UPSC Insta–DART (Daily Aptitude and Reasoning Test) 17 Dec 2024
Kartavya Desk Staff
Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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• Question 1 of 5 1. Question The minute hand of a faulty clock overtakes the hour hand at intervals of 63 minutes of correct time. How many minutes in a day does the clock lose or gain? a) 58(4/71) min b) 54(6/81) min c) 55(7/70) min d) 56(8/77) min Correct Answer: D Explanation In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min. To be together again, the minute hand must gain 60 min over the hour hand. 60 min are gained in (60/55) × 60 = 65(5/11) min But they are together after 63 min. So, gain in 63 min = 65 (5/11) – 63 = 2(5/11) = (27/11) min. So, gain in 24 hrs = [27/(11 × 63)] × 60 × 24 = 56(8/77) min. Incorrect Answer: D Explanation In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min. To be together again, the minute hand must gain 60 min over the hour hand. 60 min are gained in (60/55) × 60 = 65(5/11) min But they are together after 63 min. So, gain in 63 min = 65 (5/11) – 63 = 2(5/11) = (27/11) min. So, gain in 24 hrs = [27/(11 × 63)] × 60 × 24 = 56(8/77) min.
#### 1. Question
The minute hand of a faulty clock overtakes the hour hand at intervals of 63 minutes of correct time. How many minutes in a day does the clock lose or gain?
• a) 58(4/71) min
• b) 54(6/81) min
• c) 55(7/70) min
• d) 56(8/77) min
Explanation
In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min.
To be together again, the minute hand must gain 60 min over the hour hand.
60 min are gained in (60/55) × 60 = 65(5/11) min
But they are together after 63 min.
So, gain in 63 min = 65 (5/11) – 63 = 2(5/11) = (27/11) min.
So, gain in 24 hrs = [27/(11 × 63)] × 60 × 24 = 56(8/77) min.
Explanation
In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min.
To be together again, the minute hand must gain 60 min over the hour hand.
60 min are gained in (60/55) × 60 = 65(5/11) min
But they are together after 63 min.
So, gain in 63 min = 65 (5/11) – 63 = 2(5/11) = (27/11) min.
So, gain in 24 hrs = [27/(11 × 63)] × 60 × 24 = 56(8/77) min.
• Question 2 of 5 2. Question The time in a clock is 20 minute past 2. Find the angle between the hands of the clock. a) 60 degrees b) 50 degrees c) 45 degrees d) 120 degrees Correct Answer: B Explanation Time is 2:20. Position of the hands: Hour hand at 2 (nearly). Minute hand at 4 Angle between 2 and 4 is 60 degrees. Angular distance travelled by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute. Therefore, angle between the hands at 2:20 = 60 degrees – 10 degrees = 50 degrees Incorrect Answer: B Explanation Time is 2:20. Position of the hands: Hour hand at 2 (nearly). Minute hand at 4 Angle between 2 and 4 is 60 degrees. Angular distance travelled by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute. Therefore, angle between the hands at 2:20 = 60 degrees – 10 degrees = 50 degrees
#### 2. Question
The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.
• a) 60 degrees
• b) 50 degrees
• c) 45 degrees
• d) 120 degrees
Explanation
Time is 2:20.
Position of the hands:
- •Hour hand at 2 (nearly).
- •Minute hand at 4
Angle between 2 and 4 is 60 degrees.
Angular distance travelled by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.
Therefore, angle between the hands at 2:20 = 60 degrees – 10 degrees = 50 degrees
Explanation
Time is 2:20.
Position of the hands:
- •Hour hand at 2 (nearly).
- •Minute hand at 4
Angle between 2 and 4 is 60 degrees.
Angular distance travelled by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.
Therefore, angle between the hands at 2:20 = 60 degrees – 10 degrees = 50 degrees
• Question 3 of 5 3. Question How often between 11 O’clock and 12 O’clock are the hands of the clock together? a) 0 b) 2 c) 3 d) 6 Correct Answer: A Explanation At 11 O’clock, the hour hand is 5 spaces apart from the minute hand. During the next 60 minutes, i.e. between 11′ O clock and 12′ O clock the minute hand will move further away from the hour hand. It will eventually meet the hour hand exactly at 12 O’clock Incorrect Answer: A Explanation At 11 O’clock, the hour hand is 5 spaces apart from the minute hand. During the next 60 minutes, i.e. between 11′ O clock and 12′ O clock the minute hand will move further away from the hour hand. It will eventually meet the hour hand exactly at 12 O’clock
#### 3. Question
How often between 11 O’clock and 12 O’clock are the hands of the clock together?
Explanation
At 11 O’clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11′ O clock and 12′ O clock the minute hand will move further away from the hour hand. It will eventually meet the hour hand exactly at 12 O’clock
Explanation
At 11 O’clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11′ O clock and 12′ O clock the minute hand will move further away from the hour hand. It will eventually meet the hour hand exactly at 12 O’clock
• Question 4 of 5 4. Question What is the angle between the minute hand and the hour hand when the time is 15:40 hours? a) 150 b) 160 c) 140 d) 130 Correct Answer: D Explanation Angle between 3 and 8 on the clock = 240 – 90 = 150 degrees. The angle travelled by the hour hand from 3 = (40/60) x 30 = 20 degrees. Therefore, the net angle between the hour hand and the minute hand = 150 – 20 = 130 degrees. Incorrect Answer: D Explanation Angle between 3 and 8 on the clock = 240 – 90 = 150 degrees. The angle travelled by the hour hand from 3 = (40/60) x 30 = 20 degrees. Therefore, the net angle between the hour hand and the minute hand = 150 – 20 = 130 degrees.
#### 4. Question
What is the angle between the minute hand and the hour hand when the time is 15:40 hours?
Explanation
Angle between 3 and 8 on the clock = 240 – 90 = 150 degrees.
The angle travelled by the hour hand from 3 = (40/60) x 30 = 20 degrees.
Therefore, the net angle between the hour hand and the minute hand = 150 – 20 = 130 degrees.
Explanation
Angle between 3 and 8 on the clock = 240 – 90 = 150 degrees.
The angle travelled by the hour hand from 3 = (40/60) x 30 = 20 degrees.
Therefore, the net angle between the hour hand and the minute hand = 150 – 20 = 130 degrees.
• Question 5 of 5 5. Question A clock is set right at 10 a.m. on Monday. It loses 15 minutes in 24 hrs. What will be the true time when the clock indicates 4 a.m. on the following Saturday? a) 5:12 am b) 5:32 am c) 6:32 am d) 5:48 am Correct Answer: A Explanation From 10 am on 1st day to 4 am on 5th day there are a total of 114 hours. As the clock loses 15 min per day, so 23 hours 45 min of this clock are the same as 24 hours of correct clock, i.e. 95/4 hours of this clock = 24 hours of correct clock. So, 114 hours of this clock = (24×4/95) × 114 hours of correct clock = 115.2 hours of correct clock, which is equal to 115 hours 12 minutes. Incorrect Answer: A Explanation From 10 am on 1st day to 4 am on 5th day there are a total of 114 hours. As the clock loses 15 min per day, so 23 hours 45 min of this clock are the same as 24 hours of correct clock, i.e. 95/4 hours of this clock = 24 hours of correct clock. So, 114 hours of this clock = (24×4/95) × 114 hours of correct clock = 115.2 hours of correct clock, which is equal to 115 hours 12 minutes.
#### 5. Question
A clock is set right at 10 a.m. on Monday. It loses 15 minutes in 24 hrs. What will be the true time when the clock indicates 4 a.m. on the following Saturday?
• a) 5:12 am
• b) 5:32 am
• c) 6:32 am
• d) 5:48 am
Explanation
From 10 am on 1st day to 4 am on 5th day there are a total of 114 hours.
As the clock loses 15 min per day, so 23 hours 45 min of this clock are the same as 24 hours of correct
clock, i.e. 95/4 hours of this clock = 24 hours of correct clock.
So, 114 hours of this clock = (24×4/95) × 114 hours of correct clock = 115.2 hours of correct clock, which is equal to 115 hours 12 minutes.
Explanation
From 10 am on 1st day to 4 am on 5th day there are a total of 114 hours.
As the clock loses 15 min per day, so 23 hours 45 min of this clock are the same as 24 hours of correct
clock, i.e. 95/4 hours of this clock = 24 hours of correct clock.
So, 114 hours of this clock = (24×4/95) × 114 hours of correct clock = 115.2 hours of correct clock, which is equal to 115 hours 12 minutes.
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