PART III: MATHEMATICS

SECTION 1 (Maximum Marks: 24)

• This section contains SIX (06) questions.

• Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s).

• For each question, choose the correct option(s) to answer the question.

• Answer to each question will be evaluated according to the following marking scheme:

Full Marks: +4 If only (all) the correct option(s) is (are) chosen.

Partial Marks: + 3 If all the four options are correct but ONLY three options are chosen.

Partial Marks: +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options.

Partial Marks: +1 If two or more options are correct but ONLY one option is chosen and it is a correct option.

Zero Marks: 0 If none of the options is chosen (i.e. the question is unanswered).

Negative Marks: - 2 In all other cases.

• For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in -2 marks.

For any positive integer n, define as

for all

(Here, the inverse trigonometric function tan -1 x assumes values in )

Then, which of the following statement(s) is (are) TRUE ?