One mole of a monoatomic ideal gas starting from state A, goes through B and C to state D, as shown in the figure. Total change in entropy (in J K$^{-1}$) during this process is ...............

The number of chiral carbon centers in the following molecule is ...............

Consider the following matrices A and B.
\[ A = \begin{pmatrix} 1 & 2 & 0 & 0 \\ 3 & 4 & 0 & 0 \\ 0 & 5 & 5 & 0 \\ 0 & 0 & 6 & 7 \\ 0 & 0 & 8 & 9 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 10 & 11 & 0 & 0 & 0 \\ 12 & 13 & 0 & 0 & 0 \\ 0 & 0 & 4 & 0 & 0 \\ 0 & 0 & 15 & 16 & 0 \\ 0 & 0 & 17 & 18 & 0 \end{pmatrix} \]

If $ C = AB $, the sum of the diagonal elements of $ C $ is ..............

A tube fitted with a semipermeable membrane is dipped into 0.001 M NaCl solution at 300 K as shown in the figure. Assume density of the solvent and solution are the same. At equilibrium, the height of the liquid column $ h $ (in cm) is .........

An electron at rest is accelerated through 10 kV potential. The de Broglie wavelength (in A) of the electron is .............

The number of stereoisomers possible for the following compound is ..............

Number of $ ^1H $ NMR signals observed for the following compound is .............

Consider $ \mathbf{C} = \mathbf{A} \times \mathbf{B} $, where $ \mathbf{A} = 3\hat{i} - 2\hat{j} + 5\hat{k} $ and $ \mathbf{B} $ is a unit vector in the $ xy $-plane, making an angle of 37° with the $ x $-axis. The projection of $ \mathbf{C} $ on the $ x $-axis is ................ (round off to one decimal place)

\[ \int_0^\infty x e^{-x} dx = \text{...............} \] (round off to the nearest integer)

The product(s) in the following transformation is(are)