Which of the following isomerism is not possible for complexes having molecular formulae?
$(I) Pt(SCN)_2 \cdot 3PEt_3$,$(II) CoBr \cdot SO_4 \cdot 5NH_3$,$(III) FeCl_2 \cdot 6H_2O$

The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$. The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury, and $T_3$ when it is half-filled with mercury. Which of the following is true?

$A$ cannon ball is fired with a velocity $200\, m/s$ at an angle of $60^{\circ}$ with the horizontal. At the highest point of its flight,it explodes into $3$ equal fragments. One fragment goes vertically upwards with a velocity $100\, m/s$,and the second one falls vertically downwards with a velocity $100\, m/s$. What will be the velocity of the third fragment?

If the equation $px^2 + (2 - q)xy + 3y^2 - 6qx + 30y + 6q = 0$ represents a circle,then the values of $p$ and $q$ are:

The polar equation of the line perpendicular to the line $\sin \theta - \cos \theta = \frac{1}{r}$ and passing through the point $\left(2, \frac{\pi}{6}\right)$ is

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. When a person walks on a rough surface, the direction of the frictional force exerted by the surface on the person is in the direction of his motion.
$B$. When a cycle is in motion, the force of friction exerted by the ground on the front wheel is in the backward direction.