A differential equation associated to the primitive `y=a+b e^(5x)+c e^(-7x)` is (where `y_n` is `n t h` derivative w.r.t. `x)` `(a) y_3+2y_2-y_1=0( b )4y_3+5y_2-20y_1=0 (c)y_3+2y_2-35y_1=0` (d) none of these

If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y_2+x y_1 is (where y_r represents the r t h derivative of y w.r.t. xdot (a) m^2y (b) m y^2 (c) m^2y^2 (d) none of these

If y=sinp x and y_n is the n t h derivative of y , then |[y, y_1,y_2],[y_3,y_4,y_5],[y_6,y_7,y_8]|i s (a)1 (b) 0 (c) -1 (d) none of these

If the foci of a hyperbola lie on y=x and one of the asymptotes is y=2x , then the equation of the hyperbola, given that it passes through (3, 4), is (a) x^2-y^2-5/2x y+5=0 (b) 2x^2-2y^2+5x y+5=0 (c) 2x^2+2y^2-5x y+10=0 (d) none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

The locus of the image of the point (2,3) in the line (x-2y+3)+lambda(2x-3y+4)=0 is (lambda in R) (a) x^2+y^2-3x-4y-4=0 (b) 2x^2+3y^2+2x+4y-7=0 (c) x^2+y^2-2x-4y+4=0 (d) none of these

If x e^(x y)-y=sin^2x then (dy)/(dx)a tx=0 is a. 0 b. 1 c. -1 d. none of these

For hyperbola whose center is at (1, 2) and the asymptotes are parallel to lines 2x+3y=0 and x+2y=1 , the equation of the hyperbola passing through (2, 4) is (a) (2x+3y-5)(x+2y-8)=40 (b) (2x+3y-8)(x+2y-5)=40 (c) (2x+3y-8)(x+2y-5)=30 (d) none of these

The center of a rectangular hyperbola lies on the line y=2xdot If one of the asymptotes is x+y+c=0 , then the other asymptote is: (a) 6x+3y-4c=0 (b) 3x+6y-5c=0 (c) 3x-6y-c=0 (d) none of these

The equation of straight line passing through (-a ,0) and making a triangle with the axes of area T is (a) 2T x+a^2y+2a T=0 (b) 2T x-a^2y+2a T=0 (c) 2T x-a^2y-2a T=0 (d)none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these