For the galvanic cell
Ag | AgCl(s), KCl (0.2M) || KBr (0.001M), AgBr(s) | Ag
Calculate the EMF generated and assign correct polarity to each electrode for a spontaneous process after taking into account the cell reaction at 25^oC.
[K_sp(AgCl) = 2.8 $$times$$ 10^-10; K_sp(AgBr) = 3.3 $$times$$ 10^-13]

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