`y=ae^(-1/x)+b` is a solution of `dy/dx=y/x^2`,then (a)`ainR` (b)`b=0` (c)`b=1` (d)`a` takes finite number of values

The system of equations -2x+y+z=a , x-2y+z=b , x+y-2z=c , has: (a)no solution if a+b+c!=0 (b)unique solution if a+b+c=0 (c)infinite number of solutions if a+b+c=0 (d)none of these

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

If the solution of the differential equation (dy)/(dx)-y=1-e^(-x) and y(0)=y_0 has a finite value, when x->oo, then the value of |2/(y_0)| is__

If the solution of the differential equation (dy)/(dx)-y=1-e^(-x) and y(0)=y_0 has a finite value, when xvecoo, then the value of |2/(y_0)| is__

The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d) oo

Number of values of m in N for which y=e^(m x) is a solution of the differential equation (d^3y)/(dx^3)-3(d^2y)/(dx^2)-4(dy)/(dx)+12 y=0 (a) 0 (b) 1 (c) 2 (d) More than 2

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

The solution of (dy)/(dx)=(a x+h)/(b y+k) represent a parabola when (a) (a) a=0,b!=0 (b) a!=0,b!=0 (c) b=0,a!=0 (d) a=0,b in R

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

x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= 1 b. 2 c. 3 d. 4