If $\log _{10}(x^{2}-6x+45)=2$,then the values of $x$ are

If the inequality $kx^2 - 2x + k \geq 0$ holds good for at least one real $x$,then the complete set of values of $k$ is

Wheels of diameters $7 \,cm$ and $14 \,cm$ start rolling simultaneously from $X$ and $Y$,which are $1990.50 \,cm$ apart,towards each other in opposite directions. Both of them make the same number of revolutions per second. Both of them meet after $10 \,s$.
Quantity $1$: Speed of the smaller wheel.
Quantity $2$: $21 \pi \,cm/s$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2} = 14641$
$II.$ $y = \sqrt{14641}$

The roots of the equation $4^x - 3 \cdot 2^{x+2} + 32 = 0$ are

$x=3$ is a solution of the equation $3x^{2} + (k-1)x + 9 = 0$ if $k$ has the value: