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The value of underset( n rarroo)(lim) un...

The value of `underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(sqrt(n))/(sqrt(r ) (3 sqrt(r)+4)sqrt(n)^(2))` is equal to

A

`1/7`

B

`1/10`

C

`1/14`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, I (2) = int (0) ^(1) 2 ^(x ^(3...

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  2. If u (n) = int (0) ^(pi//2) x ^(n) sin x dx, n in N then the value of ...

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  3. The vlaue of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  4. In = int0^(pi/4) tan^n x dx , then the value of n(l(n-1) + I(n+1)) is

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  5. The value of the integral l = int(0)^(1) x(1-x)^(n) dx is

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  6. Let I (1) = int (0) ^(1) (e ^(x) dx )/( 1 + x) and I (2) = int (0) ^(1...

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  7. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

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  8. If underset(0)overset(100)intf(x) dx = a, then underset(r=1)overset(10...

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  9. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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  10. underset(2-ln3)overset(3+ln3)int(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal...

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  11. If [x] stands for the greatest integer function, the value of overset(...

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  12. Find the value of the function f(x)=1+x+int1^x((lnt)^2+2lnt) dt where ...

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  13. If f(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4) then f^(prime)(2) has th...

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  14. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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  15. If y(x)=\ int(pi^2//16)^(x^2)(cos xdotcossqrt(theta))/(1+sin^2sqrt(the...

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  16. lim( n to oo) (sin ""(pi)/(2n) . sin ""(2pi)/(2n). sin ""(3pi)/(2n)......

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  17. The value of underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(...

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  18. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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  19. Evaluate : lim(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim(n->oo) (1^3+2^3...

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  20. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

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