x=2, y=−1 is a solution of the linear equation (a) x+2y=0 (b)  x+2y=4  (c) 2x+y=0 (d)  2x+y=5

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

The general solution of the differential equation (y dx-x dy)/y=0 is(A) x y = C (B) x=C y^2 (C) y = C x (D) y=C x^2

Show that x=2,\ \ y=1 is a solution of the system of simultaneous linear equations: 3x-2y=4;\ \ \ 2x+y=5 .

A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has equation. (a) x^2+5y^2+4x y-1=0 (b) x^2+5y^2+4x y+1=0 (c) x^2+5y^2-4x y-1=0 (d) 4x^2+5y^2+4x y+1=0

The general solution of the differential equation (y dx-x dy)/y=0 is (A) x y" "=" "C (B) x=C y^2 (C) y" "=" "C x (D) y=C x^2

Show that y^2-x^2 - x y=a is a solution of the differential equation (x-2y)(dy)/(dx)+2x + y=0

Show that x=2,\ \ y=1 is not a solution of the system of simultaneous linear equations: 2x+7y=11 ;\ \ \ x-3y=5

The general solution of the differential equation y dx+(x+2y^2)dy=0 is a) x y+y^2=c b) 3x y+y^2=c c) x y+2y^3=c d) 3x y+2y^3=c

Verify that y=-x-1 is a solution of the differential equation (y-x)dy-(y^2-x^2)dx=0.

Let (2,3) be the focus of a parabola and x + y = 0 and x-y= 0 be its two tangents. Then equation of its directrix will be (a) 2x - 3y = 0 (b) 3x +4y = 0 (c) x +y = 5 (d) 12x -5y +1 = 0