Question55:-Let f: R’->°R is differentiable for every x ‘epsi’ R, such that ‘lim_(x->00)° f'(x) = ‏کل‎ Then 1൩0൨-0൦)" 7
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Correct Answer:- Option-C

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Question56:-Let t be a positive integer and define a sequence *{x_n}* by *x_(n+1)=t+* 3 for all n’ >="0 with *x_0=0". If
the sequence is convergent, then :

As t= U4

0:-1 (൮/൪)
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 *f (x) = a_l* sin ‘x + a_2° sin ‘2x +...+ a_n’ sin nx such that |f (x)|"<="| sin x| ലാട. ന്ന
*Ja_1+2a_2+...+ 6:
A:-cannot find
B:-0
C:-greater than *(n (n+1))/2° 7
D:-less than or equal to 1
Correct Answer:- Option-D
Question59:-Let ` {5.0} ` 0€ a sequence of real numbers defined by *S_1=sqrt(2)* and “S_(n+1)=sqrt(2+S_n),*
then (51) 8:
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 :
A:-f is measurable if it is monotonically increasing
B:-f is always measurable
C:-f need not be measurable
D:-none of the above
Correct Answer:- Option-C
Question61:-The value of ‘int_C***1/z*2 dz,* where C is the curve *|z - i] = 1/2,” is:
Ae
B:-0
‏“لمع‎
‎0; - 19/53:
Correct Answer:- Option-B
Question62:-Which of the following is a bounded complex valued function :
A--f (z) = sin z, in the complex plane
8:- (2) - e*z/z,* in the complex plane with |z| > 0
C:-f (z) = cosh z, in the complex plane
D:-None of the above (A), (B) and (C)
Correct Answer:- Option-D
Question63:-The function *g(z) = (z)/(e*z-1), z!= 0,` has:
A:-Essential singularity at z = 1
B:-Pole at the origin
C:-Essential singularity at the origin
D:-Removable singularity at the origin