Mathematics (NDA/NA SOLVED PAPER 2022-II) (01 to 50)

Total Questions: 50

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

Correct Answer: (a) 625
Solution:

2. equal to?

Correct Answer: (b) 3ⁿ
Solution:

3. If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there.in the list before the first word that starts with C?

Correct Answer: (c) 907200
Solution:

4. Consider the following statements:

1. If f is the subset of Z × Z defined by f = {(xy, x - y); x, y € Z } , then f is a function from Z to Z.
2. If f is the subset of N × N defined by f= {(xy, x + y); x, y € N}, then f is a function from N to N.
Which of the statements given above is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:

5. Consider the determinant

If  a₁₃ = yz, a₂₃ = zx, a₃₃ = xy and the minors of a₁₃, a₂₃, a₃₃ are respectively (z - y), (z - x), (y - x) then what is the value of  Δ?

Correct Answer: (a) (z - y) (z - x) (y - x)
Solution:(a)

6. Find the value?

1. A + adj A is a null matrix
2. A⁻¹ + adjA is a null matrix
3. A - A⁻¹ is a null matrix
Select the correct answer using the code given below :

Correct Answer: (d) 1, 2 and 3
Solution:(d)

7. If X is a matrix of order 3 × 3 Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2 , then which of the following are correct?

1. (ZY) X is a square matrix having 9 entries.
2. Y(XZ) is a square matrix having 4 entries..
3. X(YZ) is not defined.
Select the correct answer using the code given below!

Correct Answer: (d) 1, 2 and 3
Solution:

8. For how many quadratic equations, the sum of equal to the product of roots?

Correct Answer: (d) Infinitely many
Solution:

9. Consider the following statements:

1. The set of all irrational numbers between √2 a is an infinite set.
2. The set of all odd integers less than 100 is a finite
Which of the statements given above is/are correct?

Correct Answer: (a) 1 only
Solution:

10. Consider the following statements:

1. 2 + 4 + 6 +____+ 2n = n² + n
2. The expression n² + n + 41 always gives a prime number for every natural number n
Which of the above statements is/are correct?

Correct Answer: (a) 1 only
Solution: