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Which of the following are false : Sta...

Which of the following are false :
Statement-I : (`int_(0)^(pi//2) (sqrt(cos x))/(sqrt(cos x + sqrt(sin x)))= pi/2`
Statement-II : `int_(0)^(pi//2) log(tan x) dx=1`
Statement-III: `int_(0)^(pi//2) log sin x dx = - pi log 2`

A

Only I, II

B

Only II, III

C

Both I and II

D

All the three

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. I= int(0)^(1)e^(x^(2))dx rArr

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  2. If I(1) = int(0)^(1) 2^(x^(2))dx, I(2) = int(0)^(1) 2^(x^(3))dx, I(3) ...

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  3. If [x] denotes the greatest integer less than or equal to x then int(1...

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  4. int(0)^(oo)[(2)/(e^(x))]dx=

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  5. Let I = int(0)^(1) (sin x)/(sqrt(x)) dx and J= int(0)^(1) (cos x)/(sqr...

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  6. Which of the following is true Statement-I : int(0)^(2pi) sqrt((1-cos2...

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  7. Which of the following are false : Statement-I : (int(0)^(pi//2) (sq...

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  8. Which of the following are true: I : int(0)^(4) sqrt(x^(2)-4x +4)dx=...

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  9. Arrange the following according to their values in ascending order A...

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  10. If 2 int(0)^(1) tan^(-1) x dx = int(0)^(1) cot^(-1) (1- x+x^(2))dx, th...

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  11. Arrange the following according to their values in ascending order A...

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  12. Match the following : {:(" LIST - I","LIST - II"),("I)" int(0)^(2)|...

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  13. If I(n) = int(0)^(pi//2) x^(n).cos x dx then the value of I(9)+72I(7)=

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  14. int(-pi//4)^(pi//4)((x+pi//4)/(2-cos2x))dx=

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  15. For x in R, x != 0, if y(x) is a differentiable function such that x i...

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  16. Lt(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=

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  17. int(-2)^(3) |1-x^(2)|dx=

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  18. Evaluate (iii) int(0)^(pi)(x sin^(3)x)/(1+cos^(2)x)dx

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  19. Match the following {:("List - 1","List - II"),("I) "int(-1)^(1)x|x|d...

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  20. int(0)^(pi) (x dx)/(4 cos^(2) x + 9 sin^(2) x)=

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