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### An empty LPG cylinder weighs 14.8 kg ....

An empty LPG cylinder weighs 14.8 kg. When full, it weighs 29.0 kg and shows a pressure of 3.47 atm. In the course of use at ambient temperature, the mass of the cylinder is reduced to 23.0 kg. The final pressure inside the cylinder is _ _ _ _ atm. (Nearest integer)
(Assume LPG to be an ideal gas)

Solution

Weight of gas before use = 29.0 - 14.8 = 14.2 kg

Weight of gas after use = 23.0 - 14.8 = 8.2 kg

Now, $\frac {P_1}{n_1} = \frac {P_2}{n_2}$

$\therefore \frac {3.47}{14.2} = \frac {P_2}{8.2}$

$\Rightarrow P_2 = \frac {3.47 \times 8.2}{14.2} \approx 2 atm$

### 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 = ${}^{12}{C_6} = 924$