If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth,is

Which of the following statements is true?

$A$ person walks along a straight road from his house to a market $2.5 \ km$ away with a speed of $5 \ km/h$ and instantly turns back and reaches his house with a speed of $7.5 \ km/h$. The average speed of the person during the time interval $0$ to $50 \ min$ is (in $m/s$):

In the following figure,a body of mass $m$ is tied at one end of a light string and this string is wrapped around a solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$,the system starts moving. If the friction is negligible,the angular velocity at time $t$ would be

The resultant gate and its Boolean expression in the given circuit is

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre,the ratio of $i_1: i_2$ is