$A$ ball is falling freely from a height. When it reaches $10 ~m$ height from the ground,its velocity is $v_0$. It collides with the ground,loses $50 \%$ of its energy,and rises back to a height of $10 ~m$. Then the velocity $v_0$ is (in $~m/s$)

Given below are two statements:-
Statement-$I$: Morphine is a narcotic analgesic. It helps in relieving pain without producing sleep.
Statement-$II$: Morphine and its derivatives are obtained from opium poppy.
In the light of the above statements,choose the correct answer from the options given below.

Observe the following statements:
$A$. Integrating factor of $\frac{dy}{dx} + y = x^2$ is $e^x$.
$R$. Integrating factor of $\frac{dy}{dx} + P(x)y = Q(x)$ is $e^{\int P(x) dx}$.
Then,the true statement among the following is:

$A$ magnetic needle lying parallel to a magnetic field is turned through $60^{\circ}$. The work done on it is $W$. The torque required to maintain the magnetic needle in the position mentioned above is

Cardiac muscles contract:

The differential equation of the family of parabolas with vertex at $(0, -1)$ and having axis along the $Y$-axis is