The Recurrence T(N) = 3T(N/2) + cN and T(1) = 1 .
N is a power of 2, so, N = 2k and K = Log N
Total time at 1st level :--> cN
Total time at 2nd level :--> 3(cN/2) = (3/2)cn
Total time at 3rd level :--> 32(cn/22) = (3/2)2cn
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Total Time Complexity => $\left \{ 1 + 3/2 + (3/2)^{2} + ... + (3/2)^{K - 1} \right \} cN + N^{Log 3}$
=> $\left \{ 1 * (3/2)^{K - 1}) / (3/2-1) \right \} cN + N^{Log 3}$
=> $\left \{ 2c + 1 \right \} N^{Log 3} - 2cN$
Take c = 1
=> $3 * 3^{Log N} - 2N$
Option C is correct .