$A$ particle of mass $m$ moves in the $XY$ plane with a velocity $V$ along the straight line $AB$. If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$,then

If $A = \begin{bmatrix} -8 & 5 \\ 2 & 4 \end{bmatrix}$ satisfies the equation $x^2 + 4x - p = 0$,then $p$ is equal to

$A$ wire of resistance $4\,\Omega$ is stretched to twice its original length. The resistance of the stretched wire would be ................ $\Omega$.

$A$ magnet makes $40$ oscillations per minute at a place having a magnetic field of $0.1 \times 10^{-5} \, T$. At another place, it takes $2.5 \, s$ to complete one vibration. The value of the Earth's horizontal magnetic field at that place is:

The equations of the circle which pass through the origin and make intercepts of lengths $4$ and $8$ on the $x$ and $y$-axes respectively are

$A$ small quantity of solution containing $Na^{24}$ radio nuclide of activity $1 \, \mu Ci$ is injected into the blood of a person. $A$ sample of the blood of volume $1 \, cm^3$ taken after $5 \, hours$ shows an activity of $296$ disintegrations per minute. What will be the total volume of the blood in the body of the person? Assume that the radioactive solution mixes uniformly in the blood of the person. (Take $1 \, Ci = 3.7 \times 10^{10} \, dps$ and $e^{-\lambda t} = 0.7927$; where $\lambda$ = disintegration constant)