Matrices & Determinants · NDA previous year questions

2026 9 questions

1. Q662026 · 12 Apr 2026
   
   1. A.I only
   2. B.II only
   3. C.Both I and II
   4. D.Neither I nor II
   Show answer

   Answer: C

2. Q672026 · 12 Apr 2026

   If $M^T$ is the transpose of a $2\times 2$ matrix $M$, then which of the following is/are correct ? I. $|M+M^T|=|M|+|M^T|$ if $M$ is symmetric. II. $|M+M^T|=0$ if $M$ is anti-symmetric. Select the answer using the code given below :

   1. A.I only
   2. B.II only
   3. C.Both I and II
   4. D.Neither I nor II
   Show answer

   Answer: B

3. Q682026 · 12 Apr 2026

   If $M_k=\left[\begin{array}{cc}k& k-1\\ k-1& k\end{array}\right]$ where $k$ is a natural number, then what is $|M_1|+|M_2|+|M_3|+\dots +|M_{50}|$ equal to ?

   1. A.50
   2. B.1250
   3. C.2500
   4. D.5000
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   Answer: C

4. Q692026 · 12 Apr 2026

   Consider the following statements : I. If $n\times n$ ($n>1$) matrix is symmetric, then its inverse is also a symmetric matrix. II. If $n\times n$ ($n>1$) matrix is singular, then its adjoint is also a singular matrix. Which of the statements given above is/are correct ?

   1. A.I only
   2. B.II only
   3. C.Both I and II
   4. D.Neither I nor II
   Show answer

   Answer: C

5. Q702026 · 12 Apr 2026

   Let $p=(x+y+z)$ and $q=xyz$. If $\left|\begin{array}{ccc}x& 1& 1\\ 1& y& 1\\ 1& 1& z\end{array}\right|$ is positive, then which one of the following is correct ?

   1. A.$q>p$
   2. B.$q+1>p$
   3. C.$q+2>p$
   4. D.$q+2\ge p$
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   Answer: C, D

6. Q712026 · 12 Apr 2026
   
   1. A.8
   2. B.64
   3. C.256
   4. D.512
   Show answer

   Answer: D

7. Q722026 · 12 Apr 2026
   
   1. A.I only
   2. B.II only
   3. C.Both I and II
   4. D.Neither I nor II
   Show answer

   Answer: D

8. Q732026 · 12 Apr 2026
   
   1. A.$-1$
   2. B.0
   3. C.$\frac{1}{2}$
   4. D.1
   Show answer

   Answer: B

9. Q742026 · 12 Apr 2026
   
   1. A.$-1$
   2. B.0
   3. C.1
   4. D.$q$
   Show answer

   Answer: B