In the cell

Pt$$\left| {\left( s \right)} \right|$$H₂(g, 1 bar)$$\left| {HCl\left( {aq} \right)} \right|$$AgCl$$\left| {\left( s \right)} \right|$$Ag(s)|Pt(s)

the cell potential is 0.92 V when a 10^–6 molal HCl solution is used. The standard electrode potential of (AgCl/ AgCl^– ) electrode is :
$$\left\{ {} \right.$$Given,  $${{2.303RT} \over F} = 0.06V$$  at  $$\left. {298} \right\}$$

5.1 g NH₄SH is introduced in 3.0 L evacuated flask at 327ºC. 30% of the solid NH₄SH decomposed to NH₃ and H₂S as gases . The Kp of the reaction at 327^oC is (R = 0.082 L atm mol^–1 K^–1, Molar mass of S = 32 g mol^–1 molar mass of N = 14 g mol^–1)

If  $$\int \, $$x⁵.e^$$-$$4x3 dx = $${1 \over {48}}$$e^$$-$$4x3 f(x) + C, where C is a constant of inegration, then f(x) is equal to -

Let a₁, a₂, a₃, ..... a₁₀ be in G.P. with a_i > 0 for i = 1, 2, ….., 10 and S be the set of pairs (r, k), r, k $$ \in $$ N (the set of natural numbers) for which

$$\left| {\matrix{ {{{\log }_e}\,{a_1}^r{a_2}^k} & {{{\log }_e}\,{a_2}^r{a_3}^k} & {{{\log }_e}\,{a_3}^r{a_4}^k} \cr {{{\log }_e}\,{a_4}^r{a_5}^k} & {{{\log }_e}\,{a_5}^r{a_6}^k} & {{{\log }_e}\,{a_6}^r{a_7}^k} \cr {{{\log }_e}\,{a_7}^r{a_8}^k} & {{{\log }_e}\,{a_8}^r{a_9}^k} & {{{\log }_e}\,{a_9}^r{a_{10}}^k} \cr } } \right|$$ $$=$$ 0.

Then the number of elements in S, is -