One mole of an ideal gas at 900 K, undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $$\ln {{{V_3}} \over {{V_2}}}$$ is _________.


(U : internal energy, S : entropy, p : pressure, V : volume, R : gas constant)

(Given : molar heat capacity at constant volume, C_V,m of the gas is $${5 \over 2}$$R)

Consider a helium (He) atom that absorbs a photon of wavelength 330 nm. The change in the velocity (in cm s^$$-$$1) of He atom after the photon absorption is __________.

(Assume : Momentum is conserved when photon is absorbed.

Use : Planck constant = 6.6 $$\times$$ 10^$$-$$34 J s, Avogadro number = 6 $$\times$$ 10²³ mol^$$-$$1, Molar mass of He = 4 g mol^$$-$$1)

Ozonolysis of ClO₂ produces an oxide of chlorine. The average oxidation state of chlorine in this oxide is __________.

Let

$${S_1} = \left\{ {(i,j,k):i,j,k \in \{ 1,2,....,10\} } \right\}$$,

$${S_2} = \left\{ {(i,j):1 \le i < j + 2 \le 10,i,j \in \{ 1,2,...,10\} } \right\}$$,

$${S_3} = \left\{ {(i,j,k,l):1 \le i < j < k < l,i,j,k,l \in \{ 1,2,...,10\} } \right\}$$ and

$${S_4} = \{ (i,j,k,l):i,j,k$$ and $$l$$ are distinct elements in {1, 2, ...., 10}.

If the total number of elements in the set S_r is n_r, r = 1, 2, 3, 4, then which of the following statements is(are) TRUE?