`(xy)^(a-b)*(xy)^(b-c)(xy)^(c-a)`

If two positive integers a and b are written as a=x^(3)y^(2) and b=xy^(3);x,y are prime numbers then HCF(a,b) is (a) xy (b) xy^(2) (c) x^(3)y^(3) (d) x^(2)y^(2)

The differential equations of all circle touching the x-axis at orgin is (a) (y^(2)-x^(2))=2xy((dy)/(dx)) (b) (x^(2)-y^(2))(dy)/(dx)=2xy ( c ) (x^(2)-y^(2))=2xy((dy)/(dx)) (d) None of these

(xy)/(x+y)=6/5 ; (xy)/(y-x)=6

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

Solve: {(xy)cos(xy)+sin(xy)}dx+x^2cos(xy)dy=0

The solution of y(2xy+e^x)dx-e^xdy=0 is (A) x^2+ye^(-x)=C (B) xy^2+e^(-x)=C (C) x/y+e^(-x)/x^2=C (D) x^2+e^x/y=C

(1-x^(2))(dy/dx)+xy=xy^(2)

If sin theta = x and sec theta = y , then tan theta is (a) xy (b) x/y (c) y/x (d) 1/(xy)

If f(x)=sin(logx) then f(xy)+f(x/y)-2f(x)cos(logy)= (A) cos(logx) (B) sin(logy) (C) cos(log(xy)) (D) 0

Value of the determinant |(x,1,1),(0,1+x, 1),(-y, 1+x, 1+y)| is (A) xy (B) xy(x+2) (C) x(x+1)(y+1) (D) xy(x+1)