The number of values of `x` for which `|||x^2-x+4|-2|-3|=x^2+x-12` is______________

The number of value/values of x for which sin y=x^(2)-2x si possible is

The number of values of a for which (a^2-3a+2)x^2+(a^2-5a+6)x+a^2-4=0 is an identity in x is

The number of values of x for which sin^(-1)(x^2-(x^4)/3+(x^6)/9)+cos^(-1)(x^4-(x^8)/3+(x^(12))/9ddot)=pi/2, where 0lt=|x|

The number of distinct real roots of x^4-4x^3+12 x ^2+x-1=0 is ________

The values of 'a' for which 4^x-(a-4) 2^x+(9a)/4<0 AAx in(1,2) 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

(2x-3)/(x^(2) + 4x - 12 )

The number of solutions of 12 cos^(3) x-7 cos^(2) x+4 cos x=9 is

The complete set of values of x for which (x^(3)(x-1)^(2)(x+4))/((x+1)(x-3)) ge 0 is

The number of nonzero integral values of a for which the function f(x)=x^4+a x^3+(3x^2)/2+1 is concave upward along the entire real line is___________