There are two identical red, two identical black, and two identical white balls. In how many different ways can the balls be placed in the cells such that balls of the same color do not occupy any two consecutive cells

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2008

There are two identical red, two identical black, and two identical white balls. In how many different ways can the balls be placed in the cells such that balls of the same color do not occupy any two consecutive cells?

(a)

(b)

(c)

(d)

Correct Answer

(c)

Explanation

The balls can be placed in 24 ways while avoiding consecutive same-colored balls.

Microtheme: CSAT —
54 questions asked in Prelims in the past.

[2010] In a meeting, the map of a village was placed in such a manner that south-east becomes north, north-east becomes west and so on. What will south become ?
- (a) North
- (b) North-East
- (c) North-West
- (d) West
Correct Answer: (B) North-East
[2010] In how many ways can four children be made to stand in a line such that two of them, A and B are always together ?
- (a) 6
- (b) 12
- (c) 18
- (d) 24
Correct Answer: (B) 12
[2010] A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% in the test and all questions carried equal marks, then what is the number of questions in the test ?
- (a) 36
- (b) 30
- (c) 25
- (d) 20
Correct Answer: (D) 20
[2010] When ten persons shake hands with one another, in how many ways is it possible ?
- (a) 20
- (b) 25
- (c) 40
- (d) 45
Correct Answer: (D) 45
[2010] The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2-50. What is the difference between their rates ?
- (a) 0.25%
- (b) 0.5%
- (c) 1%
- (d) 2.5%
Correct Answer: (A) 0.25%
[2010] The diameters of two circular coins are in the ratio of 1:3. The smaller coin is made to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times the smaller coin rolled around the bigger coin ?
- (a) 9
- (b) 6
- (c) 3
- (d) 1.5
Correct Answer: (C) 3
[2010] A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days the basket was 1/4thfull ?
- (a) 6
- (b) 12
- (c) 17
- (d) 22
Correct Answer: (D) 22
[2010] P, Q, R’ and S are four men. P is the oldest but not the poorest. R is the richest but not the oldest. Q is older than S but not than P or R. P is richer than Q but not than S. The four men can be ordered (descending) in respect of age and richness, respectively, as
- (a) PQRS, RPSQ
- (b) PRQS, RSPQ
- (c) PRQS, RSQP
- (d) PRSQ, RSPQ
Correct Answer: (B) PRQS, RSPQ
[2010] Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5-5 and 8 kmph respectively. When will they meet at the starting point for the first time?
- (a) After 11 hours
- (b) After 21 hours
- (c) After 22 hours
- (d) After 33 hours
Correct Answer: (C) After 22 hours
[2010] Each person’s performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons?
- (a) 66
- (b) 55
- (c) 54
- (d) 45
Correct Answer: (B) 55
[2010] Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are below twenty five. Then, which one of the following is certainly true?
- (a) All the villagers who have their own houses are literate
- (b) Some villagers under twenty five are literate
- (c) A quarter of the villagers who have their own houses cultivate paddy.
- (d) Half of the villagers who cultivate paddy are literate
Correct Answer: (B) Some villagers under twenty five are literate
[2010] In a group of five persons A, B, C, D and E, there is a professor, a doctor and lawyer. A and D are unmarried ladies, and do not work. Of the married couple in the Group, E is the husband. B is the brother of A and is neither a doctor nor a lawyer. Who is the professor?
- (a) B
- (b) C
- (c) A
- (d) Cannot be determined
Correct Answer: (A) B
[2010] How many numbers from 0 to 999 are divisible by either 5 or 7?
- (a) 313
- (b) 341
- (c) 686
- (d) 786
Correct Answer: (C) 686
[2010] A person travelled a distance of 50 km in 8 hours. He covered a part of the distance on food at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much distance did he travel on foot?
- (a) 10km
- (b) 20km
- (c) 30km
- (d) 40km
Correct Answer: (B) 20km
[2010] Examine the following statements:
1. All colours are pleasant
2. Some colours are pleasant
3. No colour is pleasant
4. Some colours are not pleasant
Given that the statement 4 is true, what can be definitely concluded?
- (a) 1 and 2 are true
- (b) 1 is false
- (c) 2 is false
- (d) 3 is true
Correct Answer: (B) 1 is false
[2010] Two numbers X and Y are respectively 20% ad 28% less than a third number Z. By what percentage is the number Y less than the number X?
- (a) 8%
- (b) 9%
- (c) 10%
- (d) 12%
Correct Answer: (C) 10%
[2010] A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is
- (a) 16
- (b) 15
- (c) 12
- (d) 8
Correct Answer: (B) 15
[2010] Six persons M, N, O, P, Q and R are sitting in two rows, three in each. Q is not at the end of any row. P is second to the left of R, O is the neighbour of Q and is sitting diagonally opposite to P. N is the neighbour of R. On the basis of above information, who is facing N ?
- (a) R
- (b) Q
- (c) P
- (d) M
Correct Answer: (B) Q
[2010] Running at a speed of 60 km per hour, a train passed through a 1-5 km long tunnel in two minutes. What is the length of the train ?
- (a) 250 m
- (b) 500 m
- (c) 1000 m
- (d) 1500 m
Correct Answer: (B) 500 m
[2010] Six books A, B, C, D, E and F are placed side by side. B, C and E have blue cover and the other books have red cover. Only D and F are new books and the rest are old. A, C and D are law reports and others are Gazetteers. What book is a new law report with a red colour ?
- (a) A
- (b) B
- (c) C
- (d) D
Correct Answer: (D) D
[2010] A paper had ten questions. Each could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?
- (a) (a)20
- (b) 40
- (c) 512
- (d) 1024
Correct Answer: (D) 1024
[2010] Two trains leave New Delhi at the same time. One travels north at 60 kmph and the other travels south at 40 kmph. After how many hours will the trains be 150 km apart ?
- (a) 3/2
- (b) 4/3
- (c) 3/4
- (d) 15/2
Correct Answer: (A) 3/2
[2010] In a tournament 14 teams play league matches. If each team plays against every other team once only then how many matches are played ?
- (a) 105
- (b) 91
- (c) 85
- (d) 78
Correct Answer: (B) 91
[2010] A cuboid has six sides of different colours. The red side is opposite to black. The blue side is adjacent to white. The brown side is adjacent to blue. The red side is face down.
Which one of the following would be the opposite to brown?
- (a) Red
- (b) Black
- (c) White
- (d) Blue
Correct Answer: (C) White
[2009] There are three cans A, B and C. The capacities of A, B and C are 6 litres, 10 litres and 16 litres respectively. The can C contains 16 litres of milk. The milk has to be divided in them using these three cans only. Consider the following statements :
1. It is possible to have 6 litres of milk each in can A and can B.
2. It is possible to have 8 litres of milk each in can B and can C.
Which of the statements given above is/are correct ?
- (a) 1 only
- (b) 2 only
- (c) Both 1 and 2
- (d) Neither 1 nor 2
Correct Answer: (C) Both 1 and 2
[2009] In a carrom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other-player was a girl. Consider the following statements :
1. The total number of students that participated in the competition is 30.
2. The number of games in which both players were girls is 78.
Which of the statements given above is/are correct ?
- (a) 1 only
- (b) 2 only
- (c) Both 1 and 2
- (d) Neither 1 nor 2
Correct Answer: (C) Both 1 and 2
[2009] There are 240 balls and n number of boxes B1, B2, B3, … , Bn. The balls are to be placed in the boxes such that should contain 4 balls more than B2, B2 should contain: 4 balls more than B3, and so on.
Which one of the following cannot be the possible value of n ?
- (a) 4
- (b) 5
- (c) 6
- (d) 7
Correct Answer: (D) 7
[2009] How many times are an hour hand and a minute hand of a clock at right angles during their motion from
1.00 p.m. to 10.00 p.m. ?
- (a) 9
- (b) 10
- (c) 18
- (d) 20
Correct Answer: (C) 18
[2009] There is a family of 6 persons A, B, C, D, E and F. There are two married couples in the family. The family members are lawyer, teacher, salesman, engineer, accountant and doctor. D, the salesman is married to the lady teacher. The doctor is married to the lawyer. F, the accountant is the son of B and brother of E. C, the lawyer is the daughter-in-law of A. E is the unmarried engineer. A is the grandmother of F. How is E related to F ?
- (a) Brother
- (b) Sister
- (c) Father
- (d) Cannot be determined
Correct Answer: (D) Cannot be determined
[2009] In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed iv A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between
- (a) 42% and 84%
- (b) 42% and 78%
- (c) 58% and 78%
- (d) 58% and 84%
Correct Answer: (A) 42% and 84%
[2009] Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut ?
- (a) 27
- (b) 36
- (c) 43
- (d) 480
Correct Answer: (B) 36
[2009] While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed ?
- (a) 11
- (b) 12
- (c) 13
- (d) 14
Correct Answer: (C) 13
[2009] There are four persons A, B, C, D; and A has some coins. A gave half of the coins to B and 4 more besides. B gave half of the coins to C and 4 more besides. C gave half of the coins to D and 4 more besides. Both B and D end up with same number of coins. How many coins did A have originally
- (a) 96
- (b) 84
- (c) 72
- (d) 64
Correct Answer: (C) 72
[2009] How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order
- (a) 80
- (b) 81
- (c) 83
- (d) 84
Correct Answer: (D) 84
[2009] How many letters of the English alphabet (capitals) appear same when looked at in a mirror ?
- (a) 9
- (b) 10
- (c) 11
- (d) 12
Correct Answer: (C) 11
[2009] How many numbers lie between 300 and 500 in which 4 comes only one time ?
- (a) 99
- (b) 100
- (c) 110
- (d) 120
Correct Answer: (A) 99
[2009] A person has 4 coins each of different denomination. What is the number of different sums of money the person can form (using one or more coins at a time) ?
- (a) 16
- (b) 15
- (c) 12
- (d) 11
Correct Answer: (B) 15
[2009] Six persons A, B, C, D, E and F are standing in a row. C and D are standing close to each other alongside E. B is standing beside A only. A is fourth from P. Who are standing on the extremes ?
- (a) A and F
- (b) B and D
- (c) B and F
- (d) None of the above
Correct Answer: (C) B and F
[2009] A person travels 12 km due North then 15 km due East after that 15 km due West and then 18 km due South. How far is he from the starting point?
- (a) 6 km
- (b) 12 km
- (c) 33 km
- (d) 60 km
Correct Answer: (A) 6 km
[2008] March 1, 2008 was Saturday. Which day was it on March 1, 2002?
- (a) Thursday
- (b) Friday
- (c) Saturday
- (d) Sunday
Correct Answer: (B) Friday
[2008] A schoolteacher has to select the maximum possible number of different groups of 3 students out of a total of 6 students. In how many groups will any particular student be included?
- (a) 6
- (b) 8
- (c) 10
- (d) 12
Correct Answer: (C) 10
[2008] In an examination, 70% of the students passed in Paper I, and 60% of the students passed in Paper II. 15% of the students failed in both papers while 270 students passed in both papers. What is the total number of students?
- (a) 600
- (b) 580
- (c) 560
- (d) 540
Correct Answer: (A) 600
[2008] A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is Rs 600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%?
- (a) Rs. 802.50
- (b) Rs. 811.25
- (c) Rs. 862.50
- (d) Rs. 875
Correct Answer: (C) Rs. 862.50
[2008] In how many different ways can four books A, B, C, and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?
- (a) 9
- (b) 12
- (c) 14
- (d) 79
Correct Answer: (B) 12
[2008] Carpenter A can make a chair in 6 hours, carpenter B in 7 hours, and carpenter C in 8 hours. If each carpenter works for 8 hours per day, how many chairs will be made in 21 days?
- (a) 61
- (b) 67
- (c) 73
- (d) 79
Correct Answer: (C) 73
[2008] What is the number of terms in the series 117, 120, 123, 126,….., 333?
- (a) 72
- (b) 73
- (c) 76
- (d) 79
Correct Answer: (B) 73
[2008] In the series AABABCABCDABCDE…… Which letter occupies the 100th position?
- (a) H
- (b) I
- (c) J
- (d) K
Correct Answer: (B) I
[2008] Which one of the following is the correct sequence in respect of the Roman numerals-C, D, L, and M?
- (a) C > D > L > M
- (b) M < L > D > C
- (c) M > D > C > L
- (d) L > C < D > M
Correct Answer: (C) M > D > C > L
[2008] How can the height of a person who is six feet tall be expressed (approximately) in nanometers?
- (a) nanometers
- (b) nanometers
- (c) nanometers
- (d) nanometers
Correct Answer: (C) nanometers
[2008] A person is sitting in a car which is at rest. The reaction from the road at each of the four wheels of the car is R. When the car runs on a straight level road, how will the reaction at either of the front wheels vary?
- (a) It will be greater than R
- (b) It will be less than R
- (c) It will be equal to R
- (d) It shall depend on the material of the road
Correct Answer: (C) It will be equal to R
[2008] How many different triangles are there in the figure shown above?
- (a) 28
- (b) 24
- (c) 20
- (d) 16
Correct Answer: (A) 28
[2008] There are two identical red, two identical black, and two identical white balls. In how many different ways can the balls be placed in the cells such that balls of the same color do not occupy any two consecutive cells?
- (a) 15
- (b) 18
- (c) 24
- (d) 30
Correct Answer: (C) 24
[2008] There are 6 different letters and 6 correspondingly addressed envelopes. If the letters are randomly put in the envelopes, what is the probability that exactly 5 letters go into the correctly addressed envelopes?
- (a) Zero
- (b) 1/6
- (c) 1/2
- (d) 5/6
Correct Answer: (A) Zero
[2008] In how many different ways can all of 5 identical balls be placed in the cells such that each row contains at least 1 ball?
- (a) 64
- (b) 81
- (c) 84
- (d) 108
Correct Answer: (D) 108