For the parabola $y^2+6y-2x+5=0$:
$(I)$ The vertex is $(-2,-3)$
$(II)$ The directrix is $y+3=0$
Which of the following is correct?

The internal energy of a monoatomic gas is $3 \ nRT$. $1$ mole of helium is kept in a cylinder having internal cross section area of $17 \ cm^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling $126 \ J$ heat. If the temperature rises by $4 \ ^\circ C$, then the piston will move $. . . . . . \ cm$.
(atmospheric pressure $= 10^5 \ Pa$)

The sum of the last eight coefficients in the expansion of $(1 + x)^{15}$ is:

The potential difference between $A$ and $B$ in the figure is ................. $V$.

In a mass spectrometer used for measuring the masses of ions,the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant,the ratio $\left( \frac{\text{charge on the ion}}{\text{mass of the ion}} \right)$ will be proportional to

$A$ bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased,while keeping the voltage of the source constant,then