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
#Q103 If f(x) is a function of bounded variation, then which of the following is/are true
Anonymous Quiz
58%
f(x) is bounded in that interval
7%
f(x) is unbounded in that interval
31%
f(x) is continuous in [a,b]
5%
f(x) is not continuous in [a,b]
#Q104 If =z ฬ
, then which of the following must hold?
Anonymous Quiz
26%
z is purely real
39%
z is purely imaginary
6%
z=0
29%
Allof the above
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Dear Friends , Today Quiz will start at 3:00 PM. Total 10 Questions - Part B - Mathematical Science. Thanks
#Q105 Which of the following property hold by real numbers but not by complex numbers?
Anonymous Quiz
13%
Field
44%
Ordered
22%
Commutative
21%
all properties are same
โค1
#Q107 |z-z_1 |=|z-z_2 | is the locus of (where z_1 and z_2 are fixed points)
Anonymous Quiz
35%
Line segment between z_1 andz_2
37%
Circle through z_1 and z_2
25%
Perpendicular bisector of line joining z_1 and z_2
3%
None of the above
#Q108 Ifz ฬ
+|z|=9+3i, then
Anonymous Quiz
43%
Im(z) = -3
33%
Im(z)= 3
13%
|z|=9
10%
z is purely real
#Q110 Let u=1/z where z=x+iy then;
Anonymous Quiz
6%
Re(u)=Re(z)
41%
Re(u)=kRe(z), where k is positive constant
46%
Re(z)Im(u)+Re(u)Im(z)=0
7%
None of the above