Number of integral values of `b` for which the equation `(x^3)/3-x=b` has three distinct solutions is____

Minimum integral value of k for which the equation e^(x)=kx^(2) has exactly three real distinct solution,

The number of integral values of b, for which the equation x^(2)+bx-16=0 has integral roots, is

Number of integral values of a for which the equation cos^2x-sinx+a=0 has roots when x in (0,pi/2) is____________

Find the number of integral values of k for which the equation 7 cos x+5 sin x=2k+1 has at least one solution.

Number of integral value(s) of m for which the equation sinx-sqrt(3)cosx=(4m-6)/(4-m) has solutions, x in [0,2pi] , is ________

Find the value of k for which the equation x^2 −6x+k=0 has distinct roots.

Number of integral values of a for which the equation x^2-(a+1)x+a-1=0 , has integral roots, is equal to -

The number of integer values of k for which the equation sin^(-1)x+tan^(-1)x=2k+1 has a solution is (a)1 (b) 2 (c) 3 (d) 4

Find the values of a for which the equation ||x-2|+a|=4 can have four distinct real solutions.

The number of integral values of x satisfying the equation |x-|x-4||=4 is