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

Ans:A

62.E={p’in’’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 ‘QQ’

D.E is a compact subset of ‘QQ’

Ans:D

63.Let function n(x)={(n-1)x raise to n, if x is
rational(first row),1-(n-1)x raise to n,if x is irrational(second row).Then
which of the following function is discontinuous everywhere on [0,1]?

A.’g_(1)’

B.’g_(2)’

C.’g_(3)’

D.All of these

Ans:A

64.Let f(x)={ x+x raise to 2 sin 1/x,if x not equal
to 0(first row),0 if x=0(second row)

The f’(0) is

A.0

B.1

C.2

D.Does not exists

Ans:B

65.Which of the following is not uniformly
continuous on ‘RR’?

A.x

B.sin x

C.x sin x

D.’(1)/(1+x^(2))’

Ans:C

66.Let ‘s_(n)’=’1/1^(2)+1/2^(2)+….+1/(n^(2))’.Then
which is false?

A.{‘s_(n)’} is a sequence in ‘QQ’

B.{‘s_(n)’} is a Cauchy sequency in ‘QQ’

C.{‘s_(n)’} is convergent in ‘QQ’

D.None of these

Ans:C

67.Let ‘f_(n)’:’RR’’->’’RR’ defined by fn(x)={0
if x elements of (- infinity,n)(first row),n,if x elements of [n,infinity)

Then choose the most correct answer

A.’{f_(n)}’ does not convergent on ‘RR’

B.’{f_(n)}’ converges to zero function on ‘RR’

C.’{‘f_(n)’}converges to zero function on ‘RR’
uniformly

D.None of these

Ans:B

68.Which is false?

A.There exists a function f:’RR’’->’’RR’ which is
continuous exactly at one point

B.There exists a function f:’RR’’->RR’ which is
differentiable exactly at one point

C.There exists a function f:’RR’’->’’RR’ which is
discontinuous everywhere

D.None of these

Ans:D

69.Which of the following subset of ‘RR^(3)’has
positive Lebesgue measure?

70.If ‘int_(1)^(00)’f(x) dx=L where
0<L<’oo’;then ‘lim_(x->oo)’f(x)is

A.0

B.’oo’’’

C.Always exists

D.Need not exists

Ans:D

71.Which is false?

A.cos z=5 has a solution in ‘CC’

B.sin z is a polynomial in ‘CC’

C.’sin ^(z)’+’cos z^(2)’=1 for all z ‘in’’CC’

D.Every non constant polynomial in ‘CC’[x] has a
zero in ‘CC’

Ans:B

72.The image of the line y=1 under the mapping w=sin
z is

A.Parabola

B.Ellipse

C.Rectangular Hyperbola

D.None of these

Ans:B

73.The value of ‘’’int_(C)’’(1)/(z^(3)(z+1)’ dz
where C is |z|=3;is

A.2’pi’i

B.-4’pi’i

C.4’pi’i

D.0

Ans:D

74.Consider the metric space (‘NN’,d)where d is
given by d(m,n)=|’1/m’-‘1/n’|.Then which is false?

A.d is a bounded metric on ‘NN’

B.d induces the discrete topology on ‘NN’

C.’{1/n}’ converges to 0

D.This space is Hausdorff

Ans:C

75.Which is not a productive property?

A.Connectedness

B.Compactness

C.Locally connectedness

D.Path connectedness

Ans:C

76.Let X=(0,1) and Y=’RR’.Then which is true?

A.X and Y are the same as metric spaces

B.X and Y are the same as topological spaces

C.Both (a) and (b)

D.Neither (a) nor(b)

Ans:B

77.Which of the following topological property is
not preserved under a continuous function?

A.Connectedness

B.Compactness

C.First countability

D.None of these

Ans:C

78.Which is true?

A.On’RR’co-finite topology is weaker than usual
topology

B.On’RR’usual topology is weaker than co-finite
topology

C.On’RR’ co-finite topology and usual topology are
not comparable

D.On’RR’co-finite topology and usual topology are
the same

Ans:A

79.If every closed interval[a,b] with a<b is open
with respect to some topology on’RR’;then with respect to this topology,closure
of [27,37]is

A.[27,37]

B.(-‘oo’,37]

C.[27,’oo’)

D.’RR’

Ans:A

80.For the space ‘RR’with co-countable
topology,which is false?

A.Uniqueness of limits exists in this space for the
convergence of sequences

B.This space is not Hausdorff

C.{‘1/n’} is divergent in this space’’

D.None of these

Ans:D

81.If f:’RR’’->’’RR’ is a twice differentiable
function with ‘lim_(x->oo)’(2f(x)+3f’(x))=0 with
‘lim_(x->oo)’f(x)=’lim_(x->oo)’f’(x)=1;then ‘lim_(x->oo)’f’’(x)is

A.0

B.1

C.10

D.11

Ans:D

82.The third approximation ‘y_(3)’(x) for the
I.V.P.,y’=2x(1+y);y(0)=0 by Pickard’s method is

A.’x’+’x^(2)/2’+’x^(3)/6’

B.’x^(2)’+’x^(4)/2’+’x^(6)/6’

C.’x’+’x^(2)/2+x^(8)/6’

D.None of these

Ans:B

83.Consider the vector space V={f:’RR’’->’’RR’
such that f’’-2f’+f=0 over ‘RR’.Then which of the following is a basis for V?

A.{‘e^(t)’}

B.{‘e^(t),te^(t)’}

C.{e^(-t)’}

D.None of these

Ans:B

84.If F(a,b,c,x) is the hyper geometric series,then
‘lim_(b->oo)’F(a,b,a,’x/b’)is

A.’(1+x)^(a)’

B.log(1+x)

C.’e^(x)’

D.sin x

Ans:C

85.If ‘P_(n)(x)’ is the Legendre Polynomial ,then
‘P_(n)(-1)’is

A.1

B.-1

C.’(-1)^(n)’

D.0

Ans:C

86.The equation ‘U_(xxxx_)+x^(2)U_(yy)’=0 is

A.Elliptic

B.Parabolic

C.Hyperbolic

D.None of these

Ans:A

87.If a,b,c are three constants such that
‘U_(x)’=a,’U_(y)’=b and ‘U_(z)’=c with u(x,y,z)=0 at (0,0,0); then U(1,0,0)is

A.a

B.b

C.c

D.None of these

Ans:A

88.If 0<s<1,then ‘int_0^oo(x^(s-1))/(1+x)dx’is

A.’beta’(1,s)

B.’beta’(1-s,1)

C.’beta’(1-s,s)

D.Divergent

Ans:C

89.The Laplace transform L{‘(sin omegat)/(t)’} is

A.’cot^(-1)((s)/(w))’

B.’(omega)/(s^(2)+omega^(2))’

C.’(s)/(s^(2)+omega^(2))’

D.None of these

Ans:A

90.Which of the following is a periodic function on
‘RR’?

A.x-[x]

B.x

C.[x]

D.none of these

Ans:A

91.A velocity field is given by q( raist to
bar)=xi+(y+t)j.Then the stream line for this field at t=2 is

A.Circle

B.Ellipse

C.Hyperbola

D.Rectangular hyperbola

Ans:D

92.Consider the fuzzy sets A and B on X=[0,’(pi)/(2)’]where
A(x)=sin x and B(x)=cos x.Then o.8-cut of A’nn’B is

A.’Phi’

B.X

C.An uncountable subset of X

D.A denumerable subset of X

Ans:A

93.Which is false about the Cantor set?
A.Cantor set is perfect

B.Cantor set is compact

C.Cantor set is fractal

D.Cantor set is an uncountable set with positive
Lebesgue measure

Ans:D

94.The Voltra integral equation corresponding to the
differential equation y”+xy=1,y(0)=y’(0)=0 is

A.’y(x)’=’(x^(2))/(2)’-‘int_0^xty(t)dt’

B.’y(x)=x^(2)/2’-‘int_0^x(x-t)y(t)dt’

C.’y(x)=(x^(2))/(2)-‘int _0^(x)(x-t)ty(t)dt’

D.’y(x)=(x)/(2)’-‘int_0^x(x-t)ty(t)dt’

Ans:C

95.The derivative of the Weierstrass function is

A.Elliptic

B.Even

C.Pole of order 2

D.All the above

Ans:A

96.The function ‘zeta’ (z)is

A.Weierstrass (z)

B.Weierstrass raise to 1(z)

C.-Weierstrass raise to 1(z)

D.Weierstrass (z)

Ans:D

97.For the Euler’s gamma function symbol(z)symbol(1-z)is

A.’(pi)/(cospiz)’

B.’(pi)/(sinpiz)’

C.’(pi)/(cotpiz)’

D.None of these

Ans:B

98.Which of the following is not a maximal geodesic
for the cylinder ‘x_(1)^(2)’+’x_(2)^(2)’=1 in ‘RR^(3)’?

A.Vertical line

B.Horizontal circle

C.Helix

D.None of these

Ans:D

99.Which of the following linear transformation is a
possible Weingarten map for the unit n-sphere ‘x_(1)^(2)+’’x_(2)^(2)’+’x_(3)^(2)’=1
in ‘RR^(3)’ oriented by its inward unit normal?

A.Traise to
x bar=0

B.T raise to x bar=x bar

C.T raise to x bar=2 x bar

D.T raise to x bar=3 x bar

Ans:B

100.Which of the following is reducible over ‘RR’?

A.’x^(2)’+1

B.’x^(2)’+2

C.’x^(5)’+’x^(3)+’’x^(2)’+x+1

D.None of these

Ans:C

SOLVED PAPER AND EXAM PRACTICE REGISTERED USERS ONLY

Please Give Us Your 1 Minute In Sharing This Post!

Look at a day when you are supremely satisfied at the end.It is not a day when you lounge around doing nothing.It's when you have had everything to do and you have done it.-Margaret Thatcher

Dear Valuable Customer, Thank you for giving us the opportunity to serve you better,please help us by taking few seconds to tell us about the service you received.As your Feedback is very important for us.We appreciate your comments and make sure we meet your expectations.Your satisfaction reflects our liking of service which gives us positive results to run healthy business,feel free to give comments as per satisfaction.Thanks for being awesome customer.May All Your Dreams and Wishes Come True,and May Prosperity Touch Your Feet.Wishing You a Happy Learning.

Look at a day when you are supremely satisfied at the end.It is not a day when you lounge around doing nothing.It's when you have had everything to do and you have done it.-Margaret Thatcher

ReplyDelete