Minimum positive integral value of `k` for which `f(x)=k cos2x-4cos^(3)x` has exactly one critical point in `(0,pi)` ,is

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

Number of integral values of k for which the equation 4cos^(-1)(-|x|)=k has exactly two solutions,is:

Let f (x) is a real valued function defined on R such that f(x) = sqrt(4+sqrt(16x^2 - 8x^3 +x^4)) . The number of integral values of 'k' for which f(x) =k has exactly 2 distinct solutions for k in [0,5] is

The possible positive integral value of 'k' for which 5x ^(2) -2k x +1lt 0 has exactly one integral solution may be divisible by :

Find the number of positive integral values of k for which kx ^(2) +(k-3)x+1 lt 0 for atleast one positive x.

Let f(x)=(x^(2))/(9-x^(2)) and l= number of integers in the domain of f(x) where f(x) is increasing m= number of solutions of f(x)=sin xn= least positive integral value of k for which f(x)=k posses exactly 3 different solutions then

Find the no.of integral values of k for which the equation 7cos x+5sin x=2k+1 has atleast one solution.

Find the sum of all possible integral values of in [1,100] for which the function f(x)=2x^(3)-3(2+alpha)x^(2) has exactly one local maximum and one local minimum.

The value of k for which f(x)= {((1-cos 2x )/(x^2 )", " x ne 0 ),(k ", "x=0):} continuous at x=0, is :