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underset(nrarroo)("lim")[(1+(1)/(n^(2)))...

`underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(n^(2))/(n^(2)))]^(1//n)` is equal to :

A

`(e^(pi//2))/(2e^(2))`

B

`2 e^(2)e^(pi//2)`

C

`(2)/(e^(2)) e^(pi//2)`

D

none of these

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Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. If int(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

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  2. The value of integral int(1)^(e) (log x)^(3)dx , is

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  3. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

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  4. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  5. underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(...

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  6. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

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  7. If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x...

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  8. The value of the integral int(0)^(1) cot^(-1) (1-x+x^(2))dx, is

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  9. The integral int(-1)^(1) (|x+2|)/(x+2)dx is equal to

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  10. Let I= int(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral ...

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  11. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  12. int(pi)^(10n) |sin x|dx is equla to

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  13. about to only mathematics

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  14. If int(0)^(oo)e^(-ax)dx=(1)/(a)," then "int(0)^(oo)x^(n)e^(-ax)dx is

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  15. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

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  16. If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int0^1f(x)dx=(2A...

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  17. If I(m,n)= int(0)^(1) x^(m) (ln x)^(n)dx then I(m,n) is also equal to

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  18. lim(n->oo)(1^(99)+2^(99)+3^(99)+.......n^(99))/(n^(100))=

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  19. I(n)=int(0)^(pi//4)tan^(n)xdx, then lim(n to oo)n[I(n)+I(n+2)] equals ...

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  20. Let int(0)^(a)f(x)dx = lambda and int(0)^(a)f(2a-x)dx=mu. Then int(0)^...

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