# UPSC NDA 2019 (2) Mathematics Question Paper

There are total 120 objective-type questions in the paper.

1. If both p and q belong to the set {1, 2, 3, 4}, then how many equations of the form px2 + qx + 1 = 0 will have real roots ?

• (a) 12
• (b) 10
• (c) 7
• (d) 6

2. What is the value of 1 - 2 + 3 - 4 + 5 - ... + 101 ?

• (a) 51
• (b) 55
• (c) 110
• (d) 111

4. If the sum of first n terms of a series is (n + 12), then what is its third term ?

• (a) 1
• (b) 2
• (c) 3
• (d) 4

10. What is the number of diagonals of an octagon ?

• (a) 48
• (b) 50
• (c) 28
• (d) 20

19. In a school, 50% students play cricket and 40% play football. If 10% of students play both the games, then what per cent of students play neither cricket nor football ?

• (a) 10%
• (b) 15%
• (c) 20%
• (d) 25%

24. How many terms are there in the expansion of (1 + 2x + x2)5 + (1+ 4y + 4y2)5 ?

• (a) 12
• (b) 20
• (c) 21
• (d) 22

27. If n! has 17 zeros, then what is the value of n?

• (a) 95
• (b) 85
• (c) 80
• (d) No such value of n exists

32. How many two-digit numbers are divisible by 4?

• (a) 21
• (b) 22
• (c) 24
• (d) 25

37. How many real roots does the equation x2 + 3|x| + 2 = 0 have ?

• (a) Zero
• (b) One
• (c) Two
• (d) Four

43. A ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60°. What is the height of the flagstaff ?

• (a) 9 m
• (b) 10.5 m
• (c) 13.5 m
• (d) 15 m

47. If the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference, then which one of the following is correct ?

• (a) The vectors are parallel
• (b) The vectors are perpendicular
• (c) The vectors are anti-parallel
• (d) The vectors must be unit vectors