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The value of lim(n to oo) (1^(p)+2^(p)+...

The value of `lim_(n to oo) (1^(p)+2^(p)+3^(p)+…+n^(p))/(n^(p+1))` is -

A

`(1)/(p+1)`

B

`(1)/(1-p)`

C

`(1)/(p+2)`

D

`(1)/(p)`

Text Solution

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The correct Answer is:
A
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 4
  1. If f(x) is a differentiable function for all x gt 0 and lim(y to x)(y...

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  2. If y^(2)=4ax, then the value of (d^(2)y)/(dx^(2))*(d^(2)x)/(dy^(2)) i...

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  3. The value of lim(n to oo) (1^(p)+2^(p)+3^(p)+…+n^(p))/(n^(p+1)) is -

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  4. The value of int(0)^(1.5)[x^(2)]dx is -

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  5. If I(n)=int(0)^((pi)/(4)) tan^(n)x dx, then the value of lim(n to oo...

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  6. The value of int(0)^((pi)/(2)) (sinx dx)/(sin x+cos x) is equal to -

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  7. The value of the integral int(-(pi)/(7))^((pi)/(7))x^(3)sin^(2)x dx is...

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  8. int"cosec"^(4)x dx is equal to -

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  9. The value of int(dx)/(2sqrt(x)(x+1)) is -

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  10. The value of the integral int(0)^(1) (dx)/( x^(2)+2x cos alpha +1) is...

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  11. Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt 0, If int(1)^(4) (3)/(x) ...

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  12. The value of int(0)^(1000)e^(x-[x])dx is equal to -

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  13. int(0)^(2a)f(x)dx is equal to -

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  14. int sin^(3)x cos x dx is equal to -

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  15. The value of int(0)^(1)sin[2tan^(-1)sqrt((1+x)/(1-x))]dx is equal to -

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  16. The value of int sqrt(1+"sin"(x)/(4))dx is equal to -

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  17. The value of int((1)/(e ))^(e )|log x|dx is equal to -

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  18. If f(t) is an odd function, then int(0)^(x)f(t) dt is -

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  19. The value of int((pi)/(4))^((3pi)/(4))(dx)/(1+cosx) is -

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  20. The solution of the differential equation (x+2y^(3))(dy)/(dx)=y is -

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