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 [90]
A: U (P, f_14f_2) = U (P, f.1) + 0 (९.2)
BU (P, f 1+f 2)<= U(P, f.1) +U(P, f 2)
९:०७ ४, 1+2)>= ७ (९, _1) + ७ ४, 2)
D:-None of the above
Correct Answer:- Option-B
Question68:-If *f : [a,b] -> R° is continuous and monotonic function then
is Riemann integrable on ‘[a,b]*
is not Riemann integrable on ‘[a,b]*
is Riemann integrable on *R* **
D:-None of the above
Correct Answer:- Option-A
Question69:-Which of the following is true?
A:-The set *[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 Lebesgue measurable sets is an algebra of sets
D:-All of the above
Correct Answer:- Option-D
Question70:-Given *int_0*1 (sin {1A x)})Asqrt(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 satisfies the conditions of Lagrange's mean value theorem and if *f' (x) = 0 AA x in [a,b] , then which of
the following is true?

A is constant on ‘[a,b]°
B is strictly increasing in ‘[a,b]”
C:-f* is strictly decreasing in ` [2.0].

D:-None of the above
Correct Answer:- Option-A
Question72:-‘lim_(z->0) (barz)/(z)* is
A:-0
8:-1
©: (1)/2) `
D:-Does not exist
Correct Answer:- Option-D
Question73:-The radius of convergence of the power series *sum_(n=0)*oo (2n!)/((n!)*2) (2-3i)*n > is

Correct Answer:- Option-D
Question74:-A function is said to be harmonic if
A:-\(del® 2u)(delx*2) + (del*2v)/(delx*2) = 0°
(del* 2u)(delx*2) + (del*2u)/(dely*2) = 0°
(delu)/(delx) + (delu)/(dely) = 0°
:-* (delv)/(delx) + (delv)/(dely) = 0°
Correct Answer:- Option-B
Question75:-The value of *int_c log zdz’ where ‘c’ is the unit circle is
As Pit
8:- 201.
മല
D: