$A$ metal ball of mass $2 \ kg$ moving with a velocity of $36 \ km/h$ has a head-on collision with a stationary ball of mass $3 \ kg$. After the collision,if both balls move together,the loss in kinetic energy due to the collision is: (in $J$)

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?

$A$ plane passing through the points $(0, -1, 0)$ and $(0, 0, 1)$ and making an angle $\frac{\pi}{4}$ with the plane $y - z + 5 = 0$,also passes through the point:

Which of the following is the most stable?

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If $f: R \rightarrow C$ is defined by $f(x)=e^{2 i x}$ for $x \in R$,then $f$ is (where $C$ denotes the set of all complex numbers)