Matrices & Determinants · NDA previous year questions

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2011 7 questions

Q512011 · 21 Aug 2011
1. A. $a^{3} + b^{3} + c^{3}$
2. B. $3 b c$
3. C. $a^{3} + b^{3} + c^{3} - 3 ab c$
4. D.0
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Answer: C
Q902011 · 21 Aug 2011
Consider the following statements in respect of the square matrices A and B of same order: 1. A and B are non-zero and $A B = 0 \Rightarrow$ either $∣ A ∣ = 0$ or $∣ B ∣ = 0$ 2. $A B = 0 \Rightarrow A = 0$ or $B = 0$ 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
Q912011 · 21 Aug 2011
For what value of k, are the lines $x + 2 y - 9 = 0$ and $k x + 4 y + 5 = 0$ parallel?
1. A.2
2. B. $- 1$
3. C.1
4. D.0
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Answer: A
Q242011 · 17 Apr 2011
If the matrix $A = [α β β α]$ is such that $A^{2} = I$ , then which one of the following is correct?
1. A. $α = 0, β = 1$ or $α = 1, β = 0$
2. B. $α = 0, β \neq = 1$ or $α \neq = 0, β = 1$
3. C. $α = 1, β \neq = 0$ or $α \neq = 1, β = 0$
4. D. $α \neq = 0, β \neq = 0$
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Answer: A
Q312011 · 17 Apr 2011
What is the value of the determinant $x + 1 x + 3 x + 7 x + 2 x + 5 x + 10 x + 4 x + 8 x + 14$ ?
1. A. $x + 2$
2. B. $x^{2} + 2$
3. C.2
4. D. $- 2$
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Answer: D
Q652011 · 17 Apr 2011
Consider the following statements: 1. The inverse of a square matrix, if it exists, is unique. 2. If $A$ and $B$ are singular matrices of order $n$ , then $A B$ is also a singular matrix of order $n$ . 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
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Answer: C
Q1162011 · 17 Apr 2011
If the matrix $A = 2 - x 1 - 1 1 3 - x - 3 10 - x$ is singular, then what is the solution set $S$ ?
1. A. $S = {0, 2, 3}$
2. B. $S = {- 1, 2, 3}$
3. C. $S = {1, 2, 3}$
4. D. $S = {2, 3}$
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Answer: A