Let 'S' be the set of positive integer values of a for which `(ax^2+2(a+1)x+9a+4)/(x^2+8x+32) lt 0 forall X in R` then the number of elements is 'S' is

The set of values of k for which x^(2)+(4k-1)x+9>0AA x in R is

The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x) lt 0

If 9^(x+1) + (a^(2)-4a-2) 3^(x) + 1 lt 0 "for all" x in R, then

Let Z be the set of integers. If A = {x in Z : 2^((x + 2)(x^(2) - 5x + 6)} = 1 and B = {x in Z : -3 lt 2x - 1 lt 9} , then the number of subsets of the set A xx B is

The set of values of 'a' for which ax^(2)-(4-2a)x-8lt0 for exactly three integral values of x, is

Let f:R rarr R be a function defined by f(x)={abs(cosx)} , where {x} represents fractional part of x. Let S be the set containing all real values x lying in the interval [0,2pi] for which f(x) ne abs(cosx) . The number of elements in the set S is

Let S equiv {x in R : (sqrt 3 sqrt 2)^x (sqrt 3 - sqrt 2)^x = 10} . Then the number of elements in S is :