`int_(1/n)^((an-1)/n) sqrt(x)/(sqrt(a-x)+sqrt(x))dx=` (A) `a/2` (B) `(na+2)/(2n)` (C) `(na-2)/(2n)` (D) none of these

The value of int_(1//n)^((an-1)//n) (sqrt(x))/(sqrt(a-x)+sqrtx)dx , is

int((a+bsin^(-1)x)^(n))/(sqrt(1-x^(2)))dx

Sum of 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+1/(sqrt(11)+sqrt(14))+..to n terms= (A) n/(sqrt(3n+2)-sqrt(2)) (B) 1/3 (sqrt(2)-sqrt(3n+2) (C) n/(sqrt(3n+2)+sqrt(2)) (D) none of these

sum_(n=1)^oo sin^-1( (sqrt(n)-(sqrt(n-1)))/(sqrt((n)(n+1)) )= (A) pi/4 (B) pi/2 (C) - pi/3 (D) pi/3

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (d) none of these

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

If int_0^(pi^2/4) (2sinsqrt(x)+sqrt(x)cossqrt(x))dx=pi^2/n , then n = ….

Let n be a positive integer such that sin (pi/(2n))+cos (pi/(2n))= sqrt(n)/2 then (A) n=6 (B) n=1,2,3,….8 (C) n=5 (D) none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se q u a lto (a y)/(xsqrt(a^2-x^2)) (b) (a y)/(sqrt(a^2-x^2)) (a y)/(xsqrt(a^2-x^2)) (d) none of these