$A$ river is flowing from east to west at a speed of $5\ m/min$. $A$ man on the south bank of the river,capable of swimming $10\ m/min$ in still water,wants to swim across the river in the shortest time. He should swim:

$A$ point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9 \ m$ and $25 \ m$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is

$A$ thin flexible wire of length $L$ is connected to two adjacent fixed points and carries a current $I$ in the clockwise direction,as shown in the figure. When the system is placed in a uniform magnetic field of strength $B$ directed into the plane of the paper,the wire takes the shape of a circle. The tension in the wire is

What is the quantity of electricity (in Coulombs) required to deposit all the silver from $250 \ mL$ of $1 \ M \ AgNO_3$ solution?

The area (in square units) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is