B:-closure of E* contains no non-empty open sets
C:-closure of E* contains empty open set
D:-none of the above
Correct Answer:- Option-B
Question67:-If *f 1° and *f 2* are two real-valued bounded functions defined on *[a,b]* then for every partition *P"
on [कणु
AU f 1+ 2)=U(P. f 1)+ U(P. f2)
8:-0 (P, f_14f 2)<= U(P, 1) + U (P, 2(
€~ P, f 1+ 2)>= U (P, 1) + U(P, f2)
D:-None of the above
Correct Answer:- Option-B
Question68:-If *f: [a,b] -> R* is continuous and monotonic function then
Riemann integrable on ` [8,0]
8:77 is not Riemann integrable on ` [2.0].
‏ىا ا‎ Riemann integrable ௩ ` `
D:-None of the above
Correct Answer:- Option-A
Question69:-Which of the following is true?
A:-Theset *[0,1]" is not countable
B:If 'E_1° and 'E_2" are Lebesgue measurable, then “E_1 uu E_2" is Lebesgue measurable
C:-The family *M* of Lebesque measurable sets is an algebra of sets
D:-All of the above
Correct Answer:- Option-D
Question70:-Given *int_0~1 (sin {1/(x}})}/(sqrt{x}}dx" , then
A:-Integral is divergent
B:-Integral is absolutely convergent
C:-Integral is not absolutely convergent
D:-None of the above
Correct Answer:- Option-B
Question71:-If *f* ஊரில the conditions of Lagrange's mean value theorem and if *f' (x} = 0 AA x in [a,b]" , then which of
the following ടല?
A:-'f is constant भ) ` [केण
8: is strictly increasing ‏ما‎ 1607
ரி s strictly decreasing in *[a,bI’
D:-None of the above
Correct Answer:- Option-A
Question72:-*lim_(z->0) (barz}/(z}" is
ಹಿಂ
B:-1
ய
D:-Does not exist
Correct Answer:- Option-D
Question73:-The radius of convergence of the power series “sum_{n=0}"0o (2n!}/((n})}"~2} (2-3i}*n " is
Al
B:-0
யு
0: 0/8
Correct Answer:- Option-D
Question74:-A function is said to be harmonic if
A= (del~2u)/(delx~2) + (del*2v)/(delx~2) = 0"
B:-*(del~2u)/(delx”2) + (del*2u)/(dely~2) = ‏٭”‎
‎C:-*({delu}/{delx} + (delu)/(dely) = 0*
D:- (delv)/{delx) + (delv)/(dely) = 0*
Correct Answer:- Option-B
Question75:-The value of “int_c log zdz" where *¢’ is the unit circle is