Mathematics (Solved Paper 2024 – II) (101 to 120)

Total Questions: 20

1. Let x - 3y + 4 = 0 and 2x - 7y + 8 = 0 be two lines of regression computed from some bivariate data. If If byₓ and bₓʏ are regression coefficients of lines of regression of y on x and x on y respectively, then what is the value of bₓʏ +7bʏₓ ?

Correct Answer: (d) 5
Solution:

2. The mean of n observations 1, 4, 9, 16 ,______,n² is 130. What is the value of n?

Correct Answer: (b) 19
Solution:

3. Three distinct natural numbers are chosen at random from 1 to 10. What is the probability that they are consecutive?

Correct Answer: (c) 1/15
Solution:

4. A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If 3P(B) = 4P(A) and 3P(C) = 2P(B), then what is P(A) equal to?

Correct Answer: (c) 9/29
Solution:

5. A die has two faces with number 4, three faces with number 5 and one face with number 6. If the die is rolled once, then what is the probability of getting 4 or 5?

Correct Answer: (c) 5/6
Solution:Number on faces on die are 4, 4, 5, 5, 5, 6
n(s) = 6
p(getting 4 or 5) = 5/6

6. A contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?

Correct Answer: (a) 1/6
Solution:

7. A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?

Correct Answer: (a) 1/8
Solution:

8. The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?

Correct Answer: (a) 6/35
Solution:

9. A natural number x is chosen at random from the first 100 natural numbers. What is the probability that x² + x > 50?

Correct Answer: (b) 47/50
Solution:

10. What is the mean deviation of the first 10 natural numbers?

Correct Answer: (b) 2.5
Solution: