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The value of: lim(n to infty) sum(r=1)...

The value of:
`lim_(n to infty) sum_(r=1)^(n) r^(2)/(r^(3) + n^(3))` is:

A

`pi/4`

B

`pi/2`

C

`1/3 log_(e) 2`

D

`1/2 log_(e) 2`

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WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2011-MULTIPLE CHOICE QUESTIONS
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  2. The area enclosed between y^(2) = x and y=x is:

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  3. Let f(x) = x^(3) e^(-3x) , x gt 0. Then the maximum value of f(x) is:

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  4. The area bounded by y^(2) = 4x and x^(2) = 4y is:

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  5. The acceleration of a particle starting from rest moving in a straight...

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  6. The solution of: (dy)/(dx) = y/x + tan y/x is:

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  7. Integrating Factor (I.F). Of the differential equation: (dy)/(dx) -...

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  8. The differential equation of y=ae^(bx) (a & b are parameters) is:

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  9. The value of: lim(n to infty) sum(r=1)^(n) r^(2)/(r^(3) + n^(3)) is:

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  10. The value of int(0)^(pi) sin^(50)x cos^(49) x dx is:

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  11. int 2^(x) [f'(x) + f(x) (log 2)] dx is

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  12. Let f(x) = tan^(-1) x. Then f'(x) + f''(x) is =0, when x is equal to:

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  13. If y= tan^(-1) ((sqrt(1+x^(2))-1)/x) , then y'(1)=

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  14. The value of lim(x to 1) (x+x^(2)+ ….. + x^(n) -n)/(x-1) is:

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  15. lim( x to 0) (sin (pi sin^(2)x))/x^(2) =

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  16. If the function: f(x) = {{:((x^(2)-(A+ 2)x+A)/(x-2), "for", x ne 2),...

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  17. f(x) ={{:([x]+[-x], "when" , x ne 2),(lambda, "when", x =2):}, If f(x)...

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  18. The even function of the following is:

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  19. If f(x + 2y, x-2y) =xy, then f(x,y) is equal to:

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  20. The locus of the middle points of all chords of the parabola, y^2 = 4a...

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