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Mathematics 2 > Week 1
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Type:
All
Difficulty:
All
Year:
All
48Q
01
Let
A
=
[
1
a
a
2
a
3
1
b
b
2
b
3
1
c
c
2
c
3
1
d
d
2
d
3
]
A=\begin{bmatrix}1&a&a^2&a^3\\1&b&b^2&b^3\\1&c&c^2&c^3\\1&d&d^2&d^3\end{bmatrix}
A
=
1
1
1
1
a
b
c
d
a
2
b
2
c
2
d
2
a
3
b
3
c
3
d
3
where
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are distinct real numbers. Which of the following statements are correct?
Multiple correct
MEDIUM
5 marks
15 March 2026
02
Suppose
a
=
(
1
,
2
)
a=(1,2)
a
=
(
1
,
2
)
and
b
=
(
3
,
−
1
)
b=(3,-1)
b
=
(
3
,
−
1
)
. Let
v
=
k
a
+
l
b
v=ka+lb
v
=
k
a
+
l
b
such that
v
1
=
v
2
v_1=v_2
v
1
=
v
2
and
k
+
l
=
5
k+l=5
k
+
l
=
5
. Find the value of
k
k
k
.
Numerical
EASY
4 marks
15 March 2026
03
Let
A
A
A
be a square matrix of order
n
>
1
n>1
n
>
1
. Select all the statements which imply that
det
(
A
)
=
0
\det(A)=0
det
(
A
)
=
0
.
Multiple correct
MEDIUM
6 marks
26 October 2025
04
If the sum of the two vectors
(
1
,
2
)
(1,2)
(
1
,
2
)
and
(
2
,
x
)
(2,x)
(
2
,
x
)
in
R
2
\mathbb{R}^2
R
2
is a scalar multiple of the vector
(
2
,
1
)
(2,1)
(
2
,
1
)
, then find the value of
x
x
x
.
Numerical
EASY
3 marks
26 October 2025
05
Find the minimum value of
β
\beta
β
such that the matrix
[
β
−
1
0
−
1
2
β
+
4
2
β
+
1
β
+
1
β
+
1
]
\begin{bmatrix}\beta-1&0&-1\\2&\beta+4&2\\\beta+1&\beta+1&\beta+1\end{bmatrix}
β
−
1
2
β
+
1
0
β
+
4
β
+
1
−
1
2
β
+
1
is not invertible.
Numerical
MEDIUM
3 marks
26 October 2025
06
There are two kinds of coins, Type A and Type B. Let the unknown monetary values of coins of Type A and Type B be
x
1
x_1
x
1
and
x
2
x_2
x
2
, respectively. A collection of
2
2
2
coins of Type A and
3
3
3
coins of Type B is worth Rs
19
19
19
. A collection of
1
1
1
coin of Type A and
5
5
5
coins of Type B is worth Rs
27
27
27
. Use the above information to set up a system of linear equations and find the value of
x
1
−
x
2
x_1-x_2
x
1
−
x
2
.
Numerical
EASY
4 marks
26 October 2025
07
Choose the matrix which satisfies the equation
det
(
A
−
c
I
)
=
c
2
−
5
c
+
6
\det(A-cI)=c^2-5c+6
det
(
A
−
c
I
)
=
c
2
−
5
c
+
6
.
Single correct
MEDIUM
4 marks
13 July 2025
08
Let
A
A
A
be a
3
×
3
3\times3
3
×
3
matrix such that
det
(
A
)
=
−
3
\det(A)=-3
det
(
A
)
=
−
3
. For which of the options below is the matrix
B
B
B
, obtained from
A
A
A
by performing the operations in the option, such that
det
(
B
)
=
12
\det(B)=12
det
(
B
)
=
12
?
Multiple correct
MEDIUM
5 marks
13 July 2025
09
Let
x
1
x_1
x
1
be the price of
1
1
1
pencil and
x
2
x_2
x
2
be the price of
1
1
1
pen. Choose the correct option.
Comprehension
EASY
2 marks
13 July 2025
10
Suppose Shakti tries to find the price of
1
1
1
pencil and
1
1
1
pen and hopes to have unique values for the prices. Then
b
b
b
should not be equal to
Comprehension
MEDIUM
4 marks
13 July 2025
11
Let
A
A
A
be an
m
×
n
m\times n
m
×
n
matrix. Choose the operations that are valid only when
m
=
n
m=n
m
=
n
.
Multiple correct
EASY
4 marks
23 February 2025
12
Find the number of
2
×
2
2\times2
2
×
2
scalar matrices with determinant equal to
4
4
4
.
Numerical
EASY
2 marks
23 February 2025
13
If the sum of the two vectors
(
1
,
2
)
(1,2)
(
1
,
2
)
and
(
2
,
x
)
(2,x)
(
2
,
x
)
in
R
2
\mathbb{R}^2
R
2
is a scalar multiple of the vector
(
2
,
1
)
(2,1)
(
2
,
1
)
, then find the value of
x
x
x
.
Numerical
EASY
3 marks
23 February 2025
14
Find the minimum value of
β
\beta
β
such that the matrix
[
β
−
1
0
−
1
2
β
+
4
2
β
+
1
β
+
1
β
+
1
]
\begin{bmatrix}\beta-1&0&-1\\2&\beta+4&2\\\beta+1&\beta+1&\beta+1\end{bmatrix}
β
−
1
2
β
+
1
0
β
+
4
β
+
1
−
1
2
β
+
1
is not invertible.
Numerical
MEDIUM
3 marks
23 February 2025
15
There are two kinds of coins, say of Type A and Type B. Let the unknown monetary values of coins of Type A and Type B be
x
1
x_1
x
1
and
x
2
x_2
x
2
, respectively. A collection of
2
2
2
coins of Type A and
3
3
3
coins of Type B is worth
₹
19
₹19
₹19
. A collection of
1
1
1
coin of Type A and
5
5
5
coins of Type B is worth
₹
27
₹27
₹27
. Use the above information to set up a system of linear equations and find the value of
x
1
−
x
2
x_1-x_2
x
1
−
x
2
.
Numerical
MEDIUM
4 marks
23 February 2025
16
Which of the following conditions are sufficient to deduce
det
(
A
B
)
=
0
\det(AB)=0
det
(
A
B
)
=
0
?
Comprehension
MEDIUM
6 marks
23 February 2025
17
For
α
=
3
\alpha=3
α
=
3
and
β
=
0
\beta=0
β
=
0
, find the value of
det
(
−
B
T
A
2
B
−
1
)
\det(-B^TA^2B^{-1})
det
(
−
B
T
A
2
B
−
1
)
.
Comprehension
MEDIUM
4 marks
23 February 2025
18
Choose the correct option(s) from the following:
Multiple correct
MEDIUM
3 marks
27 October 2024
19
Find the value of
α
\alpha
α
.
Comprehension
MEDIUM
1.5 marks
27 October 2024
20
Find the value of
β
\beta
β
.
Comprehension
MEDIUM
1.5 marks
27 October 2024
21
Let
A
A
A
be a
5
×
5
5\times5
5
×
5
matrix such that
A
T
=
−
A
A^T=-A
A
T
=
−
A
. Then
det
(
A
)
=
\det(A)=
det
(
A
)
=
Comprehension
EASY
1 marks
27 October 2024
22
Let
A
A
A
be a
2
×
2
2\times2
2
×
2
matrix such that
det
(
A
)
=
2
\det(A)=2
det
(
A
)
=
2
. If
B
B
B
is a matrix obtained from
A
A
A
by swapping the first and second row, and then multiplying the second row by
−
2
-2
−
2
, then
det
(
B
)
=
\det(B)=
det
(
B
)
=
Comprehension
EASY
1 marks
27 October 2024
23
Consider the matrix
A
=
[
1
0
5
−
2
3
−
4
1
4
a
]
A=\begin{bmatrix}1&0&5\\-2&3&-4\\1&4&a\end{bmatrix}
A
=
1
−
2
1
0
3
4
5
−
4
a
. Find the value of
a
a
a
if the system
A
x
=
0
Ax=0
A
x
=
0
has infinitely many solutions.
Comprehension
MEDIUM
2 marks
27 October 2024
24
A
=
(
a
i
j
)
∈
M
5
×
5
(
R
)
A=(a_{ij})\in M_{5\times5}(\mathbb{R})
A
=
(
a
ij
)
∈
M
5
×
5
(
R
)
is a matrix such that
a
i
j
+
a
j
i
=
0
a_{ij}+a_{ji}=0
a
ij
+
a
j
i
=
0
for all
1
≤
i
,
j
≤
5
1\le i,j\le5
1
≤
i
,
j
≤
5
. Find the determinant of
A
A
A
.
Numerical
EASY
2 marks
07 July 2024
25
If determinant of
A
A
A
is
−
2
-2
−
2
, find the determinant of
A
T
A
A^T A
A
T
A
.
Numerical
EASY
2 marks
07 July 2024
26
Find the value of
α
\alpha
α
.
Comprehension
MEDIUM
1.5 marks
07 July 2024
27
Find the value of
β
\beta
β
.
Comprehension
MEDIUM
1.5 marks
07 July 2024
28
Find the determinant of the matrix
[
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
]
\begin{bmatrix}0&1&0&0&0\\0&0&0&1&0\\1&0&0&0&0\\0&0&1&0&0\\0&0&0&0&1\end{bmatrix}
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
.
Comprehension
MEDIUM
2 marks
25 February 2024
29
Find the determinant of the matrix
[
a
b
0
c
d
e
5
f
g
h
4
i
0
0
−
5
0
]
\begin{bmatrix}a&b&0&c\\d&e&5&f\\g&h&4&i\\0&0&-5&0\end{bmatrix}
a
d
g
0
b
e
h
0
0
5
4
−
5
c
f
i
0
, given that
det
[
a
b
c
d
e
f
g
h
i
]
=
2
\det\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}=2
det
a
d
g
b
e
h
c
f
i
=
2
.
Comprehension
MEDIUM
2 marks
25 February 2024
30
Find the value of
c
c
c
.
Comprehension
EASY
1 marks
25 February 2024
31
Find the value of
d
d
d
.
Comprehension
EASY
1 marks
25 February 2024
32
Does there exist an
a
a
a
such that the system has no solution? If yes, find the value of
a
a
a
; else write the answer as
100
100
100
.
Comprehension
EASY
1 marks
25 February 2024
33
Consider the following images representing systems of linear equations. Choose the correct option(s) from the following statements.
Multiple correct
MEDIUM
2 marks
29 October 2023
34
Let
A
A
A
be a
3
×
3
3\times3
3
×
3
matrix such that
A
T
=
−
A
A^T=-A
A
T
=
−
A
. Then find
det
(
A
)
\det(A)
det
(
A
)
.
Comprehension
EASY
1 marks
29 October 2023
35
Let
A
A
A
be a
3
×
3
3\times3
3
×
3
matrix such that
det
(
A
)
=
2
\det(A)=2
det
(
A
)
=
2
. If
B
B
B
is a matrix obtained from
A
A
A
by swapping the second and third row, and then multiplying the first row by
−
3
-3
−
3
, then find
det
(
B
)
\det(B)
det
(
B
)
.
Comprehension
EASY
1 marks
29 October 2023
36
Let
A
=
[
1
−
2
−
3
4
]
A=\begin{bmatrix}1&-2\\-3&4\end{bmatrix}
A
=
[
1
−
3
−
2
4
]
and
det
(
A
−
x
I
)
=
x
2
−
a
x
+
b
\det(A-xI)=x^2-ax+b
det
(
A
−
x
I
)
=
x
2
−
a
x
+
b
. Find
a
−
b
a-b
a
−
b
.
Comprehension
MEDIUM
1 marks
29 October 2023
37
What is the determinant of
B
B
B
?
Comprehension
EASY
1 marks
29 October 2023
38
Match the system of linear equations in Column A with their number of solutions in Column B and their geometric representation in Column C. Choose the correct option from the following:
Single correct
MEDIUM
2 marks
16 July 2023
39
Which of the following matrices satisfy
A
k
=
0
A^k=0
A
k
=
0
for some natural number
k
k
k
?
Multiple correct
HARD
2 marks
16 July 2023
40
Let
A
=
[
2022
2023
2024
2022
2021
2022
2022
2022
2022
]
A=\begin{bmatrix}2022&2023&2024\\2022&2021&2022\\2022&2022&2022\end{bmatrix}
A
=
2022
2022
2022
2023
2021
2022
2024
2022
2022
. What is the determinant of
1
2
A
\frac{1}{2}A
2
1
A
?
Numerical
MEDIUM
2 marks
16 July 2023
41
Choose the correct option(s).
Comprehension
EASY
1 marks
16 July 2023
42
Choose the set of correct options.
Multiple correct
MEDIUM
2 marks
16 October 2022
43
NOTE: Enter your answer to the nearest integer. If
A
4
=
β
4
a
4
I
A^4=\frac{\beta}{4}a^4I
A
4
=
4
β
a
4
I
, what is the value of
β
\beta
β
?
Comprehension
MEDIUM
2 marks
16 October 2022
44
NOTE: Enter your answer to the nearest integer. Find the value of
a
+
λ
a+\lambda
a
+
λ
for which
det
(
A
−
λ
I
)
=
0
\det(A-\lambda I)=0
det
(
A
−
λ
I
)
=
0
, where
λ
\lambda
λ
is a real number and
a
a
a
is treated as a variable.
Comprehension
MEDIUM
2 marks
16 October 2022
45
If
A
+
3
I
=
0
A+3I=0
A
+
3
I
=
0
, where
A
A
A
is a
2
×
2
2\times2
2
×
2
matrix and
I
I
I
is the identity matrix of order
2
2
2
, then find
det
(
A
)
\det(A)
det
(
A
)
.
Numerical
EASY
2 marks
05 June 2022
46
If
A
=
[
3
−
3
−
3
3
]
A=\begin{bmatrix}3&-3\\-3&3\end{bmatrix}
A
=
[
3
−
3
−
3
3
]
and
A
2
=
λ
A
A^2=\lambda A
A
2
=
λ
A
, then find the value of
λ
\lambda
λ
.
Numerical
EASY
2 marks
05 June 2022
47
If
[
a
+
4
3
b
8
−
6
]
=
[
2
a
+
2
b
+
2
8
a
−
8
b
]
\begin{bmatrix}a+4&3b\\8&-6\end{bmatrix}=\begin{bmatrix}2a+2&b+2\\8&a-8b\end{bmatrix}
[
a
+
4
8
3
b
−
6
]
=
[
2
a
+
2
8
b
+
2
a
−
8
b
]
, then find the value of
a
+
2
b
a+2b
a
+
2
b
.
Numerical
EASY
2 marks
05 June 2022
48
The matrix representation to find
x
1
x_1
x
1
,
x
2
x_2
x
2
, and
x
3
x_3
x
3
is:
Comprehension
EASY
2 marks
05 June 2022
Showing 48 questions.
Mathematics 2 > Week 1
All PYQs
Topic Wise PYQs
Start Weekly Test
Type:
All
Difficulty:
All
Year:
All
48Q
01
Let
A
=
[
1
a
a
2
a
3
1
b
b
2
b
3
1
c
c
2
c
3
1
d
d
2
d
3
]
A=\begin{bmatrix}1&a&a^2&a^3\\1&b&b^2&b^3\\1&c&c^2&c^3\\1&d&d^2&d^3\end{bmatrix}
A
=
1
1
1
1
a
b
c
d
a
2
b
2
c
2
d
2
a
3
b
3
c
3
d
3
where
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are distinct real numbers. Which of the following statements are correct?
Multiple correct
MEDIUM
5 marks
15 March 2026
02
Suppose
a
=
(
1
,
2
)
a=(1,2)
a
=
(
1
,
2
)
and
b
=
(
3
,
−
1
)
b=(3,-1)
b
=
(
3
,
−
1
)
. Let
v
=
k
a
+
l
b
v=ka+lb
v
=
k
a
+
l
b
such that
v
1
=
v
2
v_1=v_2
v
1
=
v
2
and
k
+
l
=
5
k+l=5
k
+
l
=
5
. Find the value of
k
k
k
.
Numerical
EASY
4 marks
15 March 2026
03
Let
A
A
A
be a square matrix of order
n
>
1
n>1
n
>
1
. Select all the statements which imply that
det
(
A
)
=
0
\det(A)=0
det
(
A
)
=
0
.
Multiple correct
MEDIUM
6 marks
26 October 2025
04
If the sum of the two vectors
(
1
,
2
)
(1,2)
(
1
,
2
)
and
(
2
,
x
)
(2,x)
(
2
,
x
)
in
R
2
\mathbb{R}^2
R
2
is a scalar multiple of the vector
(
2
,
1
)
(2,1)
(
2
,
1
)
, then find the value of
x
x
x
.
Numerical
EASY
3 marks
26 October 2025
05
Find the minimum value of
β
\beta
β
such that the matrix
[
β
−
1
0
−
1
2
β
+
4
2
β
+
1
β
+
1
β
+
1
]
\begin{bmatrix}\beta-1&0&-1\\2&\beta+4&2\\\beta+1&\beta+1&\beta+1\end{bmatrix}
β
−
1
2
β
+
1
0
β
+
4
β
+
1
−
1
2
β
+
1
is not invertible.
Numerical
MEDIUM
3 marks
26 October 2025
06
There are two kinds of coins, Type A and Type B. Let the unknown monetary values of coins of Type A and Type B be
x
1
x_1
x
1
and
x
2
x_2
x
2
, respectively. A collection of
2
2
2
coins of Type A and
3
3
3
coins of Type B is worth Rs
19
19
19
. A collection of
1
1
1
coin of Type A and
5
5
5
coins of Type B is worth Rs
27
27
27
. Use the above information to set up a system of linear equations and find the value of
x
1
−
x
2
x_1-x_2
x
1
−
x
2
.
Numerical
EASY
4 marks
26 October 2025
07
Choose the matrix which satisfies the equation
det
(
A
−
c
I
)
=
c
2
−
5
c
+
6
\det(A-cI)=c^2-5c+6
det
(
A
−
c
I
)
=
c
2
−
5
c
+
6
.
Single correct
MEDIUM
4 marks
13 July 2025
08
Let
A
A
A
be a
3
×
3
3\times3
3
×
3
matrix such that
det
(
A
)
=
−
3
\det(A)=-3
det
(
A
)
=
−
3
. For which of the options below is the matrix
B
B
B
, obtained from
A
A
A
by performing the operations in the option, such that
det
(
B
)
=
12
\det(B)=12
det
(
B
)
=
12
?
Multiple correct
MEDIUM
5 marks
13 July 2025
09
Let
x
1
x_1
x
1
be the price of
1
1
1
pencil and
x
2
x_2
x
2
be the price of
1
1
1
pen. Choose the correct option.
Comprehension
EASY
2 marks
13 July 2025
10
Suppose Shakti tries to find the price of
1
1
1
pencil and
1
1
1
pen and hopes to have unique values for the prices. Then
b
b
b
should not be equal to
Comprehension
MEDIUM
4 marks
13 July 2025
11
Let
A
A
A
be an
m
×
n
m\times n
m
×
n
matrix. Choose the operations that are valid only when
m
=
n
m=n
m
=
n
.
Multiple correct
EASY
4 marks
23 February 2025
12
Find the number of
2
×
2
2\times2
2
×
2
scalar matrices with determinant equal to
4
4
4
.
Numerical
EASY
2 marks
23 February 2025
13
If the sum of the two vectors
(
1
,
2
)
(1,2)
(
1
,
2
)
and
(
2
,
x
)
(2,x)
(
2
,
x
)
in
R
2
\mathbb{R}^2
R
2
is a scalar multiple of the vector
(
2
,
1
)
(2,1)
(
2
,
1
)
, then find the value of
x
x
x
.
Numerical
EASY
3 marks
23 February 2025
14
Find the minimum value of
β
\beta
β
such that the matrix
[
β
−
1
0
−
1
2
β
+
4
2
β
+
1
β
+
1
β
+
1
]
\begin{bmatrix}\beta-1&0&-1\\2&\beta+4&2\\\beta+1&\beta+1&\beta+1\end{bmatrix}
β
−
1
2
β
+
1
0
β
+
4
β
+
1
−
1
2
β
+
1
is not invertible.
Numerical
MEDIUM
3 marks
23 February 2025
15
There are two kinds of coins, say of Type A and Type B. Let the unknown monetary values of coins of Type A and Type B be
x
1
x_1
x
1
and
x
2
x_2
x
2
, respectively. A collection of
2
2
2
coins of Type A and
3
3
3
coins of Type B is worth
₹
19
₹19
₹19
. A collection of
1
1
1
coin of Type A and
5
5
5
coins of Type B is worth
₹
27
₹27
₹27
. Use the above information to set up a system of linear equations and find the value of
x
1
−
x
2
x_1-x_2
x
1
−
x
2
.
Numerical
MEDIUM
4 marks
23 February 2025
16
Which of the following conditions are sufficient to deduce
det
(
A
B
)
=
0
\det(AB)=0
det
(
A
B
)
=
0
?
Comprehension
MEDIUM
6 marks
23 February 2025
17
For
α
=
3
\alpha=3
α
=
3
and
β
=
0
\beta=0
β
=
0
, find the value of
det
(
−
B
T
A
2
B
−
1
)
\det(-B^TA^2B^{-1})
det
(
−
B
T
A
2
B
−
1
)
.
Comprehension
MEDIUM
4 marks
23 February 2025
18
Choose the correct option(s) from the following:
Multiple correct
MEDIUM
3 marks
27 October 2024
19
Find the value of
α
\alpha
α
.
Comprehension
MEDIUM
1.5 marks
27 October 2024
20
Find the value of
β
\beta
β
.
Comprehension
MEDIUM
1.5 marks
27 October 2024
21
Let
A
A
A
be a
5
×
5
5\times5
5
×
5
matrix such that
A
T
=
−
A
A^T=-A
A
T
=
−
A
. Then
det
(
A
)
=
\det(A)=
det
(
A
)
=
Comprehension
EASY
1 marks
27 October 2024
22
Let
A
A
A
be a
2
×
2
2\times2
2
×
2
matrix such that
det
(
A
)
=
2
\det(A)=2
det
(
A
)
=
2
. If
B
B
B
is a matrix obtained from
A
A
A
by swapping the first and second row, and then multiplying the second row by
−
2
-2
−
2
, then
det
(
B
)
=
\det(B)=
det
(
B
)
=
Comprehension
EASY
1 marks
27 October 2024
23
Consider the matrix
A
=
[
1
0
5
−
2
3
−
4
1
4
a
]
A=\begin{bmatrix}1&0&5\\-2&3&-4\\1&4&a\end{bmatrix}
A
=
1
−
2
1
0
3
4
5
−
4
a
. Find the value of
a
a
a
if the system
A
x
=
0
Ax=0
A
x
=
0
has infinitely many solutions.
Comprehension
MEDIUM
2 marks
27 October 2024
24
A
=
(
a
i
j
)
∈
M
5
×
5
(
R
)
A=(a_{ij})\in M_{5\times5}(\mathbb{R})
A
=
(
a
ij
)
∈
M
5
×
5
(
R
)
is a matrix such that
a
i
j
+
a
j
i
=
0
a_{ij}+a_{ji}=0
a
ij
+
a
j
i
=
0
for all
1
≤
i
,
j
≤
5
1\le i,j\le5
1
≤
i
,
j
≤
5
. Find the determinant of
A
A
A
.
Numerical
EASY
2 marks
07 July 2024
25
If determinant of
A
A
A
is
−
2
-2
−
2
, find the determinant of
A
T
A
A^T A
A
T
A
.
Numerical
EASY
2 marks
07 July 2024
26
Find the value of
α
\alpha
α
.
Comprehension
MEDIUM
1.5 marks
07 July 2024
27
Find the value of
β
\beta
β
.
Comprehension
MEDIUM
1.5 marks
07 July 2024
28
Find the determinant of the matrix
[
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
]
\begin{bmatrix}0&1&0&0&0\\0&0&0&1&0\\1&0&0&0&0\\0&0&1&0&0\\0&0&0&0&1\end{bmatrix}
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
.
Comprehension
MEDIUM
2 marks
25 February 2024
29
Find the determinant of the matrix
[
a
b
0
c
d
e
5
f
g
h
4
i
0
0
−
5
0
]
\begin{bmatrix}a&b&0&c\\d&e&5&f\\g&h&4&i\\0&0&-5&0\end{bmatrix}
a
d
g
0
b
e
h
0
0
5
4
−
5
c
f
i
0
, given that
det
[
a
b
c
d
e
f
g
h
i
]
=
2
\det\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}=2
det
a
d
g
b
e
h
c
f
i
=
2
.
Comprehension
MEDIUM
2 marks
25 February 2024
30
Find the value of
c
c
c
.
Comprehension
EASY
1 marks
25 February 2024
31
Find the value of
d
d
d
.
Comprehension
EASY
1 marks
25 February 2024
32
Does there exist an
a
a
a
such that the system has no solution? If yes, find the value of
a
a
a
; else write the answer as
100
100
100
.
Comprehension
EASY
1 marks
25 February 2024
33
Consider the following images representing systems of linear equations. Choose the correct option(s) from the following statements.
Multiple correct
MEDIUM
2 marks
29 October 2023
34
Let
A
A
A
be a
3
×
3
3\times3
3
×
3
matrix such that
A
T
=
−
A
A^T=-A
A
T
=
−
A
. Then find
det
(
A
)
\det(A)
det
(
A
)
.
Comprehension
EASY
1 marks
29 October 2023
35
Let
A
A
A
be a
3
×
3
3\times3
3
×
3
matrix such that
det
(
A
)
=
2
\det(A)=2
det
(
A
)
=
2
. If
B
B
B
is a matrix obtained from
A
A
A
by swapping the second and third row, and then multiplying the first row by
−
3
-3
−
3
, then find
det
(
B
)
\det(B)
det
(
B
)
.
Comprehension
EASY
1 marks
29 October 2023
36
Let
A
=
[
1
−
2
−
3
4
]
A=\begin{bmatrix}1&-2\\-3&4\end{bmatrix}
A
=
[
1
−
3
−
2
4
]
and
det
(
A
−
x
I
)
=
x
2
−
a
x
+
b
\det(A-xI)=x^2-ax+b
det
(
A
−
x
I
)
=
x
2
−
a
x
+
b
. Find
a
−
b
a-b
a
−
b
.
Comprehension
MEDIUM
1 marks
29 October 2023
37
What is the determinant of
B
B
B
?
Comprehension
EASY
1 marks
29 October 2023
38
Match the system of linear equations in Column A with their number of solutions in Column B and their geometric representation in Column C. Choose the correct option from the following:
Single correct
MEDIUM
2 marks
16 July 2023
39
Which of the following matrices satisfy
A
k
=
0
A^k=0
A
k
=
0
for some natural number
k
k
k
?
Multiple correct
HARD
2 marks
16 July 2023
40
Let
A
=
[
2022
2023
2024
2022
2021
2022
2022
2022
2022
]
A=\begin{bmatrix}2022&2023&2024\\2022&2021&2022\\2022&2022&2022\end{bmatrix}
A
=
2022
2022
2022
2023
2021
2022
2024
2022
2022
. What is the determinant of
1
2
A
\frac{1}{2}A
2
1
A
?
Numerical
MEDIUM
2 marks
16 July 2023
41
Choose the correct option(s).
Comprehension
EASY
1 marks
16 July 2023
42
Choose the set of correct options.
Multiple correct
MEDIUM
2 marks
16 October 2022
43
NOTE: Enter your answer to the nearest integer. If
A
4
=
β
4
a
4
I
A^4=\frac{\beta}{4}a^4I
A
4
=
4
β
a
4
I
, what is the value of
β
\beta
β
?
Comprehension
MEDIUM
2 marks
16 October 2022
44
NOTE: Enter your answer to the nearest integer. Find the value of
a
+
λ
a+\lambda
a
+
λ
for which
det
(
A
−
λ
I
)
=
0
\det(A-\lambda I)=0
det
(
A
−
λ
I
)
=
0
, where
λ
\lambda
λ
is a real number and
a
a
a
is treated as a variable.
Comprehension
MEDIUM
2 marks
16 October 2022
45
If
A
+
3
I
=
0
A+3I=0
A
+
3
I
=
0
, where
A
A
A
is a
2
×
2
2\times2
2
×
2
matrix and
I
I
I
is the identity matrix of order
2
2
2
, then find
det
(
A
)
\det(A)
det
(
A
)
.
Numerical
EASY
2 marks
05 June 2022
46
If
A
=
[
3
−
3
−
3
3
]
A=\begin{bmatrix}3&-3\\-3&3\end{bmatrix}
A
=
[
3
−
3
−
3
3
]
and
A
2
=
λ
A
A^2=\lambda A
A
2
=
λ
A
, then find the value of
λ
\lambda
λ
.
Numerical
EASY
2 marks
05 June 2022
47
If
[
a
+
4
3
b
8
−
6
]
=
[
2
a
+
2
b
+
2
8
a
−
8
b
]
\begin{bmatrix}a+4&3b\\8&-6\end{bmatrix}=\begin{bmatrix}2a+2&b+2\\8&a-8b\end{bmatrix}
[
a
+
4
8
3
b
−
6
]
=
[
2
a
+
2
8
b
+
2
a
−
8
b
]
, then find the value of
a
+
2
b
a+2b
a
+
2
b
.
Numerical
EASY
2 marks
05 June 2022
48
The matrix representation to find
x
1
x_1
x
1
,
x
2
x_2
x
2
, and
x
3
x_3
x
3
is:
Comprehension
EASY
2 marks
05 June 2022
Showing 48 questions.
