NIMCET 2014 — Computer PYQ

Let $A$ be the set of bit strings starting with $0$.

Let $B$ be the set of bit strings ending with $11$.

We need to find the union: $n(A\cup B)=n(A)+n(B)-n(A\cap B)$

1. Calculate $n(A)$ (Starts with $0$):

The first bit is fixed as $0$. The remaining $7$ bits can be either $0$ or $1$.

2. Calculate $n(B)$ (Ends with $11$):

The last two bits are fixed as $11$. The remaining $6$ bits can be either $0$ or $1$.

3. Calculate $n(A\cap B)$ (Starts with $0$ AND ends with $11$):

The first bit is fixed ($0$) and the last two bits are fixed ($11$). This leaves $8-1-2=5$ bits free.

4. Final Calculation:

Correct Option: 4. $160$