#Q85 Let {a_n} be a sequence with infinite number of 1โs then which of the following Is true?
Anonymous Quiz
21%
โ sequence {a_n} which does not converges
33%
{a_n} converges always
45%
โ sequence {a_n} which is convergent
1%
None of these
#Q.86 Which of the following is true?
Anonymous Quiz
31%
โ uncountable subset of R, say S, such that โS=S
34%
โ an uncountable subsetof R, say S, such that โS=S
25%
โ countable subset S of R such that โS=S.
9%
) None of these
#Q 87 SโR, S is uncountable, T=cd(S)Where cd (S) is condensation point of S. Then
Anonymous Quiz
19%
S-T is countable, SโฉT is countable
31%
S-T is countable, SโฉT is uncountable
27%
S-T is uncountable, SโฉT is countable
24%
S-T is uncountable, SโฉT is uncountable
#Q 88 If set A is the neighborhood of any point {a}, then A is similar to
Anonymous Quiz
10%
N
17%
Q
68%
Anyuncountable set
5%
Noneof these
โค1
#Q 89 Which of the following is/are correct?
Anonymous Quiz
14%
Countableset can be the neighborhood of a point
13%
Finiteset can be the neighborhood of a point
41%
Uncountable set can be the neighborhood of a point
33%
Uncountableset must be the neighborhood of a point
#Q90 A finite set is
Anonymous Quiz
5%
Open
67%
Closed and bounded
18%
Both open and closed
9%
Noneof the above
#Q91 The subset A={xโQ:x^2<4} of R is
Anonymous Quiz
18%
Bounded above but not bounded below
58%
Bounded above and sup A=2
16%
Bounded above but not have a supremum
8%
Not bounded and does not have a supremum
โค1
#Q92 Given real numbers a and b such that aโคb+ฮต โ ฮต>0 then
Anonymous Quiz
20%
a=b
58%
aโคb
17%
aโฅb
5%
ab=1
#Q93 Consider the sequence {a_n} defined by a_n=n .e^(-n). Then
Anonymous Quiz
48%
{a_n} is convergent
23%
{a_n} is not convergent
17%
{a_n} is unbounded
12%
{a_n} is bounded but not monotonic
#Q94 Which of the following is true?
Anonymous Quiz
13%
If a_nโ โ and {b_n} is convergent then {a_n b_n} converges.
28%
If a_nโ โ and {b_n} is convergent then {a_n b_n} diverges to โ.
11%
If a_nโ โ and {b_n } is convergent then {a_n b_n } oscillates.
48%
lim(nโโ) a_n= l and lim(nโโ) b_n= m then lim(nโโ) a_n b_n= lm
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Dear Friends , Today Quiz will start at 3:00 PM. Total 10 Questions - Part B - Mathematical Science. Thanks
#Q96 If, f : (0,โ) โ(0,โ) be such that |f(x)-f(y)|โค 1/2 |x-y|. Then, has f has
Anonymous Quiz
55%
One fixed point
26%
Two fixed point
7%
Three fixed point
12%
No fixed point
#Q95 Statement -1 If f is bounded, then f is uniformly continuous. Statement-2 If f is differentiable, and if f^' is bounded, then f is uniformly continuous.Then,
Anonymous Quiz
13%
Both statements are true.
10%
Both statements are false.
17%
Statement-1 is true but statement-2 is not.
61%
Statement-2 is true but statement-1 is not.
๐คฉ2โค1
#Q98 Let f(x)=sinโก(x sinโกx ) on (0,โ), then
Anonymous Quiz
19%
f(x) is uniformly continuous
36%
f(x) is not uniformly continuous
41%
f(x) can be made uniformly continuous by redefining its values on a set of Countably many points.
4%
None of the above
#Q99 Let f(x)=[2cos x ], xโ[-ฯ,ฯ] then f(x)
Anonymous Quiz
54%
is discontinuous at exactly 4 points.
29%
is discontinuous at exactly 5 points.
7%
is discontinuous at exactly 6 points.
10%
is discontinuous at exactly 7 points.
#Q100 Let f be a function f:QโQ such thatf(x+y)=f(x)+f(y). Then,
Anonymous Quiz
51%
f(q)=cq, CโQ
10%
f(q)=cq*cq
27%
f is any bounded function
12%
f is not linear
#Q101 Let f be a function f:RโR such thatf(x+y)=f(x)+f(y), then
Anonymous Quiz
71%
The set of all such functions are of the typef(x)=cx,cโR
18%
Not all functions are of the type f(x)=cx cโR
4%
f is not linear
6%
None of these
#Q102 Let f be a function such that f(x)+f(y)=f(x+y). If it is given that there exists a positive real & such that f(h)=h โ 0<h<ฮด then
Anonymous Quiz
26%
f' (2)=2
13%
f' (3)=3
15%
f' (4)=4
46%
f' (1)=1