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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.
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Question 1 of 5
1. Question
There are 4 green and 5 red balls in first bag. And 3 green and 5 red balls in second bag. One ball is drawn from each bag. What is the probability that one ball will be green and other red?
Correct
Solution: D
The possibilities of selecting one green ball and other red ball are (1 green ball from bag 1 AND 1 red ball from bag 2) OR (1 red ball from bag 1 AND 1 green ball from bag 2).
Therefore, it can be written as (4/9 * 5/8) + (5/9 * 3/8)
= 20/72 + 15/72 = 35/72
Hence, option (d) is correct.
Incorrect
Solution: D
The possibilities of selecting one green ball and other red ball are (1 green ball from bag 1 AND 1 red ball from bag 2) OR (1 red ball from bag 1 AND 1 green ball from bag 2).
Therefore, it can be written as (4/9 * 5/8) + (5/9 * 3/8)
= 20/72 + 15/72 = 35/72
Hence, option (d) is correct.
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Question 2 of 5
2. Question
A water tank is 2/5 th full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Correct
Solution: A
Since pipe B is faster than pipe A and thus, the tank will be emptied.
Part of the tank to be emptied = 2/5
Part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15.Therefore, 1/15 : 2/5 :: 1: x
è 2/5 * 15 = 6 minutesHence, option (a) is correct.
Incorrect
Solution: A
Since pipe B is faster than pipe A and thus, the tank will be emptied.
Part of the tank to be emptied = 2/5
Part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15.Therefore, 1/15 : 2/5 :: 1: x
è 2/5 * 15 = 6 minutesHence, option (a) is correct.
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Question 3 of 5
3. Question
Out of 14 applicants for a job, there are 6 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of selected persons will be a woman is?
Correct
Solution: A
Total sample size of selecting 2 people from 14 people (6 women and 8 men)
= 14C2 = (14 * 13) / 2 = 91
The probability of selecting only men is 8c2/14c2 =14/91
Probability of selecting at least one woman = 1 – 14/91 = 77/91.
Hence, option (a) is correct.
Incorrect
Solution: A
Total sample size of selecting 2 people from 14 people (6 women and 8 men)
= 14C2 = (14 * 13) / 2 = 91
The probability of selecting only men is 8c2/14c2 =14/91
Probability of selecting at least one woman = 1 – 14/91 = 77/91.
Hence, option (a) is correct.
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Question 4 of 5
4. Question
A train passes two persons walking in opposite direction at a speed of 5 m/s and 10 m/s in 6 seconds and 5 seconds respectively. Find the length of the train?
Correct
Solution: B
Let the speed of the train be ‘s’ m/s.
Let the length of the train be ‘x’ meters.
Relative speed of train and the first person who is moving at the speed of 5 m/s in opposite direction = (s+5) m/s.
Therefore, total distanced travelled (i.e length of train) ‘x’= Relative speed X time
- x = (s+5) * 6 —-( Eq 1)
Relative speed of train and the second person who is moving at the speed of 10 m/s in opposite direction = (s+10) m/s
Therefore, total distanced travelled (i.e length of train) ‘x’ = Relative speed X time
- x = (s+10) * 5 — (Eq 2)
Since length of the train is same in both the cases, if we equate the equation 1 and equation 2 we get
- (s+5) * 6 = (s+10) * 5
- 6s+30= 5s+50
- 6s – 5s = 50 – 30
- s = 20 m/s (i.e speed of the train)
Now, putting the value of speed of the train in equation 1 (we can put the value equation 2 as well) we get
- Length of the train ‘x’ = (20+5) * 6
- x = 25 * 6
- x= 150
Therefore, length of the train is 150 meters.
Hence, option (b) is correct.
Incorrect
Solution: B
Let the speed of the train be ‘s’ m/s.
Let the length of the train be ‘x’ meters.
Relative speed of train and the first person who is moving at the speed of 5 m/s in opposite direction = (s+5) m/s.
Therefore, total distanced travelled (i.e length of train) ‘x’= Relative speed X time
- x = (s+5) * 6 —-( Eq 1)
Relative speed of train and the second person who is moving at the speed of 10 m/s in opposite direction = (s+10) m/s
Therefore, total distanced travelled (i.e length of train) ‘x’ = Relative speed X time
- x = (s+10) * 5 — (Eq 2)
Since length of the train is same in both the cases, if we equate the equation 1 and equation 2 we get
- (s+5) * 6 = (s+10) * 5
- 6s+30= 5s+50
- 6s – 5s = 50 – 30
- s = 20 m/s (i.e speed of the train)
Now, putting the value of speed of the train in equation 1 (we can put the value equation 2 as well) we get
- Length of the train ‘x’ = (20+5) * 6
- x = 25 * 6
- x= 150
Therefore, length of the train is 150 meters.
Hence, option (b) is correct.
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Question 5 of 5
5. Question
A and B together can do a work in 8 days, B and C together in 6 days, while C and A together in 10 days. If they all work together, the work will be completed in how many days?
Correct
Solution: C
Formula: A and B together can do a work in x days, B and C together in y days, while C and A together in z days. If they all work together, the work will be completed in: (2xyz)/( xy+yz+zx)
In the above given problem ‘x’ = 8 days, ‘y’= 6 days and ‘z’= 10 days.
Substituting the values x, y and z in the formula, If they all work together, the work will be completed in : (2 * 8 * 6 * 10)/((8*6)+(6*10)+(10*8))
- 960/(48+60+80)
- 960/188
- 240/47 days
Hence, option (c) is correct.
Incorrect
Solution: C
Formula: A and B together can do a work in x days, B and C together in y days, while C and A together in z days. If they all work together, the work will be completed in: (2xyz)/( xy+yz+zx)
In the above given problem ‘x’ = 8 days, ‘y’= 6 days and ‘z’= 10 days.
Substituting the values x, y and z in the formula, If they all work together, the work will be completed in : (2 * 8 * 6 * 10)/((8*6)+(6*10)+(10*8))
- 960/(48+60+80)
- 960/188
- 240/47 days
Hence, option (c) is correct.
