The surface of sodium metal is irradiated with radiation of wavelength $x$ nm. The kinetic energy of ejected electrons is $2.8 \times 10^{-20}\ \text{J}$. The work function of sodium is $2.3$ eV. The value of $x$ is ________ $\times 10^2$ nm. (Nearest integer)

(Given: $h=6.6 \times 10^{-34}\ \text{J s}$ ; $1\ \text{eV} = 1.6 \times 10^{-19}\ \text{J}$ ; $c = 3.0 \times 10^8\ \text{m s}^{-1}$)

Consider the following gas phase reaction being carried out in a closed vessel at $25 ^\circ$C.

$$2A(g) \longrightarrow 4B(g) + C(g)$$

The pressure of C(g) at 30 minutes time interval would be ________ mm Hg. (nearest integer)

Consider the following two half-cell reactions along with the standard reduction potential given :

$\mathrm{CO}_2 + 6\mathrm{H}^+ + 6e^- \longrightarrow \mathrm{CH}_3\mathrm{OH} + \mathrm{H}_2\mathrm{O}\qquad E_{\text{red}}^{\circ} = 0.02\ \mathrm{V}$

$\dfrac{1}{2} \mathrm{O}_2 + 2\mathrm{H}^+ + 2e^- \longrightarrow \mathrm{H}_2\mathrm{O}\qquad E_{\text{red}}^{\circ} = 1.23\ \mathrm{V}$

A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\mathrm{CH}_3\mathrm{OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas,

$\Delta V = \underline{\hspace{2cm}}$ m$^3$. (nearest integer)

Given : $\mathrm{F} = 96500~\mathrm{C~mol}^{-1}$

Number of paramagnetic ions among the following d- and f-block metal ions is __________.

Mn²⁺, Cu²⁺, Zn²⁺, Yb²⁺, Sc³⁺, La³⁺, Gd³⁺, Lu³⁺, Ti⁴⁺, Ce⁴⁺

(Atomic number of Mn = 25, Cu = 29, Zn = 30, Yb = 70, Sc = 21, La = 57, Gd = 64, Lu = 71, Ti = 22, Ce = 58)