Let S denote the set of all values of the parameter a for which `x+sqrt(x^(2))=a` has no solution, them S equals

The set of all values of alpha for which x^(2)-9+|x+sin alpha|<0 has a solution is

Let S be the set of all possible values of parameter 'a' for which the points of intersection of the parabolas y^(2)=3axandy=1/2(x^(2)+ax+5) are concyclic. Then S contains the interval(s)

Exhaustive set of values of parameter 'a' so that sin^(-1)x-tan^(-1)x=a has a solution is

Exhaustive set of values of parameter 'a' so that sin^(-1)x-tan^(-1)x=a has a solution is

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+ (sin alpha) 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 a) (-1,1) b) [-sqrt2,-1] c) [1,sqrt2] d) [-sqrt2,sqrt2]

Let S denote the set of all real values of a for which the roots of the equation x^(2) - 2ax + a^(2) - 1 = 0 lie between 5 and 10, then S equals

Let S denote the set of all real values of a for which the roots of the equation x^(2) - 2ax + a^(2) - 1 = 0 lie between 5 and 10, then S equals

Let S be the set of real values of parameter lamda for which the equation f(x) = 2x^(3)-3(2+lamda)x^(2)+12lamda x has exactly one local maximum and exactly one local minimum. Then S is a subset of

Let S be the set of real values of parameter lamda for which the equation f(x) = 2x^(3)-3(2+lamda)x^(2)+12lamda x has exactly one local maximum and exactly one local minimum. Then S is a subset of