NDA/NA SOLVED PAPER 2015-I (MATHEMATICS)

Total Questions: 120

21. In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is

Correct Answer: (b) 40
Solution:

22. If log₁₀ 2 log₁₀ (2ˣ - 1) and log₁₀ (2ˣ + 3) are three consecutive terms of an A.P, then the value of x is

Correct Answer: (c) log₂ 5
Solution:


23. Solve the following equation

Correct Answer: (d) skew-Hermitian
Solution:


24. Let Z be the set of integers and aRb, where a, b ∈ Z if and only if (a - b) is divisible by 5.

Consider the following statements:
1. The relation R partitions Z into five equivalent classes.
2. Any two equivalent classes are either equal or disjoint.

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2

25. Solve the following equation

Correct Answer: (d) - 3π/4
Solution:


26. If m and n are the roots of the equation (x + p)(x + q) - k = 0, then the roots of the equation (x - m)(x - n) + k = 0 are

Correct Answer: (c) -p and -9
Solution:

27. What is the sum of the series 0.5 + 0.55 + 0.555 +... to n terms?

Correct Answer: (d)
Solution:


28. If 1, ω , ω² are the cube roots of unity, then the value of (1 + omega) (1 + ω²) (1 + ω⁴) (1 + ω⁸) is

Correct Answer: (c) 1
Solution:

29. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Then the number of subsets of A containing exactly two elements is

Correct Answer: (c) 45
Solution:

30. What is the square root of i, where i = √-1 ?

Correct Answer: (c) (1 + i)/√2
Solution: