IIT JEE 1983 - 'Adapted' - Subjective to Multi-Correct Q1

Let $A$ be the area bounded by the $x$ -axis, part of the curve $y=1+\frac8{x^2}$ and the ordinates $x=2$ and $x=4$ ; and the ordinate $x=a$ divides this area into two equal parts. Then which of the following is/are true?

• (A) $A$ has 3 factors
• (B) $A$ is even
• (C) $a$ is irrational
• (D) There are two possible values of $a$

Enter your answer as a 4 digit string of 1s and 9s - 1 for correct option, 9 for wrong. Eg. 1199 indicates A and B are correct, C and D are incorrect. None, one or all may also be correct.

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .