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

The number of values of x for which sin2x + cos4x = 2 is

The maximum number of values of x is |x-2| + |x-4| = 2 is

The values of x for which (x-1)/(3x+4) lt (x-3)/(3x-2)

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 0<|x|

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 values of the pair (a, b) for which a(x+1)^2 + b(-x^2 – 3x - 2) + x + 1 = 0 is an identity in x, is

The number of values of x for which the matrix A=[(3-x,2,2),(2,4-x,1),(-2,-4,-1-x)] is singular, is

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

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