Consider the equation `2/x+5/y=1/3w h e r ex ,y in Ndot` Find the number of solutions of the equation.

Find the number of solutions of equation (2x-3)2^x=1

Find the number of positive integral solutions of the equation x+y+z=12.

Find the number of solution of the system of equation x+2y=6 and |x-3|=y

Find the number of non-negative integer solutions of equation x+y+z+2w=20.

If x = 2 – α and y = 2 + α is a solution of the equation 3x – 2y + 6 = 0 find the value of ‘α ’. Find three more solutions of the resultant equation.

Find the value of k, if x = 2, y =1 is a solution of the equation 2x + 3y = k. Find two more solutions of the resultant equation.

Solve the equation x^2-x+1=1/2+sqrt(x-3/4),w h e r exgeq3/4dot

Consider the differential equation (dy)/(dx)=(y)/(x)+logx i . Find the integrating factor of the differential equation ii . Evaluate int(1)/(x)logxdx iii . Hence find the general solution of the given differential equation.

If y=1/(t^2+t-2),w h e r et=1/(x-1), then find the number of points where f(x) is discontinuous.

Check whether the given pair of equations represent intersecting, parallel or coincident lines. Find the solution if the equations are consistent. 2x + y - 5 = 0 3x - 2y - 4 = 0