$A$ body of mass $1\, kg$ is thrown upwards with a velocity $20\, m/s$. It momentarily comes to rest after attaining a height of $18\, m$. How much energy is lost due to air friction? $(g = 10\, m/s^2)$

$A$ uniform magnetic field $B$ that is perpendicular to the plane of the page passes through the loops,as shown. The field is confined to a region of radius $a$,where $a < b$,and is changing at a constant rate. The induced emf in the wire loop of radius $b$ is $\varepsilon$. What is the induced emf in the wire loop of radius $2b$?

$A$ motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times,the power of the motor is increased to $P_1$. The ratio of $P_1$ to $P_0$ is

$A$ glass capillary tube of inner diameter $0.28 \ mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel (in $N/m^2$) is:
(Surface tension of water $= 0.07 \ N/m$,Atmospheric pressure $= 10^5 \ N/m^2$)

The numbers $a_n = 6^n - 5n$ for $n = 1, 2, 3, \ldots$ when divided by $25$ leave the remainder:

$A$ body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth,the maximum height attained by the body from the surface of the earth is