$A$ liquid drop having surface energy $E$ is spread into $512$ droplets of the same size. The final surface energy of the droplets is (in $E$)

The minimum value of $|z-1|+|z-5|$ is

If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\cos 3x - \cos x}{x^2}, & \text{for } x \neq 0 \\ \lambda, & \text{for } x = 0 \end{cases}$ and if $f$ is continuous at $x = 0$,then $\lambda$ is equal to

In the random experiment of tossing two unbiased dice,let $E$ be the event of getting the sum $8$ and $F$ be the event of getting even numbers on both the dice. Then:
$I. P(E) = \frac{7}{36}$
$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?

The number of ways that $8$ beads of different colours can be strung as a necklace is

Which of the following expressions corresponds to simple harmonic motion along a straight line,where $x$ is the displacement and $a, b, c$ are positive constants?