1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let $A$ and $B$ be matrices of order $3 \times 3$. If $|A| = \frac{1}{2 \sqrt{2}}$ and $|B| = \frac{1}{729}$, then what is the value of $|2B(adj(3A))|$?

A

27

B

$\frac{-27}{2\sqrt{2}}$

C

$\frac{27}{2}$

D

1

2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following statements in respect of two non-singular matrices $A$ and $B$ of the same order $n$:

  1. 1.$adj(AB) = (adjA)(adjB)$

  2. 2. $adj(AB) = adj(BA)$

  3. 3. $(AB) adj(AB) - |AB| I_n$ is a null matrix of order $n$

How many of the above statements are correct?
A

None

B

Only one statement

C

Only two statements

D

All three statements

3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following statements in respect of a non-singular matrix $A$ of order $n$:

1. $A(\text{adj}A^T) = A(\text{adj}A)^T$

2. If $A^2 = A$, then $A$ is identity matrix of order $n$

3. If $A^3 = A$, then $A$ is identity matrix of order $n$

Which of the statements given above are correct?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2 and 3

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following statements in respect of a skew-symmetric matrix $A$ of order $3$:

1. All diagonal elements are zero.

2. The sum of all the diagonal elements of the matrix is zero.

3. $A$ is orthogonal matrix.

Which of the statements given above are correct?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2 and 3

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