NDA II 2024 Maths Question Paper (01-Sep-2024)

Question 1

Let X be a matrix of order $3 	imes 3$, Y be a matrix of order $2 	imes 3$ and Z be a matrix of order $3 	imes 2$. Which of the following statements are correct?I. (ZY)X is defined and is a square matrix of order 3.II. Y(XZ) is defined and is a square matrix of order 2.III. X(YZ) is not defined.Select the answer using the code given below.

Accepted Answer

I, II and III

Answer

I and II only

Answer

II and III only

Answer

I and III only

Question 2

Consider the following statements :I. The set of all irrational numbers between $\sqrt{12}$ and $\sqrt{15}$ is an infinite set.II. The set of all odd integers less than 1000 is a finite set.Which of the statements given above is/are correct?

Accepted Answer

I only

Answer

II only

Answer

Both I and II

Answer

Neither I nor II

Question 3

How many 4-digit numbers are there having all digits as odd?

Accepted Answer

625

Answer

400

Answer

196

Answer

120

Question 4

If $\omega 
eq 1$ is a cube root of unity, then what is $(1 + \omega - \omega^2)^{100} + (1 - \omega + \omega^2)^{100}$ equal to?

Accepted Answer

$-2^{100}$

Answer

$2^{100} \omega^2$

Answer

$2^{100} \omega$

Answer

$2^{100}$

Question 5

Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?

Accepted Answer

B is a null matrix if A is a non-singular matrix

Answer

Both A and B are null matrices

Answer

Either A or B is a null matrix

Answer

Both A and B are singular matrices

NDA II 2024 Maths Question Paper (01-Sep-2024)

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