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IITM BS Week 1 Mathematics 1 Questions | Prasnya
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Difficulty:
All
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All
11Q
01
Let
A
2
=
A
×
A
A^2 = A \times A
A
2
=
A
×
A
. What is the value of
2
α
+
β
2\alpha + \beta
2
α
+
β
?
Numerical
HARD
4 marks
10 May 2026
02
Consider the following relations defined on the set of integers: -
R
1
=
{
(
x
,
y
)
∣
x
,
y
∈
Z
and
7
divides
(
x
−
y
)
}
R_1 = \{(x, y) \mid x, y \in \mathbb{Z} \text{ and } 7 \text{ divides } (x - y)\}
R
1
=
{(
x
,
y
)
∣
x
,
y
∈
Z
and
7
divides
(
x
−
y
)}
-
R
2
=
{
(
x
,
y
)
∣
x
,
y
∈
Z
and
x
+
y
=
2
}
R_2 = \{(x, y) \mid x, y \in \mathbb{Z} \text{ and } x + y = 2\}
R
2
=
{(
x
,
y
)
∣
x
,
y
∈
Z
and
x
+
y
=
2
}
Choose the correct option(s).
Multiple correct
EASY
4 marks
21 December 2025
03
Devendra has three sons (Jatin, Rabi, and Hem). Rabi has one son named Rathi. Hem has two sons (Avi and Manish). This family tree has been shown in the figure below. Let us define relations
R
R
R
and
S
S
S
as follows: -
R
:
=
{
(
A
,
B
)
∣
A
and
B
are first cousins, i.e., their parents are siblings
}
R := \{(A, B) \mid A \text{ and } B \text{ are first cousins, i.e., their parents are siblings}\}
R
:=
{(
A
,
B
)
∣
A
and
B
are first cousins, i.e., their parents are siblings
}
-
S
:
=
{
(
A
,
B
)
∣
A
is the son of
B
}
S := \{(A, B) \mid A \text{ is the son of } B\}
S
:=
{(
A
,
B
)
∣
A
is the son of
B
}
Which of the following is (are) true?
Multiple correct
MEDIUM
4 marks
22 December 2024
04
Consider the following relations defined on the set of integers: -
R
1
=
{
(
x
,
y
)
∣
x
,
y
∈
Z
and
7
divides
(
x
−
y
)
}
R_1 = \{(x, y) \mid x, y \in \mathbb{Z} \text{ and } 7 \text{ divides } (x - y)\}
R
1
=
{(
x
,
y
)
∣
x
,
y
∈
Z
and
7
divides
(
x
−
y
)}
-
R
2
=
{
(
x
,
y
)
∣
x
,
y
∈
Z
and
x
+
y
=
2
}
R_2 = \{(x, y) \mid x, y \in \mathbb{Z} \text{ and } x + y = 2\}
R
2
=
{(
x
,
y
)
∣
x
,
y
∈
Z
and
x
+
y
=
2
}
Choose the correct option(s).
Multiple correct
MEDIUM
3 marks
01 September 2024
05
Suppose
A
=
{
a
,
b
,
c
,
d
}
A = \{a, b, c, d\}
A
=
{
a
,
b
,
c
,
d
}
and
B
=
{
p
,
q
,
r
,
s
}
B = \{p, q, r, s\}
B
=
{
p
,
q
,
r
,
s
}
are two sets. Consider the following relations on
A
×
B
A \times B
A
×
B
: -
R
1
=
{
(
a
,
p
)
,
(
c
,
r
)
,
(
d
,
q
)
}
R_1 = \{(a, p), (c, r), (d, q)\}
R
1
=
{(
a
,
p
)
,
(
c
,
r
)
,
(
d
,
q
)}
-
R
2
=
{
(
a
,
s
)
,
(
b
,
s
)
,
(
c
,
p
)
,
(
d
,
r
)
}
R_2 = \{(a, s), (b, s), (c, p), (d, r)\}
R
2
=
{(
a
,
s
)
,
(
b
,
s
)
,
(
c
,
p
)
,
(
d
,
r
)}
-
R
3
=
{
(
a
,
p
)
,
(
b
,
r
)
,
(
b
,
s
)
,
(
d
,
q
)
}
R_3 = \{(a, p), (b, r), (b, s), (d, q)\}
R
3
=
{(
a
,
p
)
,
(
b
,
r
)
,
(
b
,
s
)
,
(
d
,
q
)}
-
R
4
=
{
(
a
,
r
)
,
(
b
,
p
)
,
(
c
,
q
)
,
(
d
,
s
)
}
R_4 = \{(a, r), (b, p), (c, q), (d, s)\}
R
4
=
{(
a
,
r
)
,
(
b
,
p
)
,
(
c
,
q
)
,
(
d
,
s
)}
Which of the following statements are correct?
Multiple correct
MEDIUM
4 marks
28 April 2024
06
Consider the sets
A
=
{
a
∈
N
∣
2
≤
a
≤
8
}
A = \{a \in \mathbb{N} \mid 2 \le a \le 8\}
A
=
{
a
∈
N
∣
2
≤
a
≤
8
}
and
B
=
{
b
∈
N
∣
4
≤
b
≤
10
}
B = \{b \in \mathbb{N} \mid 4 \le b \le 10\}
B
=
{
b
∈
N
∣
4
≤
b
≤
10
}
. Find the cardinality of the set
(
A
∩
B
)
∪
(
A
∖
B
)
∪
(
B
∖
A
)
(A \cap B) \cup (A \setminus B) \cup (B \setminus A)
(
A
∩
B
)
∪
(
A
∖
B
)
∪
(
B
∖
A
)
.
Numerical
EASY
3 marks
24 December 2023
07
Which of the following statements are correct?
Comprehension
MEDIUM
3 marks
11 December 2022
08
Consider the universal set
U
U
U
to be the set of all natural numbers less than or equal to
13
13
13
including zero. Find the cardinality of the set
A
′
∪
B
′
A' \cup B'
A
′
∪
B
′
.
Comprehension
MEDIUM
3 marks
11 December 2022
09
Let
A
A
A
be the set of all points on the curve defined by the function
f
1
(
x
)
=
x
2
−
x
−
20
f_1(x) = x^2 - x - 20
f
1
(
x
)
=
x
2
−
x
−
20
and let
B
B
B
be the set of all points on the curve
f
2
f_2
f
2
defined by the reflection of the curve
f
1
f_1
f
1
with respect to the
x
x
x
-axis. If
C
C
C
is the set of all points on the axes (i.e.,
x
x
x
and
y
y
y
axis) then find the cardinality of set
D
D
D
where
D
=
(
A
∩
B
)
∪
(
A
∩
C
)
∪
(
B
∩
C
)
D = (A \cap B) \cup (A \cap C) \cup (B \cap C)
D
=
(
A
∩
B
)
∪
(
A
∩
C
)
∪
(
B
∩
C
)
.
Numerical
HARD
4 marks
07 August 2022
10
The relation
R
R
R
on the set
S
S
S
is (are)
Comprehension
EASY
2 marks
07 August 2022
11
What is the minimum number of elements of the Cartesian product
S
×
S
S \times S
S
×
S
that need to be added to
R
R
R
such that the relation becomes symmetric?
Comprehension
EASY
2 marks
07 August 2022
Showing 11 questions.
Complete question index for this section:
Question 1 (integer):
Question 2 (multiple):
Question 3 (multiple):
Question 4 (multiple):
Question 5 (multiple):
Question 6 (integer):
Question 7 (comprehension):
Question 8 (comprehension):
Question 9 (integer):
Question 10 (comprehension):
Question 11 (comprehension):
