$A$ ball of mass $0.5\, kg$ moving with a velocity of $2\, m/s$ strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and the wall is $1\, ms$,the average force exerted by the wall on the ball is ........ $N$.

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is

In a floral formula,what does the notation $(K)$ denote?

The centre of a circle is $(2, -3)$ and the circumference is $10\pi$. Then the equation of the circle is

Fungi are filamentous with the exception of $X$ which is unicellular. Identify $X$.

The function $f(x) = x e^{-x}, \forall x \in R$ attains a maximum value at $x$ equal to