The solution of `(1-x^2) dy/dx+2xy-xsqrt(1-x^2)=0`, is (A) `y/((1-x^2))=1/sqrt(1-x^2)+C` (B) `y(1-x^2)=sqrt(1-x^2)+C` (C) `y(1-x^2)^(3/2)=sqrt(1-x^2)+C` (D) none of these

The solution of (x d x+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) is

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

int(x^3dx)/(sqrt(1+x^2)) is equal to (A) 1/3sqrt(1+x^2)(2+x^2)+C (B) 1/3sqrt(1+x^2)(x^2-1)+C (C) 1/3(1+x^2)^(3/2)+C (D) 1/3sqrt(1+x^2)(x^2-2)+C

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

intdx/(sqrt(x)(1+x^2)^(5/4))= (A) (2x)/(1+x^2)^(1/4)+c (B) (2sqrt(x))/(1+x^2)^(1/4)+c (C) (2sqrt(x))/(1+x^2)+c (D) none of these

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y), prove that (dy)/(dx)=sqrt((1-y^2)/(1-x^2))

If ysqrt(1-x^2)+xsqrt(1-y^2)=1 show that (dy)/(dx)=-sqrt((1-y^2)/(1-x^2))

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))