Find the H.C.F of $1260$ and $7344$ using Euclid's algorithm.

Divide polynomial $3x^3-8x^2+x+7$ by $x-3$ using synthetic method and write the quotient and remainder.

Some students are sitting in classroom $A$ and $B$ in a school. When $10$ students from room $A$ are sent to room $B$, the number of students in both rooms becomes equal. When $20$ students from room $B$ are sent to room $A$, then the number of students in room $A$ become twice that in room $B$. Find the number of students in each room.

Divide the line segment of length $8 \mathrm{cm}$ in the ratio of $3:5$ internally.

Construct a tangent to a circle with centre $\mathrm{P}$ and radius $3.2\mathrm{cm}$ at any point $\mathrm{M}$ on it.