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### The volume V of an enclosure contains a mixture ....

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is :

(A) $\frac {3RT}{V}$               (B) $\frac {5}{2} \frac {RT}{V}$
(C) $\frac {88RT}{V}$             (D) $\frac {4RT}{V}$

Solution

We have, $PV=nRT$

$\therefore PV = ({n_{{O_2}}} + {n_{{N_2}}} + {n_{C{O_2}}})RT$

$\Rightarrow PV = \left( {\frac{{16}}{{32}} + \frac{{28}}{{28}} + \frac{{44}}{{44}}} \right)RT = 2.5RT$

$\therefore P = \frac{5}{2}\frac{{RT}}{V}$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$