Matrices & Determinants · NDA previous year questions

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2020 8 questions

Q12020 · 6 Sept 2020
If matrix $A = [1 - i - i i 1 - i]$ where $i = - 1$ , then which one of the following is correct?
1. A. $A$ is hermitian
2. B. $A$ is skew-hermitian
3. C. $(\overset{ˉ}{A})^{T} + A$ is hermitian
4. D. $(\overset{ˉ}{A})^{T} + A$ is skew-hermitian
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Answer: C
Q52020 · 6 Sept 2020
1. A.Only one
2. B.Only two
3. C.Only four
4. D.Infinite
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Answer: D
Q92020 · 6 Sept 2020
Let $A = [x + y 2 x y x - y]$ , $B = [2 - 1]$ and $C = [32]$ . If $A B = C$ , then what is the value of the determinant of the matrix $A$ ?
1. A. $- 10$
2. B. $- 14$
3. C. $- 24$
4. D. $- 34$
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Answer: B
Q102020 · 6 Sept 2020
If $1.5 \leq x \leq 4.5$ , then which one of the following is correct?
1. A. $(2 x - 3) (2 x - 9) > 0$
2. B. $(2 x - 3) (2 x - 9) < 0$
3. C. $(2 x - 3) (2 x - 9) \geq 0$
4. D. $(2 x - 3) (2 x - 9) \leq 0$
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Answer: D
Q122020 · 6 Sept 2020
1. A.0
2. B. $- 2$
3. C. $4 i$
4. D. $- 4 i$
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Answer: D
Q132020 · 6 Sept 2020
1. A. $a x + h y + g z y z$
2. B. $a x + h y + g z h x + b y + f z z$
3. C. $[a x + h y + g z]$
4. D. $[a x + h y + g z h x + b y + f z g x + f y + cz]$
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Answer: C
Q412020 · 6 Sept 2020
If A is a matrix of order $3 \times 5$ and B is a matrix of order $5 \times 3$ , then the order of AB and BA will respectively be
1. A. $3 \times 3$ and $3 \times 3$
2. B. $3 \times 5$ and $5 \times 3$
3. C. $3 \times 3$ and $5 \times 5$
4. D. $5 \times 3$ and $3 \times 5$
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Answer: C
Q502020 · 6 Sept 2020
Consider the following in respect of a non-singular matrix of order 3: 1. $A (adj A) = (adj A) A$ 2. $∣ adj A ∣ = ∣ A ∣$ . Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: A