Matrices & Determinants · NDA previous year questions

2015 29 questions

1. Q232015 · 19 Apr 2015
   
   1. A.$\left[\begin{array}{cc}6& -10\\ 4& 26\end{array}\right]$
   2. B.$\left[\begin{array}{cc}-10& 5\\ 4& 24\end{array}\right]$
   3. C.$\left[\begin{array}{cc}-5& -6\\ 4& 20\end{array}\right]$
   4. D.$\left[\begin{array}{cc}-5& -7\\ 5& 20\end{array}\right]$
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   Answer: A

2. Q242015 · 19 Apr 2015

   If $$E(\theta )=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$ then $E(\alpha )E(\beta )$ is equal to

   1. A.$E(\alpha \beta )$
   2. B.$E(\alpha -\beta )$
   3. C.$E(\alpha +\beta )$
   4. D.$-E(\alpha +\beta )$
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   Answer: C

3. Q252015 · 19 Apr 2015

   Consider the following in respect of two non-singular matrices $A$ and $B$ of same order : 1. $\det (A+B)=\det A+\det B$ 2. $(A+B{)}^{-1}=A^{-1}+B^{-1}$ Which of the 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: D

4. Q262015 · 19 Apr 2015

   The value of $$\left|\begin{array}{ccc}1& 1& 1\\ 1& 1+x& 1\\ 1& 1& 1+y\end{array}\right|$$ is

   1. A.$x+y$
   2. B.$x-y$
   3. C.$xy$
   4. D.$1+x+y$
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   Answer: C