B:-2 tan 2x

C:-2 cot 2x. In{sin 2x}

D:-None of these

Correct Answer:- Option-D
Question47:-The ratio of the diameter of a sphere to the height of the right circular cone having the greatest volume which
can be inscribed in the sphere is :
12

8:-3 : 2 02)

6:4:3

01

Correct Answer:- Option-A
Question48:-The dimension of the dual space of the vector space of 2°xx*2 matrices with complex entries, over the field of
real numbers is :

ಹಿ

D:-

Correct Answer:- Option-B
Question4:-If f is a non-zero linear functional defined on a three dimensional vector space ೫, then the dimension of the null
spaceof fis:
ಹಿ
B:-2
6:1
D:-None of these
Correct Answer:- Option-B
Question50:-Which of the following is not a Hilbert space 7
&-0[0, 1]
8:-1^2 0, 1]
12
D:-None of these
Correct Answer:- Option-A
Question51:-Let *{x_n}" be a convergent sequence in R, the set of real numbers. Then the number of limit points ளீ
എതു 5:
A:-Exactly one
B:-Exactly one if R is under usual topology
C:-There is no limit for limit points
D:-Cannot say
Correct Answer:- Option-B

Question52:-For what values of 'a' the function :
+ 072+, > 2"
“=2a-x"2, x>=2" is continuous at every x.

0:8 4
Correct Answer:- Option-C
Question53:-If a real valued function f is defined and continuous on a closed and bounded set F of real numbers, then :
:f is a constant
is not differentiable on F
measurable
:- is uniformly continuous on F
Correct Answer:- Option-D

Question54:-Let f be a family of measurable real functions. Let G be the set of limit points of sequences of real functions in
f. Then -

A:-measurable
B:-non-measurable
C:-countable

D:-none of the above
Correct Answer:- Option-A