Matrices & Determinants · NDA previous year questions

2009 21 questions

1. Q132009 · 30 Aug 2009
   
   1. A.$\left[\begin{array}{cc}1& 3\\ -2& 1\end{array}\right]$
   2. B.$\left[\begin{array}{cc}1& 3\\ 2& 1\end{array}\right]$
   3. C.$\left[\begin{array}{cc}3& 2\\ -1& 5\end{array}\right]$
   4. D.$\left[\begin{array}{cc}3& 2\\ 1& 5\end{array}\right]$
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   Answer: C

2. Q142009 · 30 Aug 2009
   
   1. A.2
   2. B.1
   3. C.$-1$
   4. D.0
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   Answer: C

3. Q152009 · 30 Aug 2009

   If a matrix $A$ is symmetric as well as anti-symmetric, then which one of the following is correct ?

   1. A.$A$ is a diagonal matrix.
   2. B.$A$ is a null matrix.
   3. C.$A$ is a unit matrix.
   4. D.$A$ is a triangular matrix.
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   Answer: B

4. Q162009 · 30 Aug 2009
   
   1. A.$A$ is symmetric matrix.
   2. B.$A$ is anti-symmetric matrix.
   3. C.$A$ is a singular matrix.
   4. D.$A$ is a non-singular matrix.
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   Answer: D

5. Q172009 · 30 Aug 2009
   
   1. A.12
   2. B.$-12$
   3. C.7
   4. D.$-7$
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   Answer: B

6. Q262009 · 30 Aug 2009
   
   1. A.$A$
   2. B.$-A$
   3. C.Null matrix
   4. D.Identity matrix
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   Answer: A

7. Q332009 · 30 Aug 2009

   A matrix $X$ has $(a+b)$ rows and $(a+2)$ columns; and a matrix $Y$ has $(b+1)$ rows and $(a+3)$ columns. If both $XY$ and $YX$ exist, then what are the values of $a,b$ respectively ?

   1. A.3, 2
   2. B.2, 3
   3. C.2, 4
   4. D.4, 3
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   Answer: B

8. Q342009 · 30 Aug 2009

   In a football championship 153 matches were played. Every team played one match with each other team. How many teams participated in the championship ?

   1. A.21
   2. B.18
   3. C.17
   4. D.15
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   Answer: B

9. Q242009 · 19 Apr 2009

   Consider the following statements in respect of symmetric matrices $A$ and $B$: 1. $AB$ is symmetric. 2. $A^2+B^2$ is symmetric. 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
   Show answer

   Answer: B

10. Q252009 · 19 Apr 2009

    If $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$ and $C=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{array}\right]$, then which one of the following is correct?

    1. A.$C=A\cos \alpha -B\sin \alpha$
    2. B.$C=A\sin \alpha +B\cos \alpha$
    3. C.$C=A\sin \alpha -B\cos \alpha$
    4. D.$C=A\cos \alpha +B\sin \alpha$
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    Answer: D

11. Q262009 · 19 Apr 2009
    
    1. A.$\frac{-1+i\sqrt{3}}{2}$
    2. B.$\frac{1-i\sqrt{3}}{2}$
    3. C.$\frac{-1-i\sqrt{3}}{2}$
    4. D.$\frac{1+i\sqrt{3}}{2}$
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    Answer: B

12. Q272009 · 19 Apr 2009

    If $\omega$ is an imaginary cube root of unity, then what is the value of the determinant of the matrix $\left[\begin{array}{ccc}1+\omega & {\omega }^2& \omega \\ 1+{\omega }^2& \omega & {\omega }^2\\ \omega +{\omega }^2& \omega & {\omega }^2\end{array}\right]$ ?

    1. A.$0$
    2. B.$-2\omega$
    3. C.$-2{\omega }^2$
    4. D.$3{\omega }^2$
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    Answer: D

13. Q372009 · 19 Apr 2009
    
    1. A.A implies B, but B does not imply A
    2. B.B implies A, but A does not imply B
    3. C.Neither A implies B nor B implies A
    4. D.A implies B as well as B implies A
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    Answer: D

14. Q382009 · 19 Apr 2009

    If $2^x+3^y=17$ and $2^{x+2}-3^{y+1}=5$, then what is the value of $x$?

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

15. Q392009 · 19 Apr 2009

    If $P(32,6)=kC(32,6)$, then what is the value of $k$?

    1. A.$6$
    2. B.$32$
    3. C.$120$
    4. D.$720$
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    Answer: D

16. Q402009 · 19 Apr 2009

    What is $(\sqrt{3}+i)/(1+\sqrt{3}i)$ equal to?

    1. A.$1+i$
    2. B.$1-i$
    3. C.$\sqrt{3}(1-i)/2$
    4. D.$(\sqrt{3}-i)/2$
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    Answer: D

17. Q502009 · 19 Apr 2009
    
    1. A.$A^{-1}$ does not exist
    2. B.$A=(-1)I$
    3. C.$A$ is a unit matrix
    4. D.$A^2=I$
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    Answer: D

18. Q512009 · 19 Apr 2009

    The formula ${\sin }^{-1}\{2x(1-x^2)\}=2{\sin }^{-1}x$ is true for all values of $x$ lying in the interval

    1. A.$[-1,1]$
    2. B.$[0,1]$
    3. C.$[-1,0]$
    4. D.$[-1/\sqrt{2},1/\sqrt{2}]$
    Show answer

    Answer: Dropped in the final answer key (full marks to everyone)

19. Q522009 · 19 Apr 2009

    What is the value of $1-\sin 10^{\circ }\sin 50^{\circ }\sin 70^{\circ }$?

    1. A.$1/8$
    2. B.$3/8$
    3. C.$5/8$
    4. D.$7/8$
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    Answer: D

20. Q532009 · 19 Apr 2009

    The sines of two angles of a triangle are equal to $5/13$ and $99/101$. What is the cosine of the third angle?

    1. A.$255/1313$
    2. B.$265/1313$
    3. C.$275/1313$
    4. D.$770/1313$
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    Answer: A

21. Q542009 · 19 Apr 2009

    After subtending an angle of $1000^{\circ }$ from its initial position, the revolving line will be situated in which one of the following quadrants?

    1. A.First quadrant
    2. B.Second quadrant
    3. C.Third quadrant
    4. D.Fourth quadrant
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    Answer: D