MCQ
Calendar, clock and cube problems MCQ - Practice Questions with Answers
Solve 10 Calendar, clock and cube problems questions for RAS/RPSC preparation.
Practice questions
Q1Which one of the following statements is incorrect for cube-net and dice-view questions?
The incorrect statement is that every dice question must use the opposite-face sum of 7. Not to assume this rule unless the question states that a conventional dice rule is being used. In view-based reasoning, faces seen together are adjacent, and a common face across two views can be used to rotate mentally and infer opposites. Opposite faces on a cube also never share an edge. So the forced assumption of a sum of 7 is the only unsupported rule here.
Q2Consider the following statements. Statement 1: If a day is 15 days after Monday, the weekday moves forward by 1 day. Statement 2: If a day is the 15th day from Monday, with Monday counted as day 1, the weekday is Monday again. Which of the above statements is/are correct?
Elapsed wording is distinct from count-based wording. 'After 15 days' means add 15 odd days to Monday. Since 15 mod 7 = 1, the weekday moves one day forward, to Tuesday. But 'the 15th day from Monday' usually counts Monday as day 1, so only 14 days of movement are made. Since 14 is a complete multiple of 7, the weekday returns to Monday. Thus both statements are correct, but they are correct for different counting conventions.
Q3Which statement correctly applies the leap-year rule used in calendar questions?
There is a two-step leap-year rule. A non-century year divisible by 4 is a leap year, so a year such as 2024 qualifies. Century years need a stricter test: they must be divisible by 400. That is why 2000 was leap but 1900 was not. This distinction matters because a leap year contributes 2 odd days, while an ordinary year contributes only 1 odd day. Treating every century year divisible by 100 as leap would shift the weekday by one day in many calendar problems.
Q4A cube is painted on all its faces and cut into 5 equal parts along each edge. Match List I with List II. List I: 1. Cubes with 3 painted faces 2. Cubes with 2 painted faces 3. Cubes with 1 painted face 4. Cubes with no painted face List II: a. 54 b. 8 c. 27 d. 36
For a cube painted on all faces and cut into n parts along each edge, There are fixed count rules. With n = 5, three-face cubes are the 8 corners. Two-face cubes are 12(n - 2) = 12 x 3 = 36. One-face cubes are 6(n - 2)^2 = 6 x 9 = 54. Unpainted internal cubes are (n - 2)^3 = 3^3 = 27. Therefore the matching is 3 painted faces with 8, 2 painted faces with 36, 1 painted face with 54, and no painted face with 27.
Q5Assertion (A): Both 1900 and 2000 were leap years in the Gregorian calendar. Reason (R): A century year is a leap year only when it is divisible by 400.
Century years are the common leap-year trap. A non-century year divisible by 4 is a leap year, but a century year must be divisible by 400. The year 2000 was divisible by 400, so it was a leap year. The year 1900 was a century year but was not divisible by 400, so it was not a leap year. Therefore, the assertion that both 1900 and 2000 were leap years is false, while the stated reason is true.
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More questions
6Match the calendar item with the odd days it contributes. List I: 1. Ordinary year 2. Leap year 3. January in an ordinary year 4. February in an ordinary year List II: a. 2 odd days b. 3 odd days c. 1 odd day d. 0 odd days
7What is the smaller angle between the hour hand and the minute hand at 13:20?
8A cube is painted on all faces and cut into 5 equal parts along each edge. How many smaller cubes will have no painted face?
9At 2:30, what is the smaller angle between the hour hand and the minute hand of a clock?
10Assertion (A): The mirror image of 4:25 on a 12-hour clock is 7:35. Reason (R): For a mirror-image clock, the practical rule is to subtract the actual time from 11:60.