The number of integral values of b for which the equation `(3sin x-4cos x)^(2)-(b^(2)+b-5)|3sin x-4cos x|
+ b^(3)+3b^(2)+2b+6=0`,has real solution is

Number of integral values of 'a' for which the equation cos2x+3sin x+4sin^(2)x=a-3 has a real root is/are

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

The number of the solutions of the equation 3sin x+4cos x-x^(2)-16=0 is

Find the number of integral values of lambda, for which equation 4cos x+3sin x=2 lambda+1 has a solution.

The number of solutions of the equation 2(sin^(4)2x+cos^(4)2x)+3sin^(2)xcos^(2)x=0 is

Consider the expression g(x)=sin^(2)x-(b+1)sin x+3(b-2) where b is a real parameter Number of integral values of b for which the equation g(x)=0 has exactly one root in the interval (0,pi) are

The integral value of 'b' for which the function f(x)=(b^(2)-3b+2)(cos^(2)x sin^(2)x)+(b-1)x+sin(b^(2)+b+1) does not possesses any stationary point is

The Number of solutions of the equation (sin x-1)^(3)+(cos x-1)^(3)+(sin x)^(3)=(2sin x+cos x-2)^(3) in [0,2 pi] is a) 5 ,b) 2 ,c) 3, d) 4

Find the number of solution of the equation 2sin4x+16sin^(3)x cos x+3cos2x-5=0

The number of real solutions of the equation e^(x)+(a^(2)+4a+5)x^(2)+6=0 is (A) 1 (B) 2 (C) 3 (D) 0