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Week 5 Mathematics 2 Questions | Prasnya
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19Q
01
Let
A
A
A
be a
3
×
5
3\times 5
3
×
5
matrix whose row echelon form is
[
1
2
−
1
2
1
0
0
1
3
−
2
0
0
0
k
0
]
,
\begin{bmatrix}1&2&-1&2&1\\0&0&1&3&-2\\0&0&0&k&0\end{bmatrix},
1
0
0
2
0
0
−
1
1
0
2
3
k
1
−
2
0
,
where
k
∈
R
k\in\mathbb{R}
k
∈
R
. Choose the correct option.
Single correct
EASY
2 marks
03 August 2025
02
Find the maximum possible nullity of a
3
×
4
3\times4
3
×
4
matrix.
Numerical
EASY
2 marks
16 March 2025
03
If
(
α
,
β
,
2
,
−
1
)
(\alpha,\beta,2,-1)
(
α
,
β
,
2
,
−
1
)
is a vector in the nullspace of
A
A
A
, find
α
−
β
\alpha-\beta
α
−
β
.
Comprehension
MEDIUM
2 marks
16 March 2025
04
Find the nullity of the matrix
A
A
A
.
Comprehension
MEDIUM
2 marks
16 March 2025
05
Choose the correct definition for the linear transformation
T
T
T
.
Comprehension
MEDIUM
2 marks
16 March 2025
06
Find the value of
k
k
k
for which the nullity of the transformation
T
T
T
equals
2
2
2
.
Comprehension
MEDIUM
2 marks
16 March 2025
07
What is the rank of
T
T
T
?
Comprehension
EASY
1 marks
01 December 2024
08
What is the nullity of
T
T
T
?
Comprehension
EASY
1 marks
01 December 2024
09
Select all true statements.
Multiple correct
MEDIUM
3 marks
04 August 2024
10
What is the nullity of
T
T
T
?
Comprehension
EASY
1 marks
04 August 2024
11
Let
A
A
A
be a
5
×
5
5\times5
5
×
5
matrix of rank
3
3
3
. Let
b
b
b
be the third column of
A
A
A
and
W
=
{
x
∈
R
5
:
A
x
=
b
}
W=\{x\in\mathbb{R}^5:Ax=b\}
W
=
{
x
∈
R
5
:
A
x
=
b
}
be an affine subspace of
R
5
\mathbb{R}^5
R
5
. What is the dimension of
W
W
W
?
Comprehension
MEDIUM
1 marks
24 March 2024
12
Which of the following functions are linear transformations?
Multiple correct
EASY
2 marks
03 December 2023
13
Which of the following is the nullspace of
A
A
A
?
Comprehension
EASY
2 marks
03 December 2023
14
Let
B
B
B
be a square matrix of order
3
3
3
. What is the smallest value that the nullity of
B
A
BA
B
A
could take?
Comprehension
MEDIUM
1 marks
03 December 2023
15
If
A
A
A
is a
2
×
3
2\times3
2
×
3
matrix of rank
1
1
1
, what is the nullity of
A
A
T
AA^T
A
A
T
?
Numerical
EASY
2 marks
06 August 2023
16
What is the nullity of
A
A
A
?
Comprehension
MEDIUM
1 marks
06 August 2023
17
What is the nullity of
A
A
A
?
Comprehension
EASY
1 marks
02 April 2023
18
Which of the following options are true?
Multiple correct
MEDIUM
2 marks
20 November 2022
19
Find the nullity of
T
T
T
.
Comprehension
EASY
1 marks
10 July 2022
Showing 19 questions.
Mathematics 2 > Week 5
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Topic-Wise PYQs
Start Weekly Test
Mock tests
Week mock
Topic mock
Subject mock
Type:
All
Difficulty:
All
Year:
All
19Q
01
Let
A
A
A
be a
3
×
5
3\times 5
3
×
5
matrix whose row echelon form is
[
1
2
−
1
2
1
0
0
1
3
−
2
0
0
0
k
0
]
,
\begin{bmatrix}1&2&-1&2&1\\0&0&1&3&-2\\0&0&0&k&0\end{bmatrix},
1
0
0
2
0
0
−
1
1
0
2
3
k
1
−
2
0
,
where
k
∈
R
k\in\mathbb{R}
k
∈
R
. Choose the correct option.
Single correct
EASY
2 marks
03 August 2025
02
Find the maximum possible nullity of a
3
×
4
3\times4
3
×
4
matrix.
Numerical
EASY
2 marks
16 March 2025
03
If
(
α
,
β
,
2
,
−
1
)
(\alpha,\beta,2,-1)
(
α
,
β
,
2
,
−
1
)
is a vector in the nullspace of
A
A
A
, find
α
−
β
\alpha-\beta
α
−
β
.
Comprehension
MEDIUM
2 marks
16 March 2025
04
Find the nullity of the matrix
A
A
A
.
Comprehension
MEDIUM
2 marks
16 March 2025
05
Choose the correct definition for the linear transformation
T
T
T
.
Comprehension
MEDIUM
2 marks
16 March 2025
06
Find the value of
k
k
k
for which the nullity of the transformation
T
T
T
equals
2
2
2
.
Comprehension
MEDIUM
2 marks
16 March 2025
07
What is the rank of
T
T
T
?
Comprehension
EASY
1 marks
01 December 2024
08
What is the nullity of
T
T
T
?
Comprehension
EASY
1 marks
01 December 2024
09
Select all true statements.
Multiple correct
MEDIUM
3 marks
04 August 2024
10
What is the nullity of
T
T
T
?
Comprehension
EASY
1 marks
04 August 2024
11
Let
A
A
A
be a
5
×
5
5\times5
5
×
5
matrix of rank
3
3
3
. Let
b
b
b
be the third column of
A
A
A
and
W
=
{
x
∈
R
5
:
A
x
=
b
}
W=\{x\in\mathbb{R}^5:Ax=b\}
W
=
{
x
∈
R
5
:
A
x
=
b
}
be an affine subspace of
R
5
\mathbb{R}^5
R
5
. What is the dimension of
W
W
W
?
Comprehension
MEDIUM
1 marks
24 March 2024
12
Which of the following functions are linear transformations?
Multiple correct
EASY
2 marks
03 December 2023
13
Which of the following is the nullspace of
A
A
A
?
Comprehension
EASY
2 marks
03 December 2023
14
Let
B
B
B
be a square matrix of order
3
3
3
. What is the smallest value that the nullity of
B
A
BA
B
A
could take?
Comprehension
MEDIUM
1 marks
03 December 2023
15
If
A
A
A
is a
2
×
3
2\times3
2
×
3
matrix of rank
1
1
1
, what is the nullity of
A
A
T
AA^T
A
A
T
?
Numerical
EASY
2 marks
06 August 2023
16
What is the nullity of
A
A
A
?
Comprehension
MEDIUM
1 marks
06 August 2023
17
What is the nullity of
A
A
A
?
Comprehension
EASY
1 marks
02 April 2023
18
Which of the following options are true?
Multiple correct
MEDIUM
2 marks
20 November 2022
19
Find the nullity of
T
T
T
.
Comprehension
EASY
1 marks
10 July 2022
Showing 19 questions.
