-3)^(3) f(x)dx=0 when...

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  4. If I(m)=int(1)^(e )(log(e)x)^(m)dx, then the value of (I(m)+mI(m-1)) i...

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  5. If (d)/(dx)f(x)=g(x), then the value of int(a)^(b)f(x)g(x)dx is -

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  6. The value of the integral int(0)^(1) x(1-x)^(n)dx is -

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  7. The value of lim(n to oo) sum(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -

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  8. The value of int(0)^(1) (log(1+x)dx)/(1+x^(2)) is -

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  9. The value of lim(x to 0)(int(0)^(x^(2))sec^(2)t dt)/(x sin x) is equal...

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  10. If phi (x)=f(x)+x f'(x), then the value of int phi (x) dx is -

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  11. The value of the integral int(0)^(2pi)(sin x+|sin x|)dx is equal to -

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  12. The solution of the differential equation cosx siny dx+sinx cosy dy=0...

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  13. If m and n denote respectively the order and degree of a differential ...

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  14. The solution of the differential equation (dy)/(dx)=(x-y)/(x+y) is -

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  15. The solution of the differential equation y-x(dy)/(dx)=a(y^(2)+(dy)/(...

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  16. The integrating factor of the differential equation x(dy)/(dx)+(x-1)y...

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  17. The solution of differential (dy)/(dx)=(y)/(x)+(phi((y)/(x)))/(phi'( ...

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  18. The order and degree of the differential equation of the family of all...

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  19. If y(t) is the solution of the differential equation (t+1)(dy)/(dt)-t...

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  20. If f(x)=|x-3|+|x-4|, then in the interval 0 le x le 5, the function f...

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