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If f''(x) = (2x)/((1+x^(2))^(2)) where...

If `f''(x) = (2x)/((1+x^(2))^(2))` where `f'(x)=1, f(x)=2` when x=0, when the value of f(x) is -

A

`x+1+tan^(-1)x`

B

`2(x+1)-tan^(-1)x`

C

`2(x+1)+tan^(-1)x`

D

`x+1-tan^(-1)x`

Text Solution

Verified by Experts

The correct Answer is:
B
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 7
  1. The value of int sqrt(x)e^(sqrt(x))dx is -

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  2. The value of int(-1)^(1)|1-x| dx is equal to -

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  3. The value of int(0)^((pi)/(8))cos^(3)4 theta d theta is equal to -

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  4. The value of int(dx)/(sin x cos x) is equal to -

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  5. If int (e^(x)(1+sinx))/(1+cos x)dx=e^(x)f(x)+c, then the value of f(x...

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  6. The value of int(0)^(pi) (cosx dx)/(x^(4)+(pi-x)^(4)) is equal to -

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  7. The value of int ((e^(x)-e^(-x))dx)/((e^(x)+e^(-x))log(e^(x)+e^(-x)))...

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  8. The value of lim( n to oo) sum(r =1)^(n) (r )/(n^(2))"sec"^(2)(r^(2))/...

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  9. Let f:R to R be a differentiable function and f(1)=4 and f'(1)=2, then...

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  10. The value of int(-2)^(0) [x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)]dx is equal...

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  11. If a gt 0, then the value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x))dx is e...

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  12. The solution of the differential equation (2y-1)dx-(2x+3)dy=0 is -

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  13. The order and degree of the differential equation ((d^(3)y)/(dx^(3)))...

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  14. The integrating factor of the linear differential equation cos^(2)x(dy...

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  15. The general solution of the differential equation (2x-y+1)dx+(2y-x+1)...

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  16. Examine whether the function f given by f(x)= x^2 is continuous at x= ...

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  17. If f''(x) = (2x)/((1+x^(2))^(2)) where f'(x)=1, f(x)=2 when x=0, wh...

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  18. The points of discontinuity of the function f(x)=(2x^(2)+7)/(x^(3)+3x...

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  19. Which one of the following equations represent the differential equati...

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  20. The general solution of the differential equation (dy)/(dx)+1="cosec"...

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