The set of all values of `alpha` for which `x^2-9+|x+sinalpha| lt 0` has a solution is

The set of values of alpha for which the equation "sin"^(4) x + "cos"^(4) x + "sin" 2x + alpha =0 possesses a solution, is

The set of values of alpha for which the quadratic equation (alpha + 2) x^(2) - 2 alpha x - alpha = 0 has two roots on the number line symmetrically placed about the point 1 is

Let lamda and alpha real. Find the set of all values of lamda for which the system. x+(sinalpha)y+(cosalpha)z=0, x+(cosalpha)y+(sinalpha)z=0, -x+(sinalpha)y+(cosalpha)z=0 has a non trivial solution. For lamda=1 find all values of alpa.

The value of alpha , for which the equation x^2-(sinalpha-2)x-(1+sinalpha)=0 has root whose sum of square is least, is

Let lambdaa n dalpha be real. Find the set of all values of lambda for which the system of linear equations lambdax+(sinalpha)y+(cosalpha)z=0,x+(cosalpha)y+(sinalpha)z=0,-x+(sinalpha)y-(cosalpha)z=0. have trivial solution

Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains