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Matrices · Mathematics · NDA

MCQ (Single Correct Answer)
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MCQ (Single Correct Answer)

1
The matrix $$A = \left[ {\matrix{ 1 & 3 & 2 \cr 1 & {x - 1} & 1 \cr 2 & 7 & {x - 3} \cr } } \right]$$ will have inverse for every real number x except for
NDA 2015 Paper 2
2
If $$A = \left[ {\matrix{ 1 & 0 & { - 2} \cr 2 & { - 3} & 4 \cr } } \right]$$, then the matrix X for which 2X + 3A = 0 holds true is
NDA 2015 Paper 2
3
If $$A = \left[ {\matrix{ 1 & 1 & { - 1} \cr 2 & { - 3} & 4 \cr 3 & { - 2} & 3 \cr } } \right]$$ and $$B = \left[ {\matrix{ { - 1} & { - 2} & { - 1} \cr 6 & {12} & 6 \cr 5 & {10} & 5 \cr } } \right]$$, then which of the following is/are correct?

1. A and B commute.

2. AB is a null matrix.

Select the correct answer using the codes given below.
NDA 2015 Paper 2
4
Which one of the following matrices is an elementary matrix?
NDA 2015 Paper 2
5
If $$A = \left[ {\matrix{ 2 & 7 \cr 1 & 5 \cr } } \right]$$, then what is $$A + 3{A^{ - 1}}$$ equal to?

where, I is the identity matrix of order 2.
NDA 2015 Paper 2
6
The matrix $$\left[ {\matrix{ 0 & { - 4 + i} \cr {4 + i} & 0 \cr } } \right]$$ is
NDA 2015 Paper 2
7
If $$X = \left[ {\matrix{ 3 & { - 4} \cr 1 & { - 1} \cr } } \right]$$, $$B = \left[ {\matrix{ 5 & 2 \cr { - 2} & 1 \cr } } \right]$$ and $$A = \left[ {\matrix{ p & q \cr r & s \cr } } \right]$$ satisfy the equation AX = B, then the matrix A is equal to
NDA 2015 Paper 2
8
Let $$A = \left[ {\matrix{ {x + y} & y \cr {2x} & {x - y} \cr } } \right]$$, $$B = \left[ {\matrix{ 2 \cr { - 1} \cr } } \right]$$ and $$C = \left[ {\matrix{ 3 \cr 2 \cr } } \right]$$. If AB = C, then what is A2 equal to?
NDA 2015 Paper 2
9
If $$E(\theta ) = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$, then E($$\alpha$$) E($$\beta$$) is equal to
NDA 2015 Paper 2
10
If A is an orthogonal matrix of order 3 and $$B = \left[ {\matrix{ 1 & 2 & 3 \cr { - 3} & 0 & 2 \cr 2 & 5 & 0 \cr } } \right]$$, then which of the following is/are correct?

1. $$\left| {AB} \right| = \pm \,47$$ 2. AB = BA

Select the correct answer using the code given below.
NDA 2015 Paper 2
11
If $$A = \left[ {\matrix{ 1 & { - 1} \cr 2 & 3 \cr } } \right]$$ and $$B = \left[ {\matrix{ 2 & 3 \cr { - 1} & { - 2} \cr } } \right]$$, then which of the following is/are correct?

I. AB (A$$-$$1 B$$-$$1) is a unit matrix.

II. (AB)$$-$$1 = A$$-$$1 B$$-$$1.

Select the correct answer using the code given below.
NDA 2016 Paper 2
12
Consider the following in respect of the matrix $$A = \left[ {\matrix{ { - 1} & 1 \cr 1 & { - 1} \cr } } \right]$$

1. A2 = $$-$$ A

2. A3 = 4A

Which of the above is/are correct?
NDA 2016 Paper 1
13
If $$A = \left( {\matrix{ { - 2} & 2 \cr 2 & { - 2} \cr } } \right)$$, then which one of the following is correct?
NDA 2017 Paper 2
14
The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 $$-$$ y columns. Both AB and BA exist. What are the values of x and y respectively?
NDA 2017 Paper 2
15
If A is a square matrix, then the value of adj $${A^T}$$ $$-$$ (adj $${A)^T}$$ is equal to
NDA 2017 Paper 2
16
The adjoint of the matrix $$A = \left[ {\matrix{ 1 & 0 & 2 \cr 2 & 1 & 0 \cr 0 & 3 & 1 \cr } } \right]$$ is
NDA 2017 Paper 2
17
If a, b, c are non-zero real numbers, then the inverse of the matrix $$A = \left[ {\matrix{ a & 0 & 0 \cr 0 & b & 0 \cr 0 & 0 & c \cr } } \right]$$ is equal to
NDA 2017 Paper 2
18
If $$A = \left[ {\matrix{ {\cos \alpha } & {\sin \alpha } \cr { - \sin \alpha } & {\cos \alpha } \cr } } \right]$$, then what is AAT equal to (where, AT is transpose of A)?
NDA 2017 Paper 1
19
$$A = \left[ {\matrix{ {x + y} & y \cr x & {x - y} \cr } } \right]$$, $$B = \left[ {\matrix{ 3 \cr { - 2} \cr } } \right]$$ and $$C = \left[ {\matrix{ 4 \cr { - 2} \cr } } \right]$$. If AB = C, then what is A2 equal to?
NDA 2017 Paper 1
20
Consider the set A of all matrices of order 3 $$\times$$ 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is $$-$$1. Then which one of the following is correct?
NDA 2017 Paper 1
21
If $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$, then what is A3 equal to?
NDA 2017 Paper 1
22
What is the order of $$\left[ {\matrix{ x & y & z \cr } } \right]\left[ {\matrix{ a & h & g \cr h & b & f \cr g & f & c \cr } } \right]\left[ {\matrix{ x \cr y \cr z \cr } } \right]$$ ?
NDA 2017 Paper 1
23
If $$A = \left[ {\matrix{ 0 & 1 \cr 1 & 0 \cr } } \right]$$, then the value of A4 is
NDA 2017 Paper 1
24
A square matrix A is called orthogonal, if

where A' is the transpose of A
NDA 2018 Paper 2
25
If A and B are two invertible square matrices of same order, then what is (AB)$$-$$1 equal to?
NDA 2018 Paper 2
26
Consider the following in respect of matrices A, B and C of same order.

1. (A + B + C)' = A' + B' + C'

2. (AB)' = A' B'

3. (ABC)' = C' B' A'

Where, A' is the transpose of the matrix A. Which of the above are correct?
NDA 2018 Paper 2
27
Consider the following in respect of matrices A and B of same order.

1. A2 $$-$$ B2 = (A + B) (A $$-$$ B)

2. (A $$-$$ I) (I + A) = O $$ \Leftrightarrow $$ A2 = I

where, I is the identity matrix and O is the null matrix.

Which of the above is/are correct?
NDA 2018 Paper 2
28
What is the adjoint of the matrix $$\left( {\matrix{ {\cos ( - \theta )} & { - \sin ( - \theta )} \cr { - \sin ( - \theta )} & {\cos ( - \theta )} \cr } } \right)$$ ?
NDA 2018 Paper 2
29
What should be the value of x, so that the matrix $$\left( {\matrix{ 2 & 4 \cr { - 8} & x \cr } } \right)$$ does not have an inverse?
NDA 2018 Paper 2
30
If $$A = \left( {\matrix{ 1 & 2 \cr 2 & 3 \cr } } \right)$$ and $${A^2} - kA - {I_2} = O$$, where I2 is the 2 $$\times$$ 2 identity matrix, then what is the value of k?
NDA 2018 Paper 1
31
What is the inverse of the matrix $$A = \left( {\matrix{ {\cos \theta } & {\sin \theta } & 0 \cr { - \sin \theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right)$$ ?
NDA 2018 Paper 1
32
If $$A = \left[ {\matrix{ 1 & { - 1} \cr { - 1} & 1 \cr } } \right]$$, then the expression A3 $$-$$ 2A2 is
NDA 2019 Paper 2
33
If $$A = \left( {\matrix{ 1 & 2 \cr 2 & 3 \cr 3 & 4 \cr } } \right)$$ and $$B = \left( {\matrix{ 1 & 2 \cr 2 & 1 \cr } } \right)$$, then which one of the following is correct?
NDA 2019 Paper 2
34
If $$B = \left[ {\matrix{ 3 & 2 & 0 \cr 2 & 4 & 0 \cr 1 & 1 & 0 \cr } } \right]$$, then what is adjoint of B equal to?
NDA 2019 Paper 1
35
If $$A = \left[ {\matrix{ 0 & 1 \cr 1 & 0 \cr } } \right]$$, then the matrix A is a/an
NDA 2019 Paper 1
36
If $$\left[ {\matrix{ x & { - 3i} & 1 \cr y & 1 & i \cr 0 & {2i} & { - i} \cr } } \right] = 6 + 11i$$, then what are the values of x and y respectively?
NDA 2019 Paper 1
37
If A is an identity matrix of order 3, then its inverse (A$$-$$1)
NDA 2019 Paper 1
38
A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose?
NDA 2019 Paper 1
39

Let $A$ and $B$ be matrices of order $3 \times 3$. If $|A| = \frac{1}{2 \sqrt{2}}$ and $|B| = \frac{1}{729}$, then what is the value of $|2B(adj(3A))|$?

NDA Mathematics 21 April 2024
40

Consider the following statements in respect of two non-singular matrices $A$ and $B$ of the same order $n$:

  1. 1.$adj(AB) = (adjA)(adjB)$

  2. 2. $adj(AB) = adj(BA)$

  3. 3. $(AB) adj(AB) - |AB| I_n$ is a null matrix of order $n$

How many of the above statements are correct?
NDA Mathematics 21 April 2024
41

Consider the following statements in respect of a non-singular matrix $A$ of order $n$:

1. $A(\text{adj}A^T) = A(\text{adj}A)^T$

2. If $A^2 = A$, then $A$ is identity matrix of order $n$

3. If $A^3 = A$, then $A$ is identity matrix of order $n$

Which of the statements given above are correct?

NDA Mathematics 21 April 2024
42

Consider the following statements in respect of a skew-symmetric matrix $A$ of order $3$:

1. All diagonal elements are zero.

2. The sum of all the diagonal elements of the matrix is zero.

3. $A$ is orthogonal matrix.

Which of the statements given above are correct?

NDA Mathematics 21 April 2024
43
If $A=\left[\begin{array}{ccc}\sin 2 \theta & 2 \sin ^2 \theta-1 & 0 \\ \cos 2 \theta & 2 \sin \theta \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$, then which of the following statements is/are correct?

1. $A^{-1}=\operatorname{adj} A$

2. A is skew-symmetric matrix

3. $A^{-1}=A^T$

Select the correct answer using the code given below :
NDA Mathematics 21 April 2024
44

If $A=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{array}\right]$, then which of the following statements are correct?

1. An will always be singular for any positive integer n.

2. An will always be a diagonal matrix for any positive integer n.

3. An will always be a symmetric matrix for any positive integer n.

Select the correct answer using the code given below:

NDA Mathematics 3 September 2023
45
If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$, then what is 23A3 - 19A2 - 4A equal to ?
NDA Mathematics 3 September 2023
46

Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB - BA) ?

1. Its diagonal entries are equal but nonzero

2. The sum of its non-diagonal entries is zero

Select the correct answer using the code given below : 

NDA Mathematics 16 April 2023
47

Consider the following statements in respect of square matrices A, B, C each of same order n :

1. AB = AC ⇒ B = C if A is non-singular

2. If BX = CX for every column matrix X having n rows then B = C

Which of the statements given above is/are correct ?  

NDA Mathematics 16 April 2023
48

The system of linear equations

x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has  

NDA Mathematics 16 April 2023
49
Let AX = B be a system of 3 linear equations with 3-unknowns. Let X1 and X2 be its two distinct solutions. If the combination aX1 + bX2 is a solution of AX = B; where a, b are real numbers, then which one of the following is correct ? 
NDA Mathematics 16 April 2023
50

If A = $\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos \theta & \sin \theta \\ 0 & \sin \theta & −\cos \theta\end{array}\right)$, then which of the following are correct?

1. A + adj A is a null matrix

2. A−1 + adj A is a null matrix

3. A − A−1 is a null matrix

Select the correct answer using the code given below :

NDA Mathematics 4 September 2022
51

If X is a matrix of order 3 × 3, Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2, then which of the following are correct?

1. (ZY)X is a square matrix having 9 entries.

2. Y(XZ) is a square matrix having 4 entries.

3. X(YZ) is not defined.

Select the correct answer using the code given below :

NDA Mathematics 4 September 2022
52

What is P equal to ?

NDA Mathematics 4 September 2022
53

What is Q equal to ?

NDA Mathematics 4 September 2022
54

Consider the following in respect of the matrices:

A = [m n], B = [-n -m] & $ C = \begin{bmatrix} m \\ -m\end{bmatrix} $

 

1. CA = CB

2. AC = BC

3. C(A + B) = CA + CB

Which of the above statements is/are correct?

NDA Mathematics 10 April 2022
55

If $A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \\ -2\cos \theta & \sin \theta & 0 \\ -1 & 1 & 1 \end{bmatrix},$ then what is A(adj A) equal to?

(where) I is the identity matrix.

NDA Mathematics 10 April 2022
56

Let A be a non-singular matrix and B = adj A. Which of the following statements is/are correct?

1. AB = BA

2. AB is a scalar matrix

3. AB can be a null matrix

Select the correct answer using the code given below:

NDA Mathematics 10 April 2022
57

Consider the following statements in respect of square matrices A and B of same order :

1. If AB is a null matrix, then at least one of A and B is a null matrix.

2. If AB is an identity matrix, then BA = AB.

Which of the above statements is/are correct?

NDA Mathematics 10 April 2022
58

Let A and B be non-singular matrices of the same order such that AB = A and BA = B. Which of the following statements is/are correct ?

1. A2 = A

2. AB2 = A2B

Select the correct answer using the code given below:

NDA Mathematics 10 April 2022
59
What is (1110011)2 ÷ (10111)2 equal to ?
NDA Mathematics 10 April 2022
60
If x3 + y3 = (100010111)2 and x + y = (11111)2, then what is (x - y)2 + xy equal to ?
NDA Mathematics 10 April 2022
61
If A and B are two matrices such that AB is of order n × n, then which one of the following is correct?
NDA Mathematics 18 April 2021
62
How many matrices of different orders are possible with elements comprising all prime numbers less than 30?
NDA Mathematics 18 April 2021
63
If A and B are square matrices of order 2 such that det(AB) = det(BA), then which one of the following is correct?
NDA Mathematics 18 April 2021
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