If $a, b, c, d$ are four distinct numbers chosen from the set $\{1,2,3, \ldots, 9\}$, then the minimum value of $\frac{a}{b}+\frac{c}{d}$ is
$\frac{3}{8}$
$\frac{1}{3}$
$\frac{13}{36}$
$\frac{25}{72}$
The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :
If $|x - 2| + |x - 3| = 7$, then $x =$
The number of real roots of the equation, $\mathrm{e}^{4 \mathrm{x}}+\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{2 \mathrm{x}}+\mathrm{e}^{\mathrm{x}}+1=0$ is
One root of the following given equation $2{x^5} - 14{x^4} + 31{x^3} - 64{x^2} + 19x + 130 = 0$ is
$\{ x \in R:|x - 2|\,\, = {x^2}\} = $