Two bodies of masses $0.1\, kg$ and $0.4\, kg$ move towards each other with the velocities $1\, m/s$ and $0.1\, m/s$ respectively. After collision they stick together. In $10\, s$ the combined mass travels ............... $m$.

An electric fan has blades of length $30 \, cm$ as measured from the axis of rotation. If the fan is rotating at $1200 \, r.p.m.$,the acceleration of a point on the tip of the blade is approximately ........ $m/s^2$.

Which of the following ions forms a hydroxide that is readily soluble in water?

$A$ black body of mass $34.38 \ g$ and surface area $19.2 \ cm^2$ is at an initial temperature of $400 \ K$. It is allowed to cool inside an evacuated enclosure kept at a constant temperature of $300 \ K$. The rate of cooling is $0.04 \ ^{\circ}C/s$. The specific heat of the body in $J \ kg^{-1} \ K^{-1}$ is (Stefan's constant $\sigma = 5.73 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

$A$ body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is acceleration due to gravity).

Find the derivative of the function $(x+\sec x)(x-\tan x)$.