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Week 5 Mathematics 2 Questions | Prasnya
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Mathematics 2 > Week 5
All PYQs
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Type:
All
Difficulty:
All
Year:
All
9Q
01
Consider the following statements about the function
T
:
R
2
→
R
T:\mathbb{R}^2\to\mathbb{R}
T
:
R
2
→
R
defined by
T
(
x
,
y
)
=
2
x
+
y
+
1
T(x,y)=2x+y+1
T
(
x
,
y
)
=
2
x
+
y
+
1
, for all
(
x
,
y
)
∈
R
2
(x,y)\in\mathbb{R}^2
(
x
,
y
)
∈
R
2
. Statement
P
P
P
:
T
T
T
is a linear transformation. Statement
Q
Q
Q
:
T
T
T
is a one-to-one (injective) map. Choose the correct option from the following.
Single correct
EASY
2 marks
13 July 2025
02
Find the maximum possible nullity of the matrix
A
A
A
.
Comprehension
MEDIUM
4 marks
13 July 2025
03
W
1
=
{
x
∈
R
n
:
A
x
=
0
where
A
is an invertible matrix
}
W_1=\{x\in\mathbb{R}^n:Ax=0\text{ where }A\text{ is an invertible matrix}\}
W
1
=
{
x
∈
R
n
:
A
x
=
0
where
A
is an invertible matrix
}
.
Comprehension
EASY
1 marks
27 October 2024
04
A
A
A
is a square matrix of order
3
3
3
. Select all subspaces of
R
3
\mathbb{R}^3
R
3
from the options given below.
Multiple correct
EASY
3 marks
07 July 2024
05
a
a
a
is equal to
Comprehension
MEDIUM
1 marks
25 February 2024
06
b
b
b
is equal to
Comprehension
MEDIUM
1 marks
25 February 2024
07
c
c
c
is equal to
Comprehension
MEDIUM
1 marks
25 February 2024
08
Consider the set
S
S
S
of solutions of the system
A
x
=
0
Ax=0
A
x
=
0
, where
A
A
A
is as given. Clearly,
S
S
S
is a vector space with respect to usual addition and scalar multiplication. What is the dimension of
S
S
S
?
Comprehension
EASY
1 marks
16 July 2023
09
Which of the following forms a basis for
S
S
S
?
Comprehension
MEDIUM
2 marks
16 July 2023
Showing 9 questions.
Mathematics 2 > Week 5
All PYQs
Topic Wise PYQs
Start Weekly Test
Type:
All
Difficulty:
All
Year:
All
9Q
01
Consider the following statements about the function
T
:
R
2
→
R
T:\mathbb{R}^2\to\mathbb{R}
T
:
R
2
→
R
defined by
T
(
x
,
y
)
=
2
x
+
y
+
1
T(x,y)=2x+y+1
T
(
x
,
y
)
=
2
x
+
y
+
1
, for all
(
x
,
y
)
∈
R
2
(x,y)\in\mathbb{R}^2
(
x
,
y
)
∈
R
2
. Statement
P
P
P
:
T
T
T
is a linear transformation. Statement
Q
Q
Q
:
T
T
T
is a one-to-one (injective) map. Choose the correct option from the following.
Single correct
EASY
2 marks
13 July 2025
02
Find the maximum possible nullity of the matrix
A
A
A
.
Comprehension
MEDIUM
4 marks
13 July 2025
03
W
1
=
{
x
∈
R
n
:
A
x
=
0
where
A
is an invertible matrix
}
W_1=\{x\in\mathbb{R}^n:Ax=0\text{ where }A\text{ is an invertible matrix}\}
W
1
=
{
x
∈
R
n
:
A
x
=
0
where
A
is an invertible matrix
}
.
Comprehension
EASY
1 marks
27 October 2024
04
A
A
A
is a square matrix of order
3
3
3
. Select all subspaces of
R
3
\mathbb{R}^3
R
3
from the options given below.
Multiple correct
EASY
3 marks
07 July 2024
05
a
a
a
is equal to
Comprehension
MEDIUM
1 marks
25 February 2024
06
b
b
b
is equal to
Comprehension
MEDIUM
1 marks
25 February 2024
07
c
c
c
is equal to
Comprehension
MEDIUM
1 marks
25 February 2024
08
Consider the set
S
S
S
of solutions of the system
A
x
=
0
Ax=0
A
x
=
0
, where
A
A
A
is as given. Clearly,
S
S
S
is a vector space with respect to usual addition and scalar multiplication. What is the dimension of
S
S
S
?
Comprehension
EASY
1 marks
16 July 2023
09
Which of the following forms a basis for
S
S
S
?
Comprehension
MEDIUM
2 marks
16 July 2023
Showing 9 questions.
