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

If $\omega \neq 1$ is a cube root of unity, then what are the solutions of $(z-100)^3 + 1000 = 0$?

A

$10(1-\omega)$, $10(10-\omega^2)$, $100$

B

$10(10-\omega)$, $10(10-\omega^2)$, $90$

C

$10(1-\omega)$, $10(10-\omega^2)$, $1000$

D

$(1 + \omega)$, $(10 + \omega^2)$, $-1$

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

What is $(1 + i)^4 + (1 - i)^4$ equal to, where $i=\sqrt{-1}$?

A

4

B

0

C

-4

D

-8

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

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

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

Four digit numbers are formed by using the digits 1, 2, 3, 5 without repetition of digits. How many of them are divisible by 4?

A

120

B

24

C

12

D

6

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