$ICBN$ stands for

Two electric bulbs rated $P_1 \text{ watt}, V \text{ volt}$ and $P_2 \text{ watt}, V \text{ volt}$ are connected in parallel and $V \text{ volt}$ is applied to them. The total power consumed will be

If $0 < x < 1$,then $\sqrt{1+x^2}\left[\left\{x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right\}^2-1\right]^{1 / 2}$ is equal to

If the angle $\theta$ between the vectors $\overrightarrow{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}$ and $\overrightarrow{b}=7 \hat{i}-2 \hat{j}+x \hat{k}$ is such that $90^{\circ} < \theta < 180^{\circ}$, then $x$ lies in the interval

What is the maximum value of the force $F$ such that the block shown in the arrangement does not move (in $N$)? (Given: $m = \sqrt{3} \ kg$,$\mu = \frac{1}{2\sqrt{3}}$,$\theta = 60^\circ$)

Which of the following is the correct order of size of the given species?