D:-None of these
Correct Answer:- Option-A
Question56:-Let *lim_(x->0)f(x)/x=I, where 0< ‘I’ *0)° (00
A:-ls always 0
B:-Need not exists
C:-Exists, but not always zero
D:-Exists and depends on ` |
Correct Answer:- Option-A
Question57:-Which of the following function is not differentiable on (0, (01/(2))` ?
A-sin x
B:-|sin x|
C:-max{sin x, cos x}
D:-None of these
Correct Answer:- Option-C
Question58:-Let A be a 5x4 matrix and B be a 4x5 matrix. Then 1 is necessarily an eigen value of
A:-AB
B:-AB + |
C:-BA
D:-BA +1
Correct Answer:- Option-B
Question59:-The equation *x*(2)° യ്മ)” + 2xy -1 = 0 represents
A:-Parabola
B:-Ellipse
C:-Hyperbola
D:-Pair of straight lines
Correct Answer:- Option-D
Question60:-Which of the following is not a Banach space ?

Correct Answer:- Option-A
Question61:-Which is false about “NN* ?

A:-NN* cannot be written as a denumerable union of denumerable disjoint sets

B:-‘NN* is well ordered

C:-NN° is a closed subset of *RR*

D:-None of these

Correct Answer:- Option-A
Question62:-E = (2: ‘QQ* :2<‘p*(2)° <3}. Then which is false ?

A:-E is open in “QQ”

B:-E is closed in *QQ*

C:-E is a bounded subset of 00.

D:-E is a compact subset of 0௦:

Correct Answer:- Option-D
(n — 1)2" if x is rational
gn{x) = 1- (18 + 1) if x is irrational
Question63:-Let 0
Then which of the following function is discontinuous everywhere on [0 ,1] ?

“(1)_و-تم

6:-9_)3(“
D:-Alll of these
Correct Answer:- Option-A

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Question64:-Let
Then f'(0) is
A:-0