Matrices & Determinants · NDA previous year questions

2014 19 questions

1. Q172014 · 28 Sept 2014

   Let A and B be two matrices such that AB = A and BA = B. Which of the following statements are correct ? 1. $A^2=A$ 2. $B^2=B$ 3. $(AB{)}^2=AB$ Select the correct answer using the code given below :

   1. A.1 and 2 only
   2. B.2 and 3 only
   3. C.1 and 3 only
   4. D.1, 2 and 3
   Show answer

   Answer: D

2. Q182014 · 28 Sept 2014

   If the matrix A is such that $\left(\begin{array}{cc}1& 3\\ 0& 1\end{array}\right)A=\left(\begin{array}{cc}1& 1\\ 0& -1\end{array}\right)$, then what is A equal to ?

   1. A.$\left(\begin{array}{cc}1& 4\\ 0& -1\end{array}\right)$
   2. B.$\left(\begin{array}{cc}1& 4\\ 0& 1\end{array}\right)$
   3. C.$\left(\begin{array}{cc}-1& 4\\ 0& -1\end{array}\right)$
   4. D.$\left(\begin{array}{cc}1& -4\\ 0& -1\end{array}\right)$
   Show answer

   Answer: A

3. Q192014 · 28 Sept 2014

   From the matrix equation AB = AC, where A, B, C are the square matrices of same order, we can conclude B = C provided

   1. A.A is non-singular.
   2. B.A is singular.
   3. C.A is symmetric.
   4. D.A is skew symmetric.
   Show answer

   Answer: A

4. Q212014 · 28 Sept 2014

   If A and B are square matrices of second order such that $|A|=-1,|B|=3$, then what is $|3AB|$ equal to ?

   1. A.3
   2. B.-9
   3. C.-27
   4. D.None of the above
   Show answer

   Answer: C

5. Q222014 · 28 Sept 2014

   If $a\ne b\ne c$ are all positive, then the value of the determinant $\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|$ is

   1. A.non-negative
   2. B.non-positive
   3. C.negative
   4. D.positive
   Show answer

   Answer: C

6. Q232014 · 28 Sept 2014

   If $\left|\begin{array}{ccc}6i& -3i& 1\\ 4& 3i& -1\\ 20& 3& i\end{array}\right|=x+iy$, where $i=\sqrt{-1}$, then what is x equal to ?

   1. A.3
   2. B.2
   3. C.1
   4. D.0
   Show answer

   Answer: D

7. Q242014 · 28 Sept 2014

   Consider the following statements : 1. Determinant is a square matrix. 2. Determinant is a number associated with a square matrix. 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

8. Q252014 · 28 Sept 2014

   If A is an invertible matrix, then what is $\det (A^{-1})$ equal to ?

   1. A.$\det A$
   2. B.$\frac{1}{\det A}$
   3. C.1
   4. D.None of the above
   Show answer

   Answer: B

9. Q262014 · 28 Sept 2014

   If $\left|\begin{array}{ccc}a& b& 0\\ 0& a& b\\ b& 0& a\end{array}\right|=0$, then which one of the following is correct ?

   1. A.$\frac{a}{b}$ is one of the cube roots of unity.
   2. B.$\frac{a}{b}$ is one of the cube roots of $-1$.
   3. C.a is one of the cube roots of unity.
   4. D.b is one of the cube roots of unity.
   Show answer

   Answer: B

10. Q272014 · 28 Sept 2014

    What is $\sqrt{1+\sin 2\theta }$ equal to ?

    1. A.$\cos \theta -\sin \theta$
    2. B.$\cos \theta +\sin \theta$
    3. C.$2\cos \theta +\sin \theta$
    4. D.$\cos \theta +2\sin \theta$
    Show answer

    Answer: B

11. Q282014 · 28 Sept 2014

    If $\cot A=2$ and $\cot B=3$, then what is the value of $A+B$ ?

    1. A.$\pi /6$
    2. B.$\pi$
    3. C.$\pi /2$
    4. D.$\pi /4$
    Show answer

    Answer: D

12. Q292014 · 28 Sept 2014

    What is ${\sin }^{2}66{\frac{1}{2}}^{\circ }-{\sin }^{2}23{\frac{1}{2}}^{\circ }$ equal to ?

    1. A.$\sin 47^{\circ }$
    2. B.$\cos 47^{\circ }$
    3. C.$2\sin 47^{\circ }$
    4. D.$2\cos 47^{\circ }$
    Show answer

    Answer: B

13. Q302014 · 28 Sept 2014

    What is $\frac{\cos 7x-\cos 3x}{\sin 7x-2\sin 5x+\sin 3x}$ equal to ?

    1. A.$\tan x$
    2. B.$\cot x$
    3. C.$\tan 2x$
    4. D.$\cot 2x$
    Show answer

    Answer: B

14. Q232014 · 20 Apr 2014

    Consider the following statements in respect of the matrix $A=\left[\begin{array}{ccc}-1& 0& -3\\ -2& 3& 0\end{array}\right]$: 1. The matrix $A$ is skew-symmetric. 2. The matrix $A$ is symmetric. 3. The matrix $A$ is invertible. Which of the above statements is/are correct?

    1. A.1 only
    2. B.3 only
    3. C.1 and 3
    4. D.2 and 3
    Show answer

    Answer: A

15. Q242014 · 20 Apr 2014

    Consider two matrices $A=\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 2& -4\\ 2& 1& -4\end{array}\right]$. Which one of the following is correct?

    1. A.$B$ is the right inverse of $A$
    2. B.$B$ is the left inverse of $A$
    3. C.$B$ is the both sided inverse of $A$
    4. D.None of the above
    Show answer

    Answer: B

16. Q252014 · 20 Apr 2014

    If $A$ is any matrix, then the product $AA$ is defined only when $A$ is a matrix of order $m\times n$ where:

    1. A.$m>n$
    2. B.$m<n$
    3. C.$m=n$
    4. D.$m\le n$
    Show answer

    Answer: C

17. Q262014 · 20 Apr 2014

    One of the roots of $$\left|\begin{array}{ccc}x+a& b& c\\ a& x+b& c\\ a& b& x+c\end{array}\right|=0$$ is:

    1. A.$abc$
    2. B.$a+b+c$
    3. C.$-(a+b+c)$
    4. D.$-abc$
    Show answer

    Answer: C

18. Q272014 · 20 Apr 2014

    The determinant of an odd order skew symmetric matrix is always:

    1. A.Zero
    2. B.One
    3. C.Negative
    4. D.Depends on the matrix
    Show answer

    Answer: A

19. Q282014 · 20 Apr 2014

    If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant:

    1. A.Becomes zero
    2. B.Remains the same
    3. C.Changes its sign
    4. D.Is doubled
    Show answer

    Answer: C