(A) Calculate $$\Delta_r G^\circ$$ of the following reaction

$$A{g^ + }(aq.) + C{l^ - }(aq.) \to AgCl(s)$$

Given :

$$\mathrm{\Delta_r G^\circ(AgCl)\quad-109~kJ/mole}$$

$$\mathrm{\Delta_r G^\circ(Cl^-)\quad-129~kJ/mole}$$

$$\mathrm{\Delta_r G^\circ(Ag^+)\quad-77~kJ/mole}$$

(i) Represent the above reaction in form of a cell.

(ii) Calculate E$$^\circ$$ of the cell.

(iii) Find $${\log _{10}}{K_{sp}}$$ of AgCl.

(B) If $$6.539\times10^{-2}$$ g of metallic Zn (amu = 65.39) was added to 100 mL of saturated solution of AgCl, then calculate $${\log _{10}} = {{[Z{n^{2 + }}]} \over {{{[A{g^ + }]}^2}}}$$. Also find how many moles of Ag will be formed.

Given that :

$$\mathrm{Ag^++e^-\to Ag\quad E^\circ=0.80~V}$$

$$\mathrm{Zn^{2+}+2e^-\to Zn\quad E^\circ=-0.76~V}$$

A person goes office either by car, scooter, bus or train, proability of which being $$\frac{1}{7}, \frac{3}{2}, \frac{2}{7}$$ and $$\frac{1}{7}$$, respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is $$\frac{2}{9}, \frac{1}{9}, \frac{4}{9}$$ and $$\frac{1}{9}$$, respectively. Given that he reached office in time, then what is the probability that he travelled by a car?

Find the range of value of $$t$$ for which

$$2 \sin t=\frac{1-2 x+5 x^{2}}{3 x^{2}-2 x-1}, t \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$

Circles with radii 3, 4 and 5 touch each other externally if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the point of contact.