Question No. 1 is compulsory. Attempt any two questions out of the remaining three questions. In case, any candidate answers extra question(s)/ sub-question(s) over and above the required number, then only the requisite number of questions first answered in the answer book shall be valued and subsequent extra question(s) answered shall be ignored. Working notes should form part of the answer.

If $\displaystyle A = \{1, 2, 3, 4, 5\}$, $\displaystyle B = \{2, 4\}$ and $\displaystyle C = \{1, 3, 5\}$ then $\displaystyle (A - C) \times B$ is:

If $\displaystyle f(x)=x^2-5$, evaluate $\displaystyle f(3)$, $\displaystyle f(-4)$, $\displaystyle f(5)$, and $\displaystyle f(1)$.

Out of a group of $\displaystyle 20$ teachers in a school, $\displaystyle 10$ teach Mathematics, $\displaystyle 9$ teach Physics and $\displaystyle 7$ teach Chemistry. $\displaystyle 4$ teach Mathematics and Physics but none teach both Mathematics and Chemistry. How many teach Chemistry and Physics; how many teach only Physics?

If $\displaystyle A = \{1, 2, 3, 4, 5, 7, 8, 9\}$ and $\displaystyle B = \{2, 4, 6, 7, 9\}$ then how many proper subset of $\displaystyle A \cap B$ can be created?

The number of subsets of the set $\displaystyle \{0, 1, 2, 3\}$ is:

If $\displaystyle f(x) = x^2+x-1$ and $\displaystyle 4f(x) = f(2x)$, then find the value of 'x'.