If `y=(log)_e(x/a)^x` ,then `x^3y_2=` (a) `(xy_1-y)^2` (b) `((y-x y_1)/(y_1))^2` (c) none of these

If y=log_e(x/(a+b x))^x , then x^3y_2 is (a) (x y_1-y)^2 (b) (1+y)^2 (c) ((y-x y_1)/(y_1))^2 (d) none of these

If y=(sin^(-1)x)^2,\ then (1-x^2)y_2 is equal to x y_1+2 (b) x y_1-2 (c) x y_1+2 (d) none of these

If y=sin(m\ sin^(-1)x) , then (1-x^2)y_2-x y_1 is equal to m^2y (b) m y (c) -m^2y (d) none of these

The differential equation satisfying the curve (x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1 when lambda begin arbitary uknowm, is (a) (x+yy_(1))(xy_(1)-y)=(a^(2)-b^(2))y_(1) (b) (x+yy_(1))(xy_(1)-y)=y_(1) ( c ) (x-yy_(1))(xy_(1)+y)(a^(2)-b^(2))y_(1) (d) None of these

The differential equation of all conics whose centre klies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

If log(x+y)=2xy, then y'(0) is

If the image of the point (x_1, y_1) with respect to the mirror ax+by+c=0 be (x_2 , y_2) then. (a) (x_2-x_1)/a = (a x_1 + b y_1+ c)/(a^(2)+b^(2)) (b) (x_2-x_1)/a = (y_2 - y_1)/b (c) (x_2-x_1)/a = -2 ((a x_1 + b y_1+ c)/(a^(2)+b^(2))) (d) None of these

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