Least integral value of (s) of a for which `4^x-(a-2).2^x+ a <0` for at least one x in `(0, oo)` is (are)

The least integral value of x for which 33 - x(2 + 3x) gt 0 is

The least integral value of k for which (k-2)x^(2)+8x+k+4 gt Sin^(-1)(sin12)+Cos^(-1)(cos12) for all x in R , is

The least integral value of x for which tan^(-1)x>cot^(-1)x is

The least integral value of 'k' for which (k -2)x^2 +8x+k+4>0 for all xepsilonR, is:

The least integral value of 'k' for which (k -2)x^2 +8x+k+4>0 for all xepsilonR , is:

The least integral value of x for which 33-x (2+3x )gt 0 is

The least integral value of 'k' for which (k-1) x ^(2) -(k+1) x+ (k+1) is positive for all real value of x is:

The least integral value of a'a' for which the equation x^(2)+2(a-1)x+(2a+1)=0 has both the roots positive,is

The least integral value of 'a' for which the equation x^(2)-2(a-1)x+(2a+1)=0 has both the roots positive is