If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 6x + a = 0$ and satisfy the relation $3\alpha + 2\beta = 16$,then the value of $a$ is

If $a > 0, b > 0, c > 0$,then both the roots of the equation $ax^2 + bx + c = 0$:

$A$ man who swims $48 \, m/min$ in still water,swims $200 \, m$ against the current and $200 \, m$ with the current. The difference between the time taken by him against the stream and with the stream is $10 \, minutes.$
$Quantity \, 1$: Speed of current.
$Quantity \, 2$: Speed of a man who completes $3$ rounds of a circular path of radius $49 \, m$ in $14 \, minutes.$

If $(x-2)(x-p) = x^{2}-ax+6$,then the value of $(a-p)$ is

If one root of the equation $ax^2 + bx + c = 0$ is the square of the other,then $a(c - b)^3 = cX$,where $X$ is

The number of solutions of $\frac{\log 5 + \log (x^2 + 1)}{\log (x - 2)} = 2$ is