The number of solution$(s)$ of the equation $2^x = x^2$ is
$1$
$2$
$3$
$4$
The sum of all the real roots of the equation $\left( e ^{2 x }-4\right)\left(6 e ^{2 x }-5 e ^{ x }+1\right)=0$ is
If $\alpha ,\beta $are the roots of ${x^2} - ax + b = 0$ and if ${\alpha ^n} + {\beta ^n} = {V_n}$, then
If $|x - 2| + |x - 3| = 7$, then $x =$
The sum of all non-integer roots of the equation $x^5-6 x^4+11 x^3-5 x^2-3 x+2=0$ is
If for a posiive integer $n$ , the quadratic equation, $x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right) + .\;.\;.\; + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right) = 10n$ has two consecutive integral solutions, then $n$ is equal to: