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 a non-zero complex number z, let arg(z) denote the principal argument with - 
< arg(z) < 
. Then, which of the following statement(s) is (are) FALSE ?
, where 
, defined by f(t) = arg(-1+ it) for all t 
R, is continuous at all points of R, where 
- arg (z 1 ) + arg (z 2 ) is an integer multiple of 
, lies on a straight line
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a, b, d)
Arg(-1-i)=- 
Arg(-1+it)= 
Not continuous at t = 0
z, z 1 , z 2 , z 3 form a cyclic quadrilateral Hence locus of z is circle
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