# NDA/NA (1) 2018 Mathematics Paper

3. In the expansion of (1 + x)43, if the coefficients of (2r + 1)th and (r + 2)th terms are equal, then what is the value of r (r ≠ 1)?

• (a) 5
• (b) 14
• (c) 21
• (d) 22

7. How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed ?

• (a) 35
• (b) 53
• (c) 120
• (d) 60

9. If the ratio of AM to GM of two positive numbers a and b is 5 : 3, then a : b is equal to

• (a) 3 : 5
• (b) 2 : 9
• (c) 9 : 1
• (d) 5 : 3

Consider the information given below and answer the two items (02) that follow :

In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.

13. What is the number of students who are good in either Hindi or Mathematics but not in English ?

• (a) 99
• (b) 107
• (c) 125
• (d) 130

14. What is the number of students who are good in Hindi and Mathematics but not in English ?

• (a) 18
• (b) 12
• (c) 10
• (d) 8

17. The binary number expression of the decimal number 31 is

• (a) 1111
• (b) 10111
• (c) 11011
• (d) 11111

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

• (a) 6
• (b) 8
• (c) 11
• (d) 12

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

• (a) 3 x 5 matrix
• (b) 5 x 3 matrix
• (c) 3 x 2 matrix
• (d) 5 x 2 matrix

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?

• (a) 185
• (b) 175
• (c) 115
• (d) 105

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 ?

• (a) 40
• (b) 45
• (c) 50
• (d) 55

31. What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder ?

• (a) 1565
• (b) 1585
• (c) 1635
• (d) 1655

32. If 0 < a < 1, the value of log10a is negative. This is justified by

• (a) Negative power of 10 is less than 1
• (b) Negative power of 10 is between 0 and 1
• (c) Negative power of 10 is positive
• (d) Negative power of 10 is negative

33. The third term of a GP is 3. What is the product of the first five terms ?

• (a) 216
• (b) 226
• (c) 243
• (d) Cannot be determined due to insufficient data

38. What is sin 105° + cos 105° equal to ?

• (a) sin 50°
• (b) cos 50°
• (c) 1/√2
• (d) 0

43. If a flag-staff of 6 m height placed on the top of a tower throws a shadow of 2√3 m along the ground, then what is the angle that the sun makes with the ground ?

• (a) 60°
• (b) 45°
• (c) 30°
• (d) 15°

54. What is the equation of the line passing through the point of intersection of the lines x + 2y - 3 = 0 and 2x - y + 5 = 0 and parallel to the line y - x+ 10 = 0 ?

• (a) 7x - 7y + 18 = 0
• (b) 5x - 7y + 18 = 0
• (c) 5x - 5y + 18 = 0
• (d) x - y + 5 = 0