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
Five people out of whom only two can drive are to be seated in a five seater car with two seats in front and three in the rear. The people who know driving don’t sit together. Only someone who knows driving can sit on the driver’s seat. Find the number of ways the five people can be seated.
Correct
Answer: D
Explanation
Number of people who can drive = 2
Number of ways of selecting driver = 2C1
The other person who knows driving can be seated only in the rear three seats in 3 ways
Total number of ways of seating the two persons = 2C1 × 3
Number of ways of seating remaining = 3!
Total number of all five can be seated = 2C1 × 3 × 3! = 36
Hence, correct answer is 36 Hence, option D is correct.
Incorrect
Answer: D
Explanation
Number of people who can drive = 2
Number of ways of selecting driver = 2C1
The other person who knows driving can be seated only in the rear three seats in 3 ways
Total number of ways of seating the two persons = 2C1 × 3
Number of ways of seating remaining = 3!
Total number of all five can be seated = 2C1 × 3 × 3! = 36
Hence, correct answer is 36 Hence, option D is correct.
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Question 2 of 5
2. Question
Number of ways in which four different toys and five indistinguishable marbles can be distributed between Amar, Akbar and Anthony, if each child receives at least one toy and one marble, is
Correct
Answer: D
Explanation
Make 3 groups of boys 1, 1, 2
4!/(2! 112 2!) × 3! ways to distribute
Identical marbles distribution
1 2 2– 3 ways
1 1 3 – 3 ways
Total ways = 4!/(2! × 2!) × 3! × 6 = 216 Hence, option D is correct.
Incorrect
Answer: D
Explanation
Make 3 groups of boys 1, 1, 2
4!/(2! 112 2!) × 3! ways to distribute
Identical marbles distribution
1 2 2– 3 ways
1 1 3 – 3 ways
Total ways = 4!/(2! × 2!) × 3! × 6 = 216 Hence, option D is correct.
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Question 3 of 5
3. Question
Five people are to be arranged on five chairs for a photograph such that three people among them do not want to sit next to each other. Find out the number of ways in which this can be done.
Correct
Answer: C
Explanation
If three people do not want to sit next to each other, they will occupy alternate chairs, i.e. the first,
third and fifth chairs. They can be arranged on these 3 chairs in 3! Ways.
The remaining two people can be arranged on the second and the fourth chairs in 2! Ways.
∴ The total number of arrangements = 3! × 2! = 12 Hence, option C is correct.
Incorrect
Answer: C
Explanation
If three people do not want to sit next to each other, they will occupy alternate chairs, i.e. the first,
third and fifth chairs. They can be arranged on these 3 chairs in 3! Ways.
The remaining two people can be arranged on the second and the fourth chairs in 2! Ways.
∴ The total number of arrangements = 3! × 2! = 12 Hence, option C is correct.
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Question 4 of 5
4. Question
Twenty families, each comprising five members attend a wedding reception and exchanged a Diwali greetings card with every other person of a different family exactly once. Find the total number of card exchanges happening at the reception.
Correct
Answer: A
Explanation
There are 20 families total comprising five members in each family.
Total number of persons in an event = 20 × 5 = 100
Now every member of family will exchange the card with 95 other persons.
Total number of cards exchanged = 100 × 95 = 9500
As two persons exchange two cards with each other, the total number of card exchanges is half the number of cards
So, total number of card exchanges = 9500/2 = 4750 Hence, option A is correct.
Incorrect
Answer: A
Explanation
There are 20 families total comprising five members in each family.
Total number of persons in an event = 20 × 5 = 100
Now every member of family will exchange the card with 95 other persons.
Total number of cards exchanged = 100 × 95 = 9500
As two persons exchange two cards with each other, the total number of card exchanges is half the number of cards
So, total number of card exchanges = 9500/2 = 4750 Hence, option A is correct.
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Question 5 of 5
5. Question
Three chairs are arranged in a row facing three other chairs. 4 boys and 2 girls are to be seated on these chairs such that girls are always facing each other. In how many ways can they be seated?
Correct
Answer: C
Explanation
There are three sets of chairs facing each other, we select one set, ways = 3
Now the girls can be seated on these two in 2! Ways
4 boys can be seated on the remaining four chairs in 4! Ways
Total ways = 3 × 2 × 4! = 144 Hence, option C is correct
Incorrect
Answer: C
Explanation
There are three sets of chairs facing each other, we select one set, ways = 3
Now the girls can be seated on these two in 2! Ways
4 boys can be seated on the remaining four chairs in 4! Ways
Total ways = 3 × 2 × 4! = 144 Hence, option C is correct
