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 :

-3:2
273: 250ಗ(2)
0:-4:3
D:-2:1
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 :

3ھ

B:-8

C:-0

0:۰17"

Correct Answer:- Option-B

Question49:-If f is a non-zero linear functional defined on a three dimensional vector space X, then the dimension of the null
space of fis:

3ھ
2-
ای
‎D:-None of these‏
‎Correct Answer:- Option-B‏
‎Question50:-Which of the following is not a Hilbert space ?‏
‎A:-C [0, 1]‏
]1 ,1^2[0-
واج
‎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 of‏
‎“{x_n} is:‏
‎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 :
“f (x)=x*2+a, x < 2°
` = 2a-x%2, x>=2° is continuous at every x.

A:a=0

952
Cra =8
0:-2 = 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 :
A--f is a constant

-f is not differentiable on ۴

C:-f is measurable

D:-f 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 Gis :

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

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