An aqueous solution of NaCl on electrolysis gives H₂(g), Cl₂(g) and NaOH according to the reaction:
2Cl^- (aq) + 2H₂O = 2OH^- (aq) + H₂ (g) + Cl₂ (g)
A direct current of 25 amperes with a current efficiency of 62 % is passed through 20 litres of NaCl solution (20% by weight). Write down the reactions taking place at the anode and cathode. How long will it take to produce 1kg of Cl₂? What will be the molarity of the solution with respect to hydroxide ion? (Assume no loss due to evaporation)

A lot contains $$50$$ defective and $$50$$ non defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events $$A, B, C$$ are defined as
$$A=$$ (the first bulbs is defective)
$$B=$$ (the second bulbs is non-defective)
$$C=$$ (the two bulbs are both defective or both non defective)
Determine whether
(i) $$\,\,\,\,\,$$ $$A, B, C$$ are pairwise independent
(ii)$$\,\,\,\,\,$$ $$A, B, C$$ are independent

A unit vector coplanar with $$\overrightarrow i + \overrightarrow j + 2\overrightarrow k $$ and $$\overrightarrow i + 2\overrightarrow j + \overrightarrow k $$ and perpendicular to $$\overrightarrow i + \overrightarrow j + \overrightarrow k $$ is ...........

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting, points $$0,$$ $$1$$ and $$2$$ are $$0.45, 0.05$$ and $$0.50$$ respectively. Assuming that the outcomes are independent, the probability of India getting at least $$7$$ points is