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

Find the number of positive integral solutions of x y z=21600.

Find the number of positive integral solutions of the equation x+y+z=12.

Find the number of integral values of k for which the equation 7 cos x+5 sin x=2k+1 has at least one solution.

Number of integral values of b for which inequality (a^(2)+1) x^(2)+4(a+b) x+2 lt 0 is true for atleast one x forall a in R,

The number of all possible positive integral values of alpha for which the roots of the quadratic equation 6x^2-11x+alpha=0 are rational numbers is : (a) 3 (b) 2 (c) 4 (d) 5

Number of integral values of a for which the equation x^2-(a+1)x+a-1=0 , has integral roots, is equal to -

Find the least positive integral value of x for which the angel between vectors vec a=x hat i-3 hat j- hat k and vec b=2x hat i+x hat j- hat k is acute.

Find the value of k if 9x^2 + kx +1=0 has equal roots.

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

Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R