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Evalute :lim(ntooo)[(1^2)/(n^3+1^3)+(2^2...

Evalute :`lim_(ntooo)[(1^2)/(n^3+1^3)+(2^2)/(n^3+2^3)+(3^2)/(n^3+3^3)+".........."+(1)/(2n)]`.

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The correct Answer is:
`=(1)/(3)log_(e)^2`
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CHHAYA PUBLICATION-QUESTION PAPER -2018-WBJEE
  1. Evalute :lim(ntooo)[(1^2)/(n^3+1^3)+(2^2)/(n^3+2^3)+(3^2)/(n^3+3^3)+"....

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  2. The approximate value of sin31^(@) is

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  3. Let f1(x)=e^x,f2(x)=e^(f1(x)),"........",f(n+1)(x)=e^(fn(x)) for all n...

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  4. f(x)=|x| is increasing in

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  5. Let f(x)=3x^(10)-7x^8+5x^6-21x^3+3x^2-7. Then lim(hto0)(f(1-h)-f(1))/(...

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  6. Let f:[a,b]toR be such that f is differentiable in (a,b), f is continu...

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  7. Let f:Rto R be a twice continuously differentiable function such that ...

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  8. If inte^(sinx)[(xcos^3x-sinx)/(cos^2x)]dx=e^(sinx)*f(x)+c, where c is ...

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  9. If intf(x)sinxcosxdx=(1)/(2(b^2-a^2))logf(x)+c, where c is the constan...

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  10. If M=int0^((pi)/(2))(cosx)/(x+2)dx,N=int0^((pi)/(4))(sinxcosx)/((x+1)^...

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  11. The value of the integral I=int((1)/(2014))^(2014)(tan^(-1)x)/(x)dx is

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  12. Let I= int(pi//4)^(pi//3) (sinx)/(x)dx. Then

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  13. The value of I=int((pi)/(2))^((5pi)/(2))(e^(tan^(-1))(sinx))/(e^(tan^(...

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  14. The value of lim(ntooo)(1)/(n)[sec^2""(pi)/(4n)+sec^2""(2pi)/(4n)+.......

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  15. The differential equation representing the family of curves y^2=2c(x+s...

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  16. Let y(x) be a solution of (1+x^2)"" (dy)/(dx)+2xy-4x^2=0 and y(0)=-1. ...

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  17. The law or motion of a body moving along a straight line is x=(1)/(2)...

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  18. Number of common tangents of y=x^2" and " y=-x^2+4x-4 is

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  19. If |{:(-1,7,0),(2,1,-3),(3,4,1):}|=A" then"|{:(13,-11,5),(-7,-1,25),(-...

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  20. If ar=(cos2rpi+isin2rpi)^((1)/(9)), then the value of |{:(a1,a2,a3),(a...

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  21. If Sr=|{:(2r,x,n(n+1)),(6r^2-1,y,n^2(2n+3)),(4r^3-2nr,z,n^3(n+1)):}|, ...

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