Question55:-Let f: R*->"R is differentiable for every x 6051” R, such that *lim_{(x->o0)" 500 ട க்‌ பார்க ட ர
೧00೯ 6:
കഃ

1 പം 5

B:-
न
0:00.
Correct Answer:- Option-C

2

Question56:-Let t be a positive integer and define a sequence *{x_n}" by "x_(n+1)=t+" e for all 0" >="0 with ൨050. 1
the sequence is convergent, then:

47ھ )۰ھ
”8<
1/47 6:۰
‎D"t < (-1)/(&)7‏
‎Correct Answer:- Option-A‏
‎Question57:-Find the number of continuous onto maps from [0, 1] to (0, 1).‏
‎A:-Countably many‏
‎B:-None‏
‎C:-Exactly one‏
‎D:-Uncountably many‏
‎Correct Answer:- Option-B‏
‎Question58:-Let 1 (0 17 sin “x + a_2" sin “2x +...+ a_n" sin nx such that |f (x}|"<="| sin 7(| ` ಸಿಸಿ? 6೧51 8. 77೧೧‏
:6 [0 08 +...+8-1+28-2|*
‎A:-cannot find‏
‎B:-0‏
‎C:-greater (6 (5127 ``‏
‎D:-less than orequal to 1‏
‎Correct Answer:- Option-D‏
‎Question59:-Let *{S_n}" be a sequence of real numbers defined by *S_1=sqrt(2)* and *S_(n+1)=sqrt(2+5_n},"‏
‎then*{Sn} is:‏
‎A:-Monotonically increasing for all n‏
‎B:-Monotonically decreasing for all n‏
‎C:-Monotonically increasing for even n and decreasing for odd n‏
‎D:-Neither increasing nor-decreasing‏
‎Correct Answer:- Option-A‏
‎Question60:-Let f be a function on real line such that |f| is measurable. Then:‏
‎measurable 8 it is monotonically increasing‏
‎is always measurable‏ -:5
‎C:-f need not be measurable‏
‎D:-none of the above‏
‎Correct Answer:- Option-C‏
‎-The value of "int_C~*"1/z*2 dz," where Cis the curve 2 - || = 1/2, 15;‏

Correct Answer:- Option-B
0۷۵۶۱62: of the following is a bounded complex valued function :
A:f (2} = sin z, in the complex plane
B:-'f (z) = e”2z/z,” in the complex plane with |z| > 0
C:f (2} = cosh z, in the complex plane
D:-None of the above (ಸಿ), (8) 2೧6 (0)
Correct Answer:- Option-D
Question63:-The function 92) ട (2/2, മട 0 1195:
A:-Essential singularity at z =1
B:-Pole at the origin
C:-Essential singularity at the origin
D:-Removable singularity at the origin