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

Total Questions: 20

11. Find the value?

Correct Answer: (b) 95
Solution:

12. The mean of the series x₁, x₂,_____xₙ is x. If xₙ is replaced by k, then what is the new mean?

Correct Answer: (d)
Solution:

13. A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?

Correct Answer: (b) 15/32
Solution:

14. Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?

Correct Answer: (b) 7/12
Solution:

15. For two events A and B, P(A) =P(A|B) = 0.25 and P(B|A) = 0.5. Which of the following are correct?

A. A and B are independent.
B. P(Aᶜ ∪ Bᶜ ) = 0.875
C. P(Aᶜ ∪ Bᶜ ) = 0.375

Select the answer using the code given below.

Correct Answer: (d) A, B and C
Solution:A and B are independent.
P(Aᶜ ∪ Bᶜ ) = 0.875
P(Aᶜ ∪ Bᶜ ) = 0.375
So, all three statements are correct, making option (d) the correct choice.

16. Two perfect dice are thrown. What is the probability that the sum of the numbers on the faces is neither 9 nor 10?

Correct Answer: (d) 29/36
Solution:n(s) = 6 × 6 = 36

Sum of the numbers on the faces 9 = (3,6), (4,5), (5,4), (6,3)

Sum of the numbers on the faces 10 : = (4,6), (5,5), (6,4)

p (sum 9 or 10 ) = 7/36

p (Sum is neither 9 nor 10) = 1 - 7/36 = 29/36

17. The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?

Correct Answer: (a) 53/3125
Solution:

18. Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?

Correct Answer: (d) 1/2
Solution:

19. Three perfect dice D₁ , D₂ and D₃ are rolled. Let x, y and z represent the numbers on D₁ , D₂ and D₃ respectively. What is the number of possible outcomes such that x < y < z?

Correct Answer: (a) 20
Solution:

20. In a binomial distribution, if the mean is 6 and the standard deviation is √2 then, what are the values of the parameters n and p respectively?

Correct Answer: (d) 9 and 2/3
Solution: