Matrices & Determinants · NDA previous year questions

363 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2023 16 questions

Q42023 · 3 Sept 2023
1. A.15
2. B.6
3. C.0
4. D.-1
Show answer
Answer: A
Q52023 · 3 Sept 2023
If A, B and C are square matrices of order 3 and $det (B C) = 2 det (A)$ , then what is the value of $det (2 A^{- 1} B C)$ ?
1. A.16
2. B.8
3. C.4
4. D.2
Show answer
Answer: A
Q62023 · 3 Sept 2023
If the $n^{th}$ term of a sequence is $\frac{2 n + 5}{7}$ , then what is the sum of its first 140 terms?
1. A.2840
2. B.2780
3. C.2920
4. D.5700
Show answer
Answer: C
Q72023 · 3 Sept 2023
Let A be a skew-symmetric matrix of order 3. What is the value of $det (4 A^{4}) - det (3 A^{3}) + det (2 A^{2}) - det (A) + det (- I)$ where I is the identity matrix of order 3?
1. A.-1
2. B.0
3. C.1
4. D.2
Show answer
Answer: A
Q82023 · 3 Sept 2023
1. A. $A^{2}$ is symmetric matrix with $det (A^{2}) = 0$ .
2. B. $A^{2}$ is symmetric matrix with $det (A^{2}) \neq = 0$ .
3. C. $A^{2}$ is skew-symmetric matrix with $det (A^{2}) = 0$ .
4. D. $A^{2}$ is skew-symmetric matrix with $det (A^{2}) \neq = 0$ .
Show answer
Answer: A
Q92023 · 3 Sept 2023
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
Show answer
Answer: B
Q162023 · 3 Sept 2023
If all elements of a third order determinant are equal to 1 or -1, then the value of the determinant is:
1. A.0 only
2. B.an even number but not necessarily 0
3. C.an odd number
4. D.0, 1 or -1
Show answer
Answer: B
Q172023 · 3 Sept 2023
1. A.5
2. B.25
3. C.125
4. D.625
Show answer
Answer: D
Q182023 · 3 Sept 2023
1. A.Null matrix of order 3
2. B.Identity matrix of order 3
3. C. $200020002$
4. D. $[700700]$
Show answer
Answer: A
Q192023 · 3 Sept 2023
The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of determinant of $C^{2}$ ?
1. A.3
2. B.9
3. C.81
4. D.729
Show answer
Answer: C
Q202023 · 3 Sept 2023
If $A_{k} = [k - 1 k - 2 k k + 1]$ , then what is $det (A_{1}) + det (A_{2}) + det (A_{3}) + \dots + det (A_{100})$ equal to ?
1. A.100
2. B.1000
3. C.9900
4. D.10000
Show answer
Answer: D
Q42023 · 16 Apr 2023
Let A be a matrix of order $3 \times 3$ and $∣ A ∣ = 4$ . If $∣2 adj (3 A) ∣ = 2^{α} 3^{β}$ , then what is the value of $(α + β)$ ?
1. A.12
2. B.13
3. C.17
4. D.24
Show answer
Answer: B
Q52023 · 16 Apr 2023
If $α$ and $β$ are the distinct roots of equation $x^{2} - x + 1 = 0$ , then what is the value of $\frac{α ^{100} + β ^{100}}{α ^{100} - β ^{100}}$ ?
1. A. $3$
2. B. $2$
3. C.1
4. D. $\frac{1}{3}$
Show answer
Answer: D
Q62023 · 16 Apr 2023
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 :
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: B
Q72023 · 16 Apr 2023
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 ?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: C
Q82023 · 16 Apr 2023
The system of linear equations x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has
1. A.a unique solution
2. B.infinite many solutions
3. C.no solution
4. D.exactly three solutions
Show answer
Answer: C