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The value of the integral int(-pi//2)^...

The value of the integral
`int_(-pi//2)^(pi//2)(sin^(2)x)/(1+e^(x))dx`
is

A

`(pi)/(6) `

B

`(pi)/(4)`

C

`(pi)/(2)`

D

`(pi^2)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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KVPY PREVIOUS YEAR-QUESTION PAPER 2020-PART-I (MATHEMATICS)
  1. Consider the following statements : I. lim(n to oo) ( 2^n +(-2)^n)/...

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  2. Consider a regular 10-gon with its vertices on the unit circle. With o...

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  3. The value of the integral int(-pi//2)^(pi//2)(sin^(2)x)/(1+e^(x))dx ...

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  4. Let RR be the set of all real numbers and f(x) = sin^(10) x ( cos^...

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  5. A person standing on the top of a building of height 60sqrt(3) feel ob...

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  6. Assume that 3.313 le pi le 3.15. The integer closest to the value of s...

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  7. The maximum value of the function ƒ(x) = e^x + x ln x on the interval ...

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  8. Let A be a 2 xx 2 matrix of the form A = [[a,b],[1,1]], where a, b are...

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  9. Let A = (a(ij))(1 le I, j le 3) be a 3 xx 3 invertible matrix where ea...

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  10. Let x, y be real numbers such that x gt 2y gt 0 and 2log (x-2y) = lo...

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  11. Let (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1(b lt a). Be an ellipse with ...

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  12. Let A denote the set of all real numbers x such that x^(3) - [x]^(3) =...

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  13. S= lim(nrarroo) sum(k=0)^n 1/sqrt(n^2 + k ^2)

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  14. Let RR be the set of all real numbers and ƒ : RR to RR be a contin...

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  15. Let f(x) = {{:((x)/(sin x) ",",x in "(0,1)"),(1",",x=0):} Consider...

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  16. The value of the integral int(1)^(3)((x-2)^(4)sin^(3)(x-2)+(x-2)^(20...

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  17. In a regular 15-sided polygon with all its diagonals drawn, a diagonal...

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  18. Let M = 2^(30)-2^(15)+1, and M^(2) be expressed in base 2. The number ...

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  19. Let ABC be a triangle such that AB = 15 and AC = 9. The bisector of an...

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  20. The figur in the complex plane given by 10zbar(z) - 3(z^(2)+bar(z)^(...

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