MOST IMPORTANT QUESTIONS OF MATRICES AND DETERMINANT FOR NDA 2022 | HELP4NDA

MATRICES and DETERMINANTS 💧 IMPORTANT Questions for NDA 2022

syallbus for matrices and determinants :-

Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

1. If A is the value of the determinant



then what is the value of the following

determinant?



(a) pA

(b) qA

(c) (p+q)A

(d) pqA


2. If a+b+c=4 and ab + bc + ca = 0, then

what is the value of the following

determinant?

|a b c|

|b c a|

|c a b|

(a) 32

(b) – 64

(c)-128

(d) 64

3. If A and B are two matrices such that

AB is of order nxn, then which one

of the following is correct?

(a) A and B should

be square

matrices of same order.

(b) Either A or B should be a square

matrix.

(c) Both A and B should be of same

order.

(d) Orders of A and B need not be

the same.

4. How many matrices of different orders

are possible with elements comprising

all prime numbers less than 30?

(a) 2

(b) 3

(c) 4

(d) 6

5. Let,

where p, q, r and s are any four

different prime numbers less than 20.

What is the maximum value of the

determinant?

(a) 215

(b) 311

(c) 317

(d) 323

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लेकिन मेरा जज़्बा भी काम मत समझना मुश्किलें
हर मन जाएँगी लेकिन मेरा जज़्बा नहीं होशला
इतना है की दिमाग में बस यही रहता है करना
है तो बस upsc.

6. If A and B are square matrices of order

2 such that det(AB) = det(BA), then

which one of the following is correct?

(a) A must be a unit matrix.

(b) B must be a unit matrix.

(c) Both A and B must be unit

matrices.

(d) A and B need not be unit matrices.



7. If the determinant

then what is x equal to?

(a) -2 or 2

(b) -3 or 3

(c)-1 or 1

(d) 3 or 4



8. If

f(x) =



then what is f(-1) + f(0) + f(1) equal to?

(a) 0

(b) 1

(c) 100

(d) -100


9. The element in the ith row and the

jth column of a determinant of third

order is equal to 2 (i+j). What is the

value of the determinant?

(a) 0

(6) 2

(c) 4

(d) 6



10. With the numbers 2, 4, 6, 8, all the

possible determinants with these four

different elements are constructed.

What is the sum of the values of all

such determinants?

(a) 128

(b) 64

(c) 32

(d) 0

11. Let



where m, n are positive real numbers

and I is the identity matrix. What is

(m + n) equal to?

(a) o

(b) 1/2

(c) 1

(d) 3/2


12. If A is a non-singular matrix of order 3 x 3, then

adj(adjA) is equal to

(a) |𝐴|A

(b) |𝐴|2A

(c) |𝐴|-1A

(d) none of these


13. If A & B are square matrices of order 3x3 such

that A is an orthogonal matrix & B is a skew-

symmetric matrix, then which of the following

statements is true?

(a) |𝐴𝐵| = 1 (b) |𝐴𝐵| = 0

(c) |𝐴𝐵| = - 1 (d) none of these



14. If A & B are square matrices such that

B = - A-1 BA then (𝐴 + 𝐵)2 =

(a) O

(b) 𝐴2 +B2

(c) 𝐴2+B2+2AB

(d) A + B



15. A square matrix can always be expressed as

(a) the sum of a symmetric & a skew-symmetric

matrix

(b) the sum of a diagonal & a symmetric matrix

(c) a skew-symmetric matrix

(d) a skew-matrix



16. If A is a square matrix such that 𝐴2

- A + 𝐼=0,

then the inverse of A is

(a) 𝐼 - A (b) A – 𝐼 (c) A (d) A + 𝐼



17. If A is a 3x3 matrix & B is its adjoint such that

|𝐵|=64, then |𝐴| =

(a) 64 (b) ±64 (c) ±8 (d) 18

.

18. If A & B are two matrices such that AB = A &

BA = B, then 𝐵2

is equal to

(a) B (b) A (c) 1 (d) 0



19. If A = [𝑎𝑖𝑗] is a square matrix of even order such

that 𝑎𝑖𝑗 = i2 – j2 , then

(a) A is a skew-symmetric & |𝐴| = 0

(b) A is symmetric matrix & |𝐴| is a square

(c) A is symmetric matrix & |𝐴| = 0

(d) none of these



20. If A,B are two n x n non-singular matrices, then

(a) AB is non-singular (b) AB is singular

(c) (𝐴𝐵)-1=A-1B-1

(d) (𝐴𝐵)-1 does not exist



21. If the matrix AB is zero, then

(a) It is not necessary that either A=O, or B=O

(b) A=O or B=O

(c) A=O and B=O

(d) all the above statements are wrong



22. If A,B are square matrices of order 3, A is non-

singular & AB = O, then B is a

(a) null matrix (b) singular matrix

(c) unit matrix (d) non-singular matrix



23. The existence of the unique solution of the

system of equations

x + y + z = 𝜆

5x - y + 𝜇z = 10

2x + 3y - z = 6 depends on

(a) 𝜇 only (b) 𝜆 only

(c) 𝜆 & 𝜇 both (d) neither 𝜆 nor 𝜇



25. For what value of 𝜆, the system of equations

x + y + z = 6

x + 2y + 3z = 10

x + 2y + 𝜆z = 12 is consistent?

(a) 𝜆=1 (b) 𝜆=2 (c) 𝜆=- 2 (d) 𝜆=3



26. The number of values of k for which the system

of equations (k + 1)x + 8y = 4k, kx + (k + 3)y =

3k -1 has no solution, is

(a) infinite (b) 1 (c) 2 (d) 3



27. The system of linear equations

x + 𝜆y - z = 0

𝜆x - y - z = 0

x + y - 𝜆z = 0 has no-trivial solutions for:

(a) infinitely many values of 𝜆

(b) exactly one value of 𝜆

(c) exactly two values of 𝜆

(d) exactly three values of 𝜆

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