Matrices & Determinants · NDA previous year questions

2010 14 questions

1. Q22010 · 22 Aug 2010

   If $\left[\begin{array}{ccc}1& -3& 2\\ 2& -8& 5\\ 4& 2& \lambda \end{array}\right]$ is not an invertible matrix, then what is the value of $\lambda$?

   1. A.-1
   2. B.0
   3. C.1
   4. D.2
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   Answer: C

2. Q142010 · 22 Aug 2010

   If $|A|=8$, where $A$ is a square matrix of order 3, then what is $|\mathrm{adj}A|$ equal to?

   1. A.16
   2. B.24
   3. C.64
   4. D.512
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   Answer: C

3. Q172010 · 22 Aug 2010

   Consider the following statements in respect of a square matrix $A$ and its transpose $A^T$ : 1. $A+A^T$ is always symmetric. 2. $A-A^T$ is always anti-symmetric. 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

4. Q202010 · 22 Aug 2010

   If a matrix $A$ is such that $3A^3+2A^2+5A+I=0$, then what is $A^{-1}$ equal to?

   1. A.$-(3A^2+2A+5)$
   2. B.$3A^2+2A+5I$
   3. C.$3A^2-2A-5I$
   4. D.$-(3A^2+2A+5I)$
   Show answer

   Answer: D

5. Q272010 · 22 Aug 2010

   Let $A$ and $B$ be matrices of order $3\times 3$. If $AB=0$, then which of the following can be concluded?

   1. A.$A=0$ and $B=0$
   2. B.$|A|=0$ and $|B|=0$
   3. C.Either $|A|=0$ or $|B|=0$
   4. D.Either $A=0$ or $B=0$
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   Answer: C

6. Q292010 · 22 Aug 2010

   If $A$ is a square matrix, then what is $\mathrm{adj}{A}^T-(\mathrm{adj}A{)}^T$ equal to?

   1. A.$2|A|$
   2. B.$2|A|I$
   3. C.Null matrix
   4. D.Unit matrix
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   Answer: C

7. Q302010 · 22 Aug 2010

   Which one of the following is correct?

   1. A.$\sin 1^{\circ }>\sin 1$
   2. B.$\sin 1^{\circ }<\sin 1$
   3. C.$\sin 1^{\circ }=\sin 1$
   4. D.$\sin 1^{\circ }=\frac{\pi }{180}\sin 1$
   Show answer

   Answer: B

8. Q12010 · 18 Apr 2010
   
   1. A.10
   2. B.20
   3. C.40
   4. D.60
   Show answer

   Answer: D

9. Q182010 · 18 Apr 2010
   
   1. A.$\left(\begin{array}{ccc}5& 1& 4\\ 2& 6& 3\end{array}\right)$
   2. B.$\left(\begin{array}{ccc}2& 6& 3\\ 5& 1& 4\end{array}\right)$
   3. C.$\left(\begin{array}{cc}5& 2\\ 1& 6\end{array}\right)$
   4. D.$\left(\begin{array}{cc}2& 5\\ 6& 1\end{array}\right)$
   Show answer

   Answer: C

10. Q202010 · 18 Apr 2010

    Consider the following statements: 1. If $A^{\prime }=A$, then A is a singular matrix, where $A^{\prime }$ is the transpose of A. 2. If A is a square matrix such that $A^3=I$, then A is non-singular. 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: B

11. Q552010 · 18 Apr 2010

    Let $A$ be an $n\times n$ matrix. If $\det (\lambda A)={\lambda }^s\det (A)$, what is the value of $s$?

    1. A.0
    2. B.1
    3. C.$-1$
    4. D.$n$
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    Answer: D

12. Q602010 · 18 Apr 2010

    If $A$ be a real skew-symmetric matrix of order $n$ such that $A^2+I=0$, $I$ being the identity matrix of the same order as that of $A$, then what is the order of $A$?

    1. A.3
    2. B.Odd
    3. C.Prime number
    4. D.Even
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    Answer: D

13. Q772010 · 18 Apr 2010

    Let $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]=[a_{ij}]$, where i, j = 1, 2. If its inverse matrix is $[b_{ij}]$, what is $b_{22}$?

    1. A.-2
    2. B.1
    3. C.$\frac{3}{2}$
    4. D.$-\frac{1}{2}$
    Show answer

    Answer: D

14. Q782010 · 18 Apr 2010

    The angle A lies in the third quadrant and it satisfies the equation $4({\sin }^{2}x+\cos x)=1$. What is the measure of the angle A?

    1. A.$225^{\circ }$
    2. B.$240^{\circ }$
    3. C.$210^{\circ }$
    4. D.None of the above
    Show answer

    Answer: B