20 questionswith explanationsfor RAS, Patwari, VDO and other Rajasthan exams
On which day of the week did 26 January 1950, the day the Constitution of India came into force, fall?
Answer: (2) Thursday
Explanation
Odd days up to 31 December 1949 = 1 (1900 years) + 61 (49 years with 12 leap years) → 6; adding 26 days of January gives 4 odd days, i.e. Thursday.
Rajasthan Day is celebrated on 30 March because the Greater Rajasthan Union was formed on 30 March 1949. On which day of the week did 30 March 1949 fall?
Answer: (3) Wednesday
Explanation
Odd days up to 31 December 1948 = 1 (1900 years) + 60 (48 years with 12 leap years) → 5; 1 January to 30 March 1949 adds 89 days → 5; total 3 odd days, i.e. Wednesday.
How many odd days are there in 300 years?
Answer: (1) 1
Explanation
100 years have 5 odd days, so 300 years have 15 odd days, which leave 15 − 14 = 1 odd day.
The calendar of the year 2026 will be exactly repeated in which year?
Answer: (1) 2037
Explanation
Counting odd days from 2026 (1 each for the 8 ordinary years and 2 each for 2028, 2032 and 2036) the total reaches 14, a multiple of 7, at the start of 2037, which is also a non-leap year.
Which is the next year that will have exactly the same calendar as the leap year 2024?
Answer: (4) 2052
Explanation
A leap-year calendar repeats only in a leap year starting on the same day; 2024 began on Monday and the next leap year beginning on Monday is 2052 (28 years later).
26 January 2026 was a Monday. On which day of the week will 26 January 2030 fall?
Answer: (2) Saturday
Explanation
The 4 years between the dates include 29 February 2028, giving 1 + 1 + 2 + 1 = 5 odd days; Monday + 5 = Saturday.
Under the Gregorian calendar, the last day of a century (for example, 31 December 2000) cannot be a:
Answer: (3) Tuesday
Explanation
100, 200, 300 and 400 years have 5, 3, 1 and 0 odd days, so a century can end only on Friday, Wednesday, Monday or Sunday — never on Tuesday, Thursday or Saturday.
The first day of a 31-day month is a Saturday. On which date does the last Monday of that month fall?
Answer: (1) 31st
Explanation
If the 1st is Saturday, the 3rd is Monday, so Mondays fall on 3, 10, 17, 24 and 31.
Consider the following statements: 1. The year 2100 will be a leap year. 2. The calendar of 2001 was exactly repeated in 2007. Which of the statements given above is/are correct?
Answer: (2) 2 only
Explanation
A century year is a leap year only if divisible by 400, so 2100 is not; 2001 and 2007 are both non-leap years that began on Monday.
What is the smaller angle between the hour hand and the minute hand of a clock at 2:45?
Answer: (4) 172.5°
Explanation
Angle = |30 × 2 − 5.5 × 45| = |60 − 247.5| = 187.5°, so the smaller angle is 360° − 187.5° = 172.5°.
At what time between 4 o'clock and 5 o'clock will the hour hand and the minute hand of a clock coincide?
Answer: (2) 21 9/11 minutes past 4
Explanation
At 4:00 the minute hand is 120° behind; it gains 5.5° per minute, so it catches up in 120/5.5 = 21 9/11 minutes.
At what time between 2 o'clock and 3 o'clock will the hour hand and the minute hand of a clock point in exactly opposite directions?
Answer: (3) 43 7/11 minutes past 2
Explanation
The minute hand must gain 60° + 180° = 240° on the hour hand at 5.5° per minute: 240/5.5 = 43 7/11 minutes.
How many times are the hour hand and the minute hand of a clock at right angles to each other in 12 hours?
Answer: (1) 22
Explanation
The hands are at right angles twice in every hour except between 2 and 4 and between 8 and 10, where 3 o'clock and 9 o'clock are shared, giving 24 − 2 = 22 times.
A clock loses 6 minutes every hour. It is set right at 12 noon. What is the correct time when this clock shows 6 p.m. on the same day?
Answer: (4) 6:40 p.m.
Explanation
The clock shows 54 minutes for every 60 true minutes, so 6 hours (360 minutes) shown = 360 × 60/54 = 400 minutes = 6 h 40 min of true time.
A watch that gains time uniformly is 3 minutes slow at 8 a.m. on a Monday and 5 minutes fast at 8 a.m. on the following Monday. When did it show the correct time?
Answer: (2) Wednesday 11 p.m.
Explanation
It gains 8 minutes in 168 hours, so it gains the 3 minutes needed in 168 × 3/8 = 63 hours; Monday 8 a.m. + 63 hours = Wednesday 11 p.m.
A clock shows the time 8:25. What time will its image in a plane mirror (placed vertically beside the clock) appear to show?
Answer: (3) 3:35
Explanation
Mirror time = 11:60 − 8:25 = 3:35.
In a school in Jaipur, each of 120 students was asked about cricket and kabaddi. 72 students like cricket, 54 like kabaddi and 18 like neither game. How many students like both games?
Answer: (4) 24 students
Explanation
At least one game: 120 − 18 = 102; both = 72 + 54 − 102 = 24.
In a survey of 200 families, 90 read newspaper P, 80 read newspaper Q and 70 read newspaper R. 30 read both P and Q, 25 read both Q and R, 20 read both P and R, and 10 read all three. How many families read exactly one of the three newspapers?
Answer: (2) 120
Explanation
Only P = 90 − 30 − 20 + 10 = 50, only Q = 80 − 30 − 25 + 10 = 35, only R = 70 − 20 − 25 + 10 = 35; total = 120.
In a class of 60 students, 45 passed in Hindi and 38 passed in Mathematics. What is the minimum possible number of students who passed in both subjects?
Answer: (3) 23
Explanation
Since the union cannot exceed 60, both ≥ 45 + 38 − 60 = 23, and 23 is achieved when every student passes at least one subject.
Match List-I (time shown by a clock) with List-II (smaller angle between the hour and minute hands): List-I: A. 3:40 B. 6:30 C. 9:10 D. 12:24 List-II: 1. 15° 2. 130° 3. 132° 4. 145°
Answer: (4) A-2, B-1, C-4, D-3
Explanation
Using |30H − 5.5M|: 3:40 → 130°, 6:30 → 15°, 9:10 → 215° i.e. 145°, 12:24 → 132°.