# UPSC NDA 2019 (1) Mathematics Question Paper

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

1. What is the nth term of the sequence 25, -125, 625, -3125, ...?

• (a) (-5)2n-1
• (b) (-1)2n (5)n+1
• (c) (-1)2n-1 (5)n+1
• (d) (-1)n-1 (5)n+1

8. What are the roots of the equation |x2 - x - 6| = x + 2?

• (a) -2, 1, 4
• (b) 0, 2, 4
• (c) 0, 1, 4
• (d) - 2, 2, 4

13. There are 10 points in a plane. No three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points ?

• (a) 90
• (b) 45
• (c) 40
• (d) 30

Consider the following for the next 02 (two) items that follow:

In a school, all the students play at least one of three indoor games - chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.

16. What can be the minimum number of students in the school?

• (a) 123
• (b) 111
• (c) 95
• (d) 63

17. What can be the maximum number of students in the school ?

• (a) 111
• (b) 123
• (c) 125
• (d) 135

19. A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose ?

• (a) 64
• (b) 36
• (c) 32
• (d) 4

20. From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist ?

• (a) 209
• (b) 210
• (c) 246
• (d) 242

23. The numbers 1, 5 and 25 can be three terms (not necessarily consecutive) of

• (a) only one AP
• (b) more than one but finite numbers of APs
• (c) infinite number of APs
• (d) finite number of GPs

46. If the roots of the equation x2 + px + q = 0 are tan 19° and tan 26°, then which one of the following is correct?

• (a) q - p = 1
• (b) p - q = 1
• (c) p + q = 2
• (d) p + q = 3

47. What is the fourth term of an AP of n terms whose sum is n(n+1)?

• (a) 6
• (b) 8
• (c) 12
• (d) 20

50. If the angles of a triangle ABC are in the ratio 1 : 2 : 3, then the corresponding sides are in the ratio

• (a) 1 : 2 : 3
• (b) 3 : 2 : 1
• (c) 1 : √3 : 2
• (d) 1 : √3 : √2

53. The sum of the focal distances of a point on an ellipse is constant and equal to the

• (a) length of minor axis
• (b) length of major axis
• (c) length of latus rectum
• (d) sum of the lengths of semi-major and semi-minor axes

54. The equation 2x2 - 3y2 - 6 = 0 represents

• (a) a circle
• (b) a parabola
• (c) an ellipse
• (d) a hyperbola

56. The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c. What is the value of c?

• (a) 2
• (b) -2
• (c) 4
• (d) -4