sl
C:-2
D:-Does not exists
Correct Answer:- Option-B
Question65:-Which of the following is not uniformly continuous on ` रिरि` ?
Ax
B:-sin x
C:-x sinx
D:-*(1)/(1+x*(2))°
Correct Answer:- Option-C
Question66:-Let *s_(n)° ="1/1*(2)+1/2*(2)+...+1/(n*(2))° . Then which is false ?
A:-{°s_(n)* }is a sequence in ‘QQ
B:-{°s_(n)* } is a Cauchy sequence in *QQ*
C:-{*s_(n)° } is convergent in *QQ*
D:-None of these
Correct Answer:- Option-C

fal) =
Question67:-Let *f_(n)’ : *RR* *->* ‘RR’ defined by |
Then choose the most correct answer
A:- {f_(n)}* does not convergent on *RR*
B:-{f_(n)}* converges to zero function on *RR*
C:-{*f_(n)° } converges to zero function on ‘RR* uniformly
D:-None of these
Correct Answer:- Option-B
Question68:-Which is false ?
A:-There exists a function f : “RR’ *->* ‘RR’ which is continuous exactly at one point
B:-There exists a function f :RR° *->RR* which is differentiable exactly at one point
C:-There exists a function f :; RR’ *->* *RR* which is discontinuous everywhere
D:-None of these
Correct Answer:- Option-D
Question69:-Which of the following subset of *RR*(3)° has positive Lebesgue measure ?
A:-{(x, y,Z) in நாடு: ५१(2) + ४१(2) + 27(2) = 1}
B:-{(x, y, 2) रिरि? (3) :५+५+ 25 1)
(:-७ (1) + ‘W_(2)° + *W_(3)° where ` # (1) = {(> x, - x): x “in RR‘ }, ‘W_(2)° ={(x, —x, x) : x `` ` रिरि},
*w_(3)° ={(-x, x, x): x உர
D:-None of these
Correct Answer:- Option-C
Question70:-If *int_(1)*(00)* f(x) dx = Lwhere 0 < L< ‘oo’; then ‘lim_(x->00)* f(x) is
A:-0
8:-00` `
C:-always exists
D:-need not exists
Correct Answer:- Option-D
Question71:-Which is false ?
A:-cos z = 5 has a solution in 00
B:-sin z is a polynomial in 66
C:-‘sin*(z)* +°cos z*(2)° = 1 for all z ‘in’ (९
D:-Every non constant polynomial in “CC*[x] has a zero ൩ (¢
Correct Answer:- Option-B
Question72:-The image of the line y = 1 under the mapping w = sin z is
A:-Parabola
B:-Ellipse
C:-Rectangular Hyperbola
D:-None of these
Correct Answer:- Option-B
nt_(C)**(1)/(z*(3)(z+1) dz where C is |z| = 3; is