If $x, y$ are real numbers such that $3^{(x / y)+1}-3^{(x / y)-1}=24$ then the value of $(x+y) /(x-y)$ is

If $x$ is real, the expression $\frac{{x + 2}}{{2{x^2} + 3x + 6}}$ takes all value in the interval

The number of positive integers $x$ satisfying the equation $\frac{1}{x}+\frac{1}{x+1}+\frac{1}{x+2}=\frac{13}{2}$ is.

If the sum of all the roots of the equation $e^{2 x}-11 e^{x}-45 e^{-x}+\frac{81}{2}=0$ is $\log _{ e } P$, then $p$ is equal to

The number of solutions for the equation ${x^2} - 5|x| + \,6 = 0$ is

If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$, then