Loading [MathJax]/jax/output/CommonHTML/jax.js
MCQExams
0:0:1
CBSE
JEE
NTSE
NEET
Practice
Homework
×
CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 5 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Set Theory
Quiz 5
How many students in this group are not taking any of the three subjects?
Report Question
0%
8
0%
9
0%
10
0%
11
Explanation
7 students are taking Physics only.
So
7
=
n
(
P
)
−
n
(
P
∩
G
)
−
n
(
P
∩
E
)
+
n
(
P
∩
G
∩
E
)
⇒
n
(
P
)
=
7
+
n
(
P
∩
G
)
+
n
(
P
∩
E
)
−
n
(
P
∩
G
∩
E
)
So
n
(
P
)
=
7
+
24
+
30
−
16
=
45
Similarly
n
(
G
)
=
10
+
24
+
22
−
16
=
40
n
(
E
)
=
5
+
22
+
30
−
16
=
41
n
(
P
∪
G
∪
E
)
=
n
(
P
)
+
n
(
G
)
+
n
(
E
)
−
n
(
G
∩
E
)
−
n
(
P
∩
G
)
−
n
(
P
∩
E
)
+
n
(
P
∩
G
∩
E
)
=
45
+
40
+
41
−
22
−
24
−
30
+
16
=
66
75
−
66
=
9
students are not taking any of the 3 subjects.
Let
A
=
{
7
,
8
,
9
,
a
,
b
,
c
}
and
B
=
{
1
,
2
,
3
,
4
}
then number of universal relation from the set
A
to set
B
and set
B
to set
A
are
Report Question
0%
equal in counting
0%
can not be equal in counting
0%
24
0%
2
6
×
2
4
Explanation
Relation
R
is said to be universal relation from set
A
to set
B
or set
B
to set
A
if
R
=
A
×
B
∴
Number of relations from
A
to
B
for
R
=
A
×
B
=
n
(
A
)
×
n
(
B
)
=
6
×
4
=
24
Ans: C
If two intersecting circles with two points in common are drawn then how many common chords can be drawn? Draw the figure and write the answer
Report Question
0%
Only one.
0%
Many.
0%
Three.
0%
None of the options.
Explanation
W
e
k
n
o
w
t
h
a
t
t
h
e
c
o
m
m
o
n
c
h
o
r
d
o
f
t
w
o
i
n
t
e
r
s
e
c
t
i
n
g
c
i
r
c
l
e
s
i
s
p
e
r
p
e
n
d
i
c
u
l
a
r
t
o
t
h
e
l
i
n
e
j
o
i
n
i
n
g
t
h
e
c
e
n
t
r
e
s
o
f
t
h
e
c
i
r
c
l
e
s
.
H
e
r
e
a
r
e
t
w
o
i
n
t
e
r
s
e
c
t
i
n
g
c
i
r
c
l
e
s
w
i
t
h
c
e
n
t
r
e
s
O
&
O
′
.
T
h
e
c
o
m
m
o
n
c
h
o
r
d
i
s
A
B
w
h
i
c
h
i
s
p
e
r
p
e
n
d
i
c
u
l
a
r
t
o
O
O
′
a
t
P
.
N
o
w
i
f
t
h
e
c
i
r
c
l
e
s
i
n
t
e
r
s
e
c
t
i
n
m
o
r
e
t
h
a
n
t
w
o
p
o
i
n
t
s
t
h
e
n
t
h
o
s
e
c
o
m
m
o
n
c
h
o
r
d
s
w
i
l
l
h
a
v
e
d
i
f
f
e
r
e
n
t
i
n
c
i
n
a
t
i
o
n
s
w
i
t
h
t
h
e
l
i
n
e
O
O
′
r
e
s
u
l
t
i
n
g
i
n
m
a
n
y
p
e
r
p
e
n
d
i
c
u
l
a
r
s
o
n
O
O
′
w
i
t
h
d
i
f
f
e
r
e
n
t
i
n
c
l
i
n
a
t
i
o
n
s
.
T
h
i
s
a
s
s
u
m
p
t
i
o
n
i
s
i
m
p
o
s
s
i
b
l
e
.
S
o
A
B
i
s
t
h
e
o
n
l
y
c
o
m
m
o
n
c
h
o
r
d
.
A
n
s
−
O
p
t
i
o
n
A
.
Which of the following sets is/are empty?
Report Question
0%
{
x
:
x
∈
R
,
x
2
−
4
=
0
}
0%
{
x
:
x
∈
R
,
x
4
+
4
=
0
}
0%
{
x
:
x
∈
R
,
x
3
=
1
}
0%
{
x
:
x
∈
R
,
x
8
+
x
4
+
1
=
0
}
Explanation
A)
x
=
2
,
−
2
is a solution
B)
x
4
is positive always and 4 is also positive.The sum of two positive numbers is always positive.Hence x doesn't have a solution.
C)
x
3
=1
⇒
x
=
1
.
D)
x
8
+
x
4
+
1
is always positive because the individual terms are positive.Hence x here doesn't have a solution.
The set of natural number is subset of set of real numbers.
State true or false:
Report Question
0%
True
0%
False
0%
Ambiguous
0%
Data insufficient
Explanation
x
−
5
<
0
⇒
x
<
5
S
i
n
c
e
x
i
s
a
n
a
t
u
r
a
l
n
o
x
=
{
1
,
2
,
3
,
4
}
{
(
1
,
2
)
}
,
a
n
d
B
=
{
1
,
3
}
,
t
h
e
n
(
A
×
B
)
∪
(
B
×
A
)
=
{
(
1
,
3
)
,
(
2
,
3
)
,
(
3
,
1
)
,
(
3
,
2
)
,
(
1
,
1
)
,
(
1
,
2
)
,
(
2
,
1
)
,
}
Report Question
0%
True
0%
False
Explanation
A
=
{
1
,
2
}
B
=
{
1
,
3
}
A
×
B
=
{
(
1
,
1
)
,
(
1
,
3
)
,
(
2
,
1
)
,
(
2
,
3
)
}
B
×
A
=
{
(
1
,
1
)
,
(
1
,
2
)
,
(
3
,
1
)
,
(
3
,
2
)
}
∴
(
A
×
B
)
∪
(
B
×
A
)
=
{
(
1
,
1
)
,
(
1
,
3
)
,
(
1
,
2
)
,
(
2
,
1
)
,
(
2
,
3
)
,
(
3
,
1
)
(
3
,
2
)
}
True or false :
A
×
(
B
∩
C
)
=
(
A
×
B
)
∩
(
A
×
C
)
Report Question
0%
True
0%
False
Explanation
A
×
(
B
∩
C
)
=
(
A
×
B
)
∩
(
A
×
C
)
Let
(
a
,
b
)
been arbitrary elements of
A
×
(
B
∩
C
)
, then
(
a
,
b
)
∈
A
×
(
B
∩
C
)
⇒
a
∈
A
and
b
∈
(
B
∩
C
)
⇒
a
∈
A
and
(
b
∈
B
and
b
∈
C
)
⇒
(
a
∈
A
and
b
∈
B
)
and
(
a
∈
A
and
b
∈
C
)
⇒
(
a
,
b
)
∈
A
×
B
and
(
a
,
b
)
∈
A
×
C
⇒
(
a
,
b
)
∈
(
A
×
B
)
∩
(
A
×
C
)
∴
A
×
(
B
∩
C
)
⊂
(
A
×
B
)
∩
(
A
×
C
)
.....
(
1
)
Now, let
(
x
,
y
)
bean arbitrary elements of
(
A
×
B
)
∩
(
A
×
C
)
, then
(
x
,
y
)
∈
(
A
×
B
)
∩
(
A
×
C
)
⇒
(
x
,
y
)
∈
(
A
×
B
)
and
(
x
,
y
)
∈
(
A
×
C
)
⇒
(
x
∈
A
and
y
∈
B
)
and
(
x
∈
A
and
y
∈
C
)
⇒
x
∈
A
and
(
y
∈
B
and
y
∈
C
)
⇒
x
∈
A
and
y
∈
(
B
∩
C
)
⇒
(
x
,
y
)
∈
A
×
(
B
∩
C
)
∴
(
A
×
B
)
∩
(
A
×
C
)
⊂
A
×
(
B
∩
C
)
.......
(
2
)
Hence from equation
(
1
)
and
(
2
)
we get
A
×
(
B
∩
C
)
=
(
A
×
B
)
∩
(
A
×
C
)
so this equation is true.
Given the universal set
B
=
{
−
7
,
−
3
,
−
1
,
0
,
5
,
6
,
8
,
9
}
, find :
B
=
{
x
:
−
4
<
x
<
6
}
Report Question
0%
{
−
7
,
0
,
5
,
6
}
0%
{
5
,
6
,
8
,
9
}
0%
{
−
3
,
−
1
,
0
,
5
}
0%
{
0
,
5
}
Explanation
The only 4 no.s that lie in the given range are -3, 0 . -1 and 5.
A
=
{
x
:
x
≠
x
}
represents-
Report Question
0%
{
0
}
0%
{
}
0%
{
1
}
0%
{
x
}
Explanation
It is fundamental concept that a void set is defined as,
A
=
{
x
:
x
≠
x
}
=
{
}
Which of the following statements is false?
Report Question
0%
2
∈
{first five counting numbers.}
0%
f
∉
{consonants}
0%
Rose
∉
{the set of all fruits.}
0%
Asia
∈
{Continents}
Explanation
Step-1: Observing the Option 1
2 belongs to the sets of first five counting numbers
so option (A) is True.
Step-2: Observing other option
f belongs to the set of consonants so option B is false
Rose belongs to the set of all fruits so option C is True
Asia belongs to the sets of continents so option D is also True
Hence, the false statement is option B
Let
A
=
{
2
,
3
,
5
,
7
,
8
,
11
}
then which among the following is true?
Report Question
0%
7
∉
A
0%
{
2
,
3
}
⊄
o
f
A
0%
2
∈
A
0%
None of the above
Explanation
2
∈
A
means 2 is element of A which is true.
Which of the following statements is true
Report Question
0%
3
⊆
{
1
,
3
,
5
}
0%
3
∈
{
1
,
3
,
5
}
0%
{
3
}
∈
{
1
,
3
,
5
}
0%
{
3
,
5
}
∈
{
1
,
3
,
5
}
Explanation
Element/ number three is denoted by
3
and not
{
3
}
.
{
3
}
denotes a subset containing element 3. Hence
{
3
}
⊆
{
1
,
3
,
5
}
And
3
∈
{
1
,
3
,
5
}
Let
P
=
{
x
|
x
is a multiple of
3
and less than
100
,
x
∈
N
}
Q
=
{
x
|
x
is a multiple of
10
and less than
100
,
x
∈
N
}
Report Question
0%
Q
⊂
P
0%
P
∪
Q
=
{
x
|
x
is multiple of 30
;
x
∈
N
}
0%
P
∩
Q
=
ϕ
0%
P
∩
Q
=
{
x
|
x
is a multiple of 30
;
x
∈
N
}
Explanation
P =
{
3
,
6
,
9
,
12
,
15
,
18
,
21
,
24
,
27
,
30
.
.
.
,
60
,
.
.
.
,
90
,
.
.
.
.
,
99
}
Q =
{
10
,
20
,
30
,
40
,
50
,
60
,
70
,
80
,
90
}
Then looking at the multiple choices we get
P
∩
Q
=
{
30
,
60
,
90
}
⇒
P
∩
Q = {x
∣
x is a multiple of 30 x
ϵ
N}
The set of real numbers r satisfying
3
r
2
−
8
r
+
5
4
r
2
−
3
r
+
7
>
0
is
Report Question
0%
the set of all real numbers
0%
the set of all positive real numbers
0%
the set of all real numbers strictly between 1 and 5/3
0%
the set of all real numbers which are either less than 1 or greater than 5/3
Explanation
3.
r
2
−
8.
r
+
5
4.
r
2
−
3.
r
+
7
>
0
⇒
3
r
2
−
3
r
−
5
r
+
5
>
0
and
4
r
2
−
3
r
+
7
>
0
as D < 0
⇒
3
r
(
r
−
1
)
−
5
(
r
−
1
)
>
0
⇒
(
3
r
−
5
)
(
r
−
1
)
>
0
(
3
r
−
5
)
(
r
−
1
)
>
0
r
ε
(
−
∞
,
1
)
∪
(
5
/
3
,
∞
)
Find the set of all solutions of the equation
2
|
y
|
−
|
2
y
−
1
−
1
|
=
2
y
−
1
+
1
, the solution includes
Report Question
0%
y
=
−
1
0%
y
>
1
0%
y
=
1
0%
y
<
1
Explanation
Here,
2
|
y
|
−
|
2
y
−
1
−
1
|
=
2
y
−
1
+
1
We know to define modulus, we have three cases as
Case I: y< 0
⇒
2
−
y
+
(
2
y
−
1
−
1
)
=
2
y
−
1
+
1
⇒
2
−
y
=
2
1
(as when y< 0 |y|=-y and
|
2
y
−
1
−
1
|
=
−
(
2
y
−
1
−
1
)
)
Hence, y=-1, which is true when y< 0 (i)
Case II:
0
≤
y
<
1
⇒
2
y
+
(
2
y
−
1
−
1
)
=
2
y
−
1
+
1
⇒
2
y
=
2
(as when
0
≤
y
<
1
|y|=-y and
|
2
y
−
1
−
1
|
=
−
(
2
y
−
1
−
1
)
)
⇒
y
=
1
, which shows no solution as,
0
≤
y
<
1
(ii)
Case III:
y
≥
1
⇒
2
y
−
(
2
y
−
1
−
1
)
=
2
y
−
1
+
1
⇒
2
y
=
2
y
−
1
+
2
y
−
1
⇒
2
y
=
2.2
y
−
1
(as when
y
≥
0
|y|=y and
|
2
y
−
1
−
1
|
=
(
2
y
−
1
−
1
)
)
⇒
2
y
=
2
y
, which is an identity therefor, it is true
∀
y
≥
1
(iii)
Hence, from Eqs. (i), (ii), (iii) the solution of set is
{
y
:
y
≥
1
∪
y
=
−
1
}
.
If X and Y are two sets then
X
∩
(
Y
∪
X
)
′
equals:
Report Question
0%
X
0%
Y
0%
ϕ
0%
{
0
}
Explanation
We have
X
∩
(
Y
∪
X
)
′
=
X
∩
(
Y
′
∩
X
′
)
=
X
∩
Y
′
∩
X
′
=
X
∩
X
′
∩
Y
′
=
ϕ
∩
Y
′
=
ϕ
If
Q
=
{
x
:
x
=
1
y
,
where
y
∈
N
}
, then
Report Question
0%
0
∈
Q
0%
1
∈
Q
0%
2
∈
Q
0%
2
3
∈
Q
Explanation
Since
1
y
≠
0
,
1
y
≠
2
,
1
y
≠
−
2
3
[
∵
y
∈
N
]
∴
1
y
can be
1
Ans: B
reflexive, symmetric and transitive.
Report Question
0%
R
3
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
4
,
4
)
,
(
1
,
2
)
,
(
2
,
1
)
}
0%
R
3
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
4
,
4
)
,
(
1
,
2
)
,
(
2
,
1
)
,
(
1
,
3
)
,
(
3
,
1
)
,
(
4
,
1
)
,
(
1
,
4
)
}
0%
R
3
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
4
,
4
)
}
0%
none of these
Explanation
We define
R
3
as follows:
R
3
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
4
,
4
)
,
(
1
,
2
)
,
(
2
,
1
)
}
.
Then evidently
R
3
is reflexive, symmetric and transitive, that is,
R
3
is an equivalence relation on A.
(
1
,
2
)
ϵ
R
3
,
(
2
,
1
)
ϵ
R
3
⇒
(
1
,
1
)
ϵ
R
3
Given
ξ
= {x : x is a natural number}
A = {x : x is an even number x
∈
N}
B = {x : x is an odd number, x
∈
N}
Then
(
B
∩
A
)
−
(
x
−
A
)
=
.
.
.
.
Report Question
0%
ϕ
0%
A
0%
B
0%
A
−
B
Explanation
A
=
{
2
,
4
,
6
,
8
,
.
.
.
.
.
.
.
.
}
B
=
{
1
,
3
,
5
,
7
,
.
.
.
.
.
.
.
}
B
∩
A
=
{
2
,
4
,
6
,
8
,
.
.
.
.
.
}
∩
{
1
,
3
,
5
,
7
,
.
.
.
.
}
=
ϕ
ξ
−
A
=
{
1
,
2
,
3
,
4
,
5
,
6
,
.
.
.
.
}
−
{
2
,
4
,
6
,
8
,
.
.
.
.
}
=
{
1
,
3
,
5
,
7
,
.
.
.
.
}
∴
B
∩
A
−
(
ξ
−
A
)
=
ϕ
−
{
1
,
3
,
5
,
7
,
.
.
.
.
}
=
ϕ
Which of the following statements is true ?
Report Question
0%
3
⊆
{
1
,
3
,
5
}
0%
3
∈
{
1
,
3
,
5
}
0%
{
3
}
∈
{
1
,
3
,
5
}
0%
{
3
,
5
}
∈
{
1
,
3
,
5
}
Explanation
3
⊆
{
1
,
3
,
5
}
An element cannot be a subset of another set. Hence,false.
3
∈
{
1
,
3
,
5
}
3
lies in the set. Hence, true.
{
3
}
∈
{
1
,
3
,
5
}
{
3
}
doesnot lie in the set. Hence, false.
{
3
,
5
}
∈
{
1
,
3
,
5
}
{
3
,
5
}
doesnot lie in the set. Hence, false.
Hence, option B.
A
=
{
x
:
x
≠
x
}
represents:
Report Question
0%
0
0%
ϕ
0%
1
0%
x
Explanation
x
=
x
for all
x
Hence, there is no element in A.
A is an empty set .
A
=
{
}
If n (A) = 120, N(B) = 250 and n (A - B) = 52, then find
n
(
A
∪
B
)
Report Question
0%
302
0%
250
0%
368
0%
None of the above
Explanation
n
(
A
−
B
)
=
n
(
A
)
−
n
(
A
∩
B
)
⇒
52
=
120
−
n
(
A
∩
B
)
⇒
n
(
A
∩
B
)
=
120
−
52
=
68
Now
n
(
A
∪
B
)
=
n
(
A
)
+
n
(
B
)
−
n
(
A
∩
B
)
=
120
+
250
−
68
=
302
The solution set of
x
+
2
<
9
over a set of positive even integers is
Report Question
0%
{
8
,
10
,
12
,
.
.
.
}
0%
{
2
,
4
,
6
}
0%
{
1
,
2
,
3
,
4
,
5
,
6
}
0%
{
2
,
4
,
6
,
8
}
Explanation
x
+
2
<
9
x
<
7
Since
x
is even positive integer then
x
∈
[
2
,
7
)
.
Hence the set of positive even integers which fall in the above set is
{
2
,
4
,
6
}
.
The solution set of
3
x
−
4
<
8
over the set of non-negative square numbers is
Report Question
0%
{
1
,
2
,
3
}
0%
{
1
,
4
}
0%
{
1
}
0%
{
16
}
Explanation
3
x
−
4
<
8
3
x
<
12
x
<
4
Hence set of non-negative square numbers belonging to the above set is
{
1
}
.
Let
P
and
Q
be two sets then what is
(
P
∩
Q
′
)
∪
(
P
∪
Q
)
′
equal to ?
Report Question
0%
(
P
∩
Q
′
)
∪
(
P
∪
Q
)
′
=
ξ
∩
Q
′
=
ξ
∩
Q
′
=
ξ
0%
(
P
∪
Q
′
)
∪
(
P
∪
Q
)
′
=
ξ
∩
Q
′
=
ξ
∩
Q
′
=
ξ
0%
(
P
∩
Q
′
)
∪
(
P
∩
Q
)
′
=
ξ
∩
Q
′
=
ξ
∩
Q
′
=
ξ
0%
none of the above
Explanation
(
P
∩
Q
′
)
∪
(
P
∪
Q
)
′
=
(
P
∩
Q
′
)
∪
(
P
′
∩
Q
′
)
=
(
P
∪
P
′
)
∩
(
P
∪
Q
′
)
∩
(
Q
′
∪
P
′
)
∩
(
Q
′
∪
Q
′
)
=
ξ
∩
{
Q
′
∪
(
P
∩
P
′
)
}
∩
Q
′
=
ξ
∩
{
Q
′
∪
ξ
)
∩
Q
′
=
ξ
∩
Q
′
∩
Q
′
=
ξ
∩
Q
′
=
ξ
If
A
and
B
are finite sets which of the following is the correct statement?
Report Question
0%
n
(
A
−
B
)
=
n
(
A
)
−
n
(
B
)
0%
n
(
A
−
B
)
=
n
(
B
−
A
)
0%
n
(
A
−
B
)
=
n
(
A
)
−
n
(
A
∩
B
)
0%
n
(
A
−
B
)
=
n
(
B
)
−
n
(
A
∩
B
)
U is a universal set and n(U) =A, B and C are subset of U. If n(A) = 50, n(B) = 70,
n
(
B
∪
C
)
=
Φ
,
n
(
B
∩
C
)
=
15
and
A
∪
B
∪
C
=
U
. then n(C) equals
Report Question
0%
40
0%
50
0%
55
0%
60
If
n
(
A
)
=
115
,
n
(
B
)
=
326
,
n
(
A
−
B
)
=
47
, then
n
(
A
+
B
)
is equal to
Report Question
0%
373
0%
165
0%
370
0%
None
Explanation
n
(
A
−
B
)
=
47
⇒
n
(
A
)
−
n
(
A
∩
B
)
=
47
⇒
n
(
A
∩
B
)
=
115
−
47
=
68
Hence
n
(
A
+
B
)
=
115
+
326
−
68
=
373
If A and B are two disjoint sets and N is the universal set then
A
c
∪
[
(
A
∪
B
)
∩
B
c
]
is
Report Question
0%
ϕ
0%
A
0%
B
0%
N
Explanation
Since
A
and
B
are disjoint sets
B
c
∩
(
A
∪
B
)
will be only
A
as there is no intersection between
A
and
B
.
Of course
A
c
∪
A
=
N
Suppose
A
1
,
A
2
,
.
.
.
.
,
A
30
are thirty sets each having 5 elements and
B
1
,
B
2
,
.
.
.
.
,
B
n
are n sets each with 3 elements. Let
30
⋃
i
=
1
A
i
=
n
⋃
j
=
1
B
j
=
S
and each elements of S belongs to exactly 10 of the
A
i
and exactly 9 of the
B
j
. Then n is equal to-
Report Question
0%
35
0%
45
0%
55
0%
65
Explanation
A
0
,
A
1
,
.
.
.
.
.
.
.
.
.
.
.
.
.
,
A
30
⟹
each of 5 elements
B
1
,
B
2
,
B
3
.
.
.
.
.
.
.
.
.
.
.
n
⟹
each of 3 elements
The number of elements in the union of the A sets is
5
(
30
)
−
r
where 'r' is the number repeats likewise the number of elements in the B sets
3
n
−
r
B
Each element in the union (in5) is repeated 10 times in A which means if x was the real number of elements in A (not counting repeats) then q out of those 10 should be thrown away or 9x .likewise on the B side 8x of those elements should be thrown away So,
⟹
150
−
9
x
=
3
n
−
8
x
n
=
50
−
3
x
Now in figure out what x is we need to use the fact that the union of a group of sets contains every member of each sets . If every element in 'S' is repeated 10 times that means every element in the union of the n's is repeated 10 times .
This means that
10
/
10
⟹
15
is the number of in the A's without repeats counted (same for the B's aswell ) So now
50
−
15
3
=
n
n
=
45
Subset:- A proper subset is nothing but it contain atleast one more element of main set .
Ex:
{
3
,
4
,
5
}
is a set then the possible subsets are
{
3
}
,
{
4
}
,
{
5
}
,
{
1
,
5
}
,
{
3
,
4
}
0:0:1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0
Answered
1
Not Answered
29
Not Visited
Correct : 0
Incorrect : 0
Report Question
×
What's an issue?
Question is wrong
Answer is wrong
Other Reason
Want to elaborate a bit more? (optional)
Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers
<
>
Support mcqexams.com by disabling your adblocker.
×
Please disable the adBlock and continue.
Thank you.
Reload page