If `||x-1|+a|=5` has only two real solutions for `x` then number of integer values of parameter a are n .Find `n^2`

||x-1|-3|-a|=k,a in N, has eight distinct real roots for some K, then number of such values of 'a' is

If a.3^(tan x)+a*3^(-tan x)-2=0 has real solutions,x!=(pi)/(2),0<=x<=pi, then find the set of all possible values of parameter 'a'.

If t is a real number satisfying the equation 2t^(3)-9t^(2)+30-a=0, then find the values of the parameter a for which the equation x+(1)/(x)=t gives six real and distinct values of x .

If |4-x^(2)|=a such that a is integer then find number of values of a such that given equation has four solution

Find the number of integral value of n so that sin x(sin x+cos x)=n has at least one solution.

The number of real solutions of the equation (x^(2))/(1-|x-5|)=1 is

The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)|+|((1+x)^2,2x+1,x+1),((1-x)^2,3x,2x),(1-2x,3x-2,2x-3)|=0 has has (a) no real solution (b) 4 real solutions (c) two real and two non-real solutions (d) infinite number of solutions, real or non-real

Find the values of a for which the equation x^(4)+(1-2a)x^(2)+a^(2)-1=0(A) has no real solutions (B) has one real solution (C) has two distinct real solutions (D) has three real solutions(E) has four distinct real solutions