# NDA/NA (2) 2018 Mathematics Paper

2. If an infinite GP has the first term x and the sum 5, then which of the following is correct?

• a. x < -10
• b. -10 < x < 0
• c. 0 < x < 10
• d. x > 10

11. What is the coefficient of the middle term in the binomial expansion of (2 + 3x)4?

• a. 6
• b. 12
• c. 108
• d. 216

16. There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?

• a. C(17, 11)
• b. C(12, 8)
• c. C(17, 5) × (5, 3)
• d. C(5, 3) × C(12, 8)

48. What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed?

• a. 2664
• b. 3882
• c. 4044
• d. 4444

89. What is the order of the differential equation whose solution is y = a cos x + b sin x + ce-x + d, where a, b, c and d are arbitrary constants?

• a. 1
• b. 2
• c. 3
• d. 4

93. A flower in the form of a sector has been fenced by a wire of 40 m length. If the flower-bed has the greatest possible area, then what is the radius of the sector?

• a. 25 m
• b. 20 m
• c. 10 m
• d. 5 m

102. The correlation coefficient computed from a set of 30 observations is 0.8. Then the percentage of variation not explained by linear regression is

• a. 80%
• b. 20%
• c. 64%
• d. 36%

103. The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and the of the group of women is 21 years, then the percentage of men and women in the group is respectively

• a. 20, 80
• b. 40, 60
• c. 60, 40
• d. 80, 20

107. 8 coins are tossed simultaneously. The probability of getting at least 6 heads is

• a. 7/64
• b. 57/64
• c. 37/256
• d. 229/256

108. Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is

• a. 13/32
• b. 9/32
• c. 3/32
• d. 1/32

110. The variance of 25 observations is 4. If 2 is added to each observation, then the new variance of the resulting observations is

• a. 2
• b. 4
• c. 6
• d. 8

120. In which one of the following cases would you except to get a negative correlation?

• a. The ages of husbands and wives
• b. Shoe size and intelligence
• c. Insurance companies profits and the number of claims they have to pay
• d. Amount of rainfall and yield of crop