If a number is divisible by $35$, then by which two other numbers will it also be divisible?

Find the smallest value of $a$ if $10a+5$ is divisible by $3$.

If $\mathrm{N}$ is any natural number such that $\mathrm{N}÷10$ leaves remainder as $8$, then find the least value of $\mathrm{N}$.

If $35P4$ is a $4$ digit number which is divisible by $8$, then write the smallest value of $P$.

Without actual division, find the remainder when $58,969$ is divided by $3$.

Check the divisibility of $10,52,896$ by $11$.

Find the value of $Q$ in the following:

$\begin{array}{cc}1& Q\\ \times & Q\\ 7& Q\end{array}$

Find the value of the missing letters in the following multiplication:

$\begin{array}{ccc}& P& Q\\ & \times & 6\\ 5& Q& Q\end{array}$

If $2M7÷M=33$, then find the value of $M$.