Find values of k for which the equation `|x^2-1] + x = k` has (i) 4 solution (ii) 1 solution (ii) 3 solutions (iv) 2 solutions

The number of integer values of k, for which the equation 2 sin x =2k+1 has a solution, is

Find the value of k for which the equations kx-2y+z=1, x-2ky+z=-2,x-2y+kz=1 have (i) no solution (ii) unique solution (iii) infinitely many solution

Find the value of k for which the system k x+2y=5 3x+y=1 has (i) a unique solution, and (ii) no solution.

Find the value of k for which the system kx+2y=53x+y=1 has (i) a unique solution,and (ii) no solution.

Find the values(s) of k for which the system of equations k x-y=2 6x-2y=3 has (i) a unique solution (ii) no solution. Is there a value of k for which the system has infinitely many solutions?

Value of k for which system of equations kx + 2y = 5, 3x + y =1 has unique solution is

Find the values(s) of k for which the system of equations kx-y=26x-2y=3 has ( i )a unique solution (ii) no solution.Is there a value of k for which the system has infinitely many solutions?

Find the valus of k for which the system of equations x - 2y = 3, 3 x + k y = 1 has a unique solution.

The number of integral values of k for which the equation 7 cos x + 5 sinx = 2k+1, has a solution is :