Value of the given determinant is 
Expanding along the first row:

\[ = 1(6\cdot 2 - 0\cdot 4) - 3(2\cdot 2 - 4(-1)) \] \[ = 12 - 3(4 + 4) = 12 - 3(8) = 12 - 24 = -12 \]
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 ............... 
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 .............