If `y=sinp xa n dy_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 y= sin mx, them the value of the determinant |{:(y,,y_(1),,y_(2)),(y_(3),,y_(4),,y_(5)),(y_(6),,y_(7),,y_(8)):}|" Where " y_(n)=(d^(n)y)/(dx^(n)) " is "

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

The equation of conjugate axis of the hyperbola x y-3y-4x+7=0 is (a) y+x=3 (b) y+x=7 (c) y-x=3 (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) non of these

The equation of the line AB is y = x . If A and B lie on the same side of the line mirror 2x-y = 1 , then the equation of the image of AB is (a) x+y-2=0 (b) 8x+y-9=0 (c) 7x-y-6=0 (d) None of these

For the primitive integral equation y dx+y^2dy=xdy ; x in R ,y >0,y(1)=1, then y(-3) is (a) 3 (b) 2 (c) 1 (d) 5

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=3 (c) x+y=2 (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-3y-c=0 (d) none of these

If ye^(y) dx = (y^(3) + 2xe^(y))dy, y(0) = 1 , then the value of x when y = 0 is