[" The solution of "(dy)/(dx)=(1)/(2x-y^(2))" is given by "],[[" (A) "y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)],[" (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)]]

The solution of (dy)/(dx)=(1)/(2x-y^(2)) is given by , (A) y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," 4"(1)/(2)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)," (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)

The solution y'=(1-2y-4x)/(1+y+2x) is given by

2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(4z)=4

[" 1.The general solution of differential equation "(dy)/(dx)+x sin2y=x^(3)cos^(2)y" is "],[[" 1) Tany "=(x^(2)-1)/(2)+ce^(-x^(2))," 2) Tany "=(x^(2)-1)/(2)+ce^(2)],[" 3) "Tany=e^(2)+c(x^(2)-1)," 4) "Tan^(-1)((x^(2)-1)/(2))=ce^(-x^(2))]]

The solution of (dy)/(dx)=((x-1)^(2)+(y-2)^(2)tan^(-1)((y-2)/(x-1)))/((xy-2x-y+2)tan^(-1)((y-2)/(x-1))) is equal to

If sqrt(y)=4x, then (x^(2))/(y) is (a) 2 (b) (1)/(16) (c) (1)/(4) (d) 4

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

[1/(((x^7)^(1/4)y^2)xx(x^(-1)y^6)^(1/4))]^(-2)

The solution of y^2dx+(x^2-xy+y^2)dy=0 is (A) y=Ce^(tan^-1x) (B) y=Ce^(tan^-1y) (C) y=Ce^(tan^-1(y/x)) (D) y=C[tan^-1(y/x)+e^(x^2)+y^2]