Mathematics NDA/NA SOLVED PAPER 2018 (I) (01 to 50)

Total Questions: 50

21. What is the number of non-zero terms in the expansion of (1 + 2√3x)¹¹ + (1 - 2√3x)¹¹ (after simplification)?

Correct Answer: (c) 6
Solution:

22. What is the greatest integer among the following, by which the number 5⁵ + 7⁵ is divisible?

Correct Answer: (d) 12
Solution:

We know that when m is odd then (Xᵐ + Yᵐ) is divisible by (X + Y).
∴ 5⁵ + 7⁵ is divisible by 5 + 7 = 12 as m = 5 is odd.

23. If x = 1 - y + y² - y³....... up to infinite terms, where |y| < 1, then which one of the following is correct?

Correct Answer: (a)
Solution:

24. Find the answer of given equation?

Correct Answer: (a)
Solution:

25. If A is a 2 × 3 matrix and AB is a 2 × 5 matrix, then B must be a:

Correct Answer: (a) 3 × 5 matrix
Solution:

26. Simplify the equation?

Correct Answer: (a) 4
Solution:

27. What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line?

Correct Answer: (a) 185
Solution:

28. What is C(n, r) + 2C(n, r - 1) + C(n, r - 2) equal to?

Correct Answer: (d) C (n + 2, r)
Solution:

29. Let |x| denote the greatest integer function. What is the number of solutions of the equation x²− 4x + [x] = 0 in the interval [0, 2]?

Correct Answer: (b) One
Solution:

30. A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?

Correct Answer: (b) 45
Solution: