If the equation $\frac{1}{x} + \frac{1}{{x - 1}} + \frac{1}{{x - 2}} = 3{x^3}$ has $k$ real roots, then $k$ is equal to -
$2$
$3$
$4$
$6$
Suppose $m, n$ are positive integers such that $6^m+2^{m+n} \cdot 3^w+2^n=332$. The value of the expression $m^2+m n+n^2$ is
The sum of all real values of $x$ satisfying the equation ${\left( {{x^2} – 5x + 5} \right)^{{x^2} + 4x – 60}} = 1$ is ;
The number of roots of the equation $\log ( – 2x)$ $ = 2\log (x + 1)$ are
The solution set of the equation $pq{x^2} – {(p + q)^2}x + {(p + q)^2} = 0$ is
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