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

If $26! = n8^k$, where $k$ and $n$ are positive integers, then what is the maximum value of $k$?

A

$6$

B

$7$

C

$8$

D

$9$

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

How many four-digit natural numbers are there such that all of the digits are even?

A

625

B

500

C

400

D

256

EXAM MAP