Mathematics (NDA/NA SOLVED PAPER 2023-I) (01 to 50)

Total Questions: 50

1. If ω is a non-real cube root of 1, then what is the value of

Correct Answer: (a) √3
Solution:

2. What is the number of 6 digit numbers that formed only by using 0, 1, 2, 3, 4 and 5 (each once); and divisible by 6?

Correct Answer: (d) 312
Solution:Number of numbers = 4! x 4 × 2 = 192
Total numbers = 120 + 192 = 312.

3. What is the binary number equivalent to decimal number 1011?

Correct Answer: (b) 111011
Solution:

4. Find the value?

Correct Answer: (b) 13
Solution:

5. Find the value?

Correct Answer: (d) 1/√3
Solution:

6. Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB-BA)?

1. Its diagonal entries are equal but non-zero
2. The sum of its non-diagonal entries is zero
Select the correct answer using the code given below:

Correct Answer: (b) 2 only
Solution:

For symmetric matrices, A'=A, B'= B
(AB- BA)'= BA - AB = — (АB - ВА)
⇒ (AB - BA) is a skew symmetric matrix
⇒ (AB - BA) matrix have all diagonal element as zero
(statement 1 is incorrect)
Sum of all non diagonal elements in (AB - BA) = 0
... Only 2 is correct.

7. Consider the following statements in respect of square matrices A, B, C each of same order n:

1. AB = AC ⇒ B = C if A is non-singular
2. If BX = CX for every column matrix X having n rows then B = C
Which of the statement given above is/are correct?

Correct Answer: (a) 1 only
Solution:

8. The system of linear equations x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has

Correct Answer: (c) no solution
Solution:

9. Let AX = B be a system of 3 liner equations with 3-unknowns. Let X₁ and X₂ be its two distinct solutions. If the combination aX₁ + bX₂ is a solution of AX = B where a, b, are real numbers, then which one of the following is correct?

Correct Answer: (b) a + b = 1
Solution:

10. What is the sum of the roots of the equation

Correct Answer: (b) a - b + c
Solution: