In the following structure,the double bonds are marked as $I, II, III$ and $IV$. Geometrical isomerism is not possible at site$(s)$:

Let $\bar{a} = 3 \hat{i} + 2 \hat{j} + x \hat{k}$ and $\bar{b} = \hat{i} - \hat{j} + \hat{k}$,for some real $x$. Then $|\bar{a} \times \bar{b}| = r$ is possible,if

$A$ liquid of mass $m$ and specific heat $c$ is heated to a temperature of $2T$. Another liquid of mass $m/2$ and specific heat $2c$ is heated to a temperature of $T$. If these two liquids are mixed,what will be the final temperature of the mixture?

The differential equation of the family of parabolas with vertex at $(0, -1)$ and having axis along the $Y$-axis is

Which of the following is a self-adjusting force?

Which of the following pairs are isoelectronic and isostructural? $NO_3^-, CO_3^{2-}, ClO_3^-, SO_3$