Mathematics (NDA/NA SOLVED PAPER 2021-I) (101 to 120)Total Questions: 2011. For which of the following sets of numbers do the mean, median and mode have the same value?(a) 12, 12, 12, 12, 24(b) 6, 18, 18, 18, 30(c) 6, 6, 12, 30, 36(d) 6, 6, 6,12,30Correct Answer: (b) 6, 18, 18, 18, 30Solution:For set of numbers : 6, 18, 18, 18, 30 Mean = 18, Median = 18, Mode = 18.12. The mean of 12 observations is 75. If two observations are discarded, then the mean of the remaining observations is 65. What is the mean of the discarded observations?(a) 250(b) 125(c) 120(d) Cannot be determined due to insufficient dataCorrect Answer: (b) 125Solution:13. If k is one of the roots of the equation x (x + 1) + 1 = 0, then what is its other root?(a) 1(b) -k(c) k²(d) -k²Correct Answer: (c) k²Solution:14. The geometric mean of a set of observations is computed as 10. The geometric mean obtained when each observation xᵢ is replaced by 3xᵢ⁴ is(a) 810(b) 900(c) 30000(d) 81000Correct Answer: (c) 30000Solution:15. Find the value?1. A and B are independent events. 2. A and B are mutually exclusive events. Select the correct answer using the code given below.(a) 1 only(b) 2 only(c) Both 1 and 2(d) Neither 1 nor 2Correct Answer: (a) 1 onlySolution:16. The average of a set of 15 observations is recorded, but later it is found that for one observation, the digit in the tens place was wrongly recorded as 8 instead of 3. After correcting the observation, the average is(a) reduced by 1/3(b) increased by 10/3(c) reduced by 10/3(d) reduced by 50Correct Answer: (c) reduced by 10/3Solution:17. A coin is tossed twice. If E and F denote occurrence of head on first toss and second toss respectively, then what is P( E ∪ F) equal to?(a) 1/4(b) 1/2(c) 3/4(d) 1/3Correct Answer: (c) 3/4Solution:18. In a binomial distribution, the mean is 2/3 and variance is 5/9. What is the probability that random variable X = 2?(a) 5/36(b) 25/36(c) 25/54(d) 25/216Correct Answer: (d) 25/216Solution:19. If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?(a) 10(b) 12(c) 13(d) 15Correct Answer: (d) 15Solution:Mode = Data with highest frequency as mode is 15, so x = 15.20. If A and B are two events such that P(A) = 3/4 and P(B) = 5/8, then consider the following statements:1. The minimum value of P( A ∪ B) is 3/4. 2. The maximum value of P( A ∩ B) is 5/8. Which of the above statements is/are correct?(a) 1 only(b) 2 only(c) Both 1 and 2(d) Neither 1 nor 2Correct Answer: (c) Both 1 and 2Solution:Submit Quiz« Previous12