Q1: A speaks the truth 6 out of 9 times, and B speaks the truth 3 out of 6 times. What is the probability that they contradict each other?
- A) 4/5
- B) 1/2
- C) 2/3
- D) None of these
Correct Answer: Option B
Total probability of contradiction is \( \frac{1}{2} \) after considering the cases where A and B tell the truth or lie.
Q2: A mixture contains 3/4 milk, and the final mixture contains equal parts milk and water. What fraction of the mixture was replaced?
- A) 4/5
- B) 1/3
- C) 2/3
- D) None of these
Correct Answer: Option D
After setting up the equations, the fraction of the mixture replaced is \( \frac{1}{3} \).
Q3: A and B complete a task in 2 days, B and C in 4 days, and C and A in 2 days. How many days will A take to complete it alone?
- A) 5
- B) 4
- C) 3
- D) 2
Correct Answer: Option C
After solving the equations, A alone will take 3 days to complete the task.
Q4: A and B have bags containing Rs. 1 coins. After losing 5 coins each, the product of the remaining coins is 124. What was the initial product of the coins in both bags?
- A) 324
- B) 350
- C) 86
- D) 500
Correct Answer: Option A
By solving the quadratic equation, the initial product of the coins is found to be 324.
Q5: In how many ways can 7 chocolates be distributed among A, B, and C such that at least one of them gets exactly 1 chocolate?
- A) 1148
- B) 1356
- C) 1218
- D) None of these
Correct Answer: Option C
Using the inclusion-exclusion principle, the total ways are 1218.
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