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### An ideal gas undergoes a four step cycle ...

An ideal gas undergoes a four step cycle as shown in the P − V diagram below. During this cycle, heat is absorbed by the gas in

(A) steps 1 and 2           (B) steps 1 and 3
(C) steps 1 and 4           (D) steps 2 and 4

Solution

Step 1 (A to B): Isobaric

$V \propto T$

$T_B > T_A$

$Q \propto C_p \Delta T > 0$

Step 2 (B to C): Isochoric

$P \propto T$

$T_C < T_B$

$Q \propto C_v \Delta T < 0$

Step 3 (C to D): Isobaric

$V \propto T$

$T_D < T_C$

$Q \propto C_p \Delta T < 0$

Step 4 (D to A): Isochoric

$P \propto T$

$T_A > T_D$

$Q \propto C_v \Delta T > 0$

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