NIMCET 2011 — Mathematics PYQ

Using the principle of inclusion-exclusion:

2. Use De Morgan's Law:

According to De Morgan's Law, the intersection of complements is the complement of the union:

Therefore:

3. Relate to the Universal Set $X$:

The number of elements in the complement of a set is the total elements in the universal set minus the elements in that set:

4. Solve for $n(X)$:

We are given that $n(A^{\prime }\cap B^{\prime })=300$. Substitute the known values into the equation:

The correct option is (b) 700.