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If f(x)=int0^(pi/2)ln(1+xsin^2theta)/(si...

If `f(x)=int_0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0` then :

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RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n f(x) is an odd f...

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  2. The number of values of x in the interval [0,(7pi)/2] satisfying the e...

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  3. If f(x)=int0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0 the...

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  4. The term independent of x in the expansion of (x-1/x)^(4) (x+1/x)^(3) ...

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  5. The value of the definite integral int2^4x(3-x)(4+x)(6-x)(10-x)+sinx)d...

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  6. In any triangle A B C ,sumasin(B-C) in equal to a b+b c+c a b. 0 c...

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  7. Evaluate the following integral: int0^(pi//4)(s in x+cosx)/(3+s in2x)d...

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  8. In an equilateral triangle show that the in-radius and the circum-radi...

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  9. If I1=int0^1(1+x^8)/(1+x^4)dxa n dI2=int0^1(1+x^9)/(1+x^3)dx ,"t h e ...

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  10. In a bag there are 4 Red, 3 Black, 2 Green Balls are drawn one by o...

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  11. Find a continuous function f, where (x^(4)-4x^(2))lef (x) le (2x^(2)-x...

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  12. Let J=int (-1) ^(2) (cot ^(-1) ""(1)/(x )+ cot ^(-1) x ) dx, K =int (-...

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  13. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n+1)dot

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  15. If A is a square matrix of order 3, then |(A-A^T)^(105)| is equal to ...

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  16. The mean of the data set comprising of 16 observation is 16. If one ...

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  17. If N=2^(n-1).(2^n-1) where 2^n-1 is a prime, then the sum of the all ...

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  18. The value of int0^(pi/4) (e^(1/(cos^2x)).sinx)/(cos^3 x)dx equals ...

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  19. If z=sqrt(3)-2+i , then principal value of argument z is (where i=sqrt...

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  20. If 3A=[-1-2-2 2 1-2x-2y] such that AA^T=I , then which of the followin...

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