27. Let fbe a function defined on [0, 1] by

fix)=0 when x is rational

=1 when x is irrational
The Lebesgue integral of f over [0, 1] is :
(^) 0 (8) Does not exist (0) ൭ (2) 1
b

28. Suppose f2 0 and f is continuous on [a, b] and कि =0. Which of the following is

true 7

(4) fix)=0forall x¢[a, b

18) flx)=11orallxe[a b

(€) fis monotonic increasing on [a, 9]

(D) Image of fis [0, =)
29. Which of the following is true ?

(¢) एष्टा Lebesgue integrable function is Riemann integrable

(B) Every Riemann integrable function is Lebesgue integrable

(6) Limits of Riemann integrable functions are always Riemann integrable

(D) Limits of measurable functions need not be measurable
30. The measure of the cantor set is :

(ಡಿ) = 8) 1 © 0 (D) not measurable
31. Ifw=1isan n® root of unity, then 1+ 20+ 362+ .. + nwt-1 =

1 c =5 n

(५) 0 8 ൽ ‏بس ات‎ 0
32. Which one of the following functions is not the real part of an analytic function ?

(^) "(य ॥) => - ४२ © ॥ (५, ४) ‏تقد‎

(ಲ) ५ (, 9) =" -ञ्‌/2 - / (0) ५ (४) = ९ ८८5 |
33... 1110 0೧೦ 0! the fallowing is not true about f{z) = sin z ?

(है) itis a bounded function (B) it is an entire function

) itis a periodic function (D) 15 മാടെ ലയ isolated
34. Choose the correct statement ‏؛‎

∕∣

≼⋀⋮∎∫∹≖⊢−∁⋅⋅↥∣∎↷⋝∂∏⊵⋮≊∉∏∐⋅∄∣ singularily at z= =

(B) = ~ 1 hasa simple pole 21 2 ಎ0

(£) flz)=2%+1 has a pole of order 2 at z= ‏ہ‎

ಎ. ಆ ರಊ' ಲ್‌ =0

ति
z

121/2014 6 A