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Let fn= int0^(pi/2)(sum(k=1)^n sin ^(k-1...

Let `f_n= int_0^(pi/2)(sum_(k=1)^n sin ^(k-1) x)(sum_(k=1)^n(2k-1)sin^(k-1)x)cos x dx ,n in NN ` .Then `f_(21) -f_(20)` is equal to ___.

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2023-Question
  1. The random variable X follows binomialdistribution B(n,p) ,for which t...

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  2. The area of the region {(x,y):x^2ley le|x^2-4|,,yge1} is

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  3. Let fn= int0^(pi/2)(sum(k=1)^n sin ^(k-1) x)(sum(k=1)^n(2k-1)sin^(k-1)...

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  4. Let f(x) =sum(k=1)^(10)k x^k , x in RR . If 2f(2) +f '(2) = 119(2)^n+...

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  5. Let [alpha] denote the greatest integer lealpha .Then [sqrt1]+ [sqrt2]...

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  6. If y =y(x) is the solution of the differential equation (dy)/(dx)+(4x)...

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  7. The remainder , when 7^(103) is divided by 17, is

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  8. Let A ={-4,-3,-2,0,1,3,4,} and R ={(a,b) in A times A : b^2=a+1} be a ...

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  9. Total numbers of 3-digit numbers that are divicible by 6and can be for...

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  10. The foci of hyperbola are (pm2,0) and its eccentricity is 3/2 .A tange...

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  11. For x in (-1,1)], the numberof solutions of the equation sin^(-1)x=2 t...

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  12. The mean and standard deviation of the marks of 10 students were found...

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  13. The straight lines l 1 and l2 pass through the origin and trisect the ...

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  17. Let the position vectors of the points A, B, C and D be 5hati+5j+2lamb...

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  18. Let I(x)int (x^2 (x sec^2+tanx))/(xtanx +1)^2dx If i(0) =0, then l(pi/...

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  19. Let veca = 2hatj + 3hatj + 4hatk ,vecb= hati - 2hatj - 2hatk and vecc ...

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  20. Let 5f(x)+4f(1/x)=1/x+3 ,x >0 . Then 18int1^2 f(x)dx is equal to

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