CSAT – UPSC Prelims PYQs

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 (each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?

How many different triangles are there in the figure shown above?

(Each small circle represents a different station) Refer to the figure showing a network between station A and station B. What is the maximum number of different paths that exist between station A and station B?

In how many maximum different ways can 3 identical balls be placed in 12 squares (each ball is placed in the exact centre of a square) shown in the figure above such that they do not lie along the same straight line? The original figure is not available for this question.

In the figure shown above, what is the maximum number of different ways in which 8 identical balls can be placed in small triangles 1, 2, 3 and 4 such that each triangle contains at least one ball?

Amit has five friends: 3 girls and 2 boys. Amit’s wife also has five friends: 3 boys and 2 girls. In how many maximum different ways can they invite 2 boys and 2 girls such that two of them are Amit’s friends and two are his wife’s friends?

Five balls of different colours are to be placed in three different boxes such that any box contains at least one ball. What is the maximum number of different ways in which this can be done?

All six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as a dictionary. What will be the position of the word SACHIN in that sequence?

Three dice (each having six faces with each face showing one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows the number 2?

Groups, each containing 3 boys, are to be formed out of 5 boys – A, B, C, D and E – such that no one group contains both C and D together. What is the maximum number of different groups?

Six faces of a cube are numbered from 1 to 6, each face carrying one different number. Further,

1. The face 2 is opposite to the face 6.
2. The face 1 is opposite to the face 5.
3. The face 3 is between the face 1 and face 5.
4. The face 4 is adjacent to the face 2.

Which one of the following is correct?

Each of the 3 persons is to be given some identical items such that the product of the numbers of items received by each of the three persons is equal to 30. In how many maximum different ways can this distribution be done?

Six equidistant vertical lines are drawn on a board. Six equidistant horizontal lines are also drawn on the board cutting the six vertical lines and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed?

A person has to completely put each of three liquids – 403 litres of petrol, 465 litres of diesel and 496 litres of mobile oil – in bottles of equal size without mixing any of the three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job?

If all the numbers from 501 to 700 are written, what is the total number of times the digit 6 appears?

Amit starts from a point A, walks to another point B and then returns from B to A by his car, taking a total time of 6 hours 45 minutes. If he had driven both ways in his car, he would have taken 2 hours less. How long would it take for him to walk both ways?

A watch showed a time of fourteen minutes past nine (9 hrs 14 minutes). The positions of the hour-hand and the minute-hand of the watch are exactly interchanged. The new time shown by the watch is closest to which one of the following?

Each of 8 identical balls is to be placed in the squares shown in the figure given above in a horizontal direction such that one horizontal row contains 6 balls and the other horizontal row contains 2 balls. In how many maximum different ways can this be done?

In a tournament each of the participants was to play one match against each of the other participants. 3 players fell ill after each of them had played three matches and had to leave the tournament. What was the total number of participants at the beginning, if the total number of matches played was 75 ?

P, Q, R, S and T reside in a 5-storeyed (Ground + 4) building, and each of them resides on a separate floor. Further,

1. T does not reside on the topmost floor.
2. Q does not reside on the ground floor.
3. S resides on one storey above that of P and one storey below that of R. To know as to which of the 5 persons resides on the ground floor which of the above statements are sufficient / insufficient?

A box contains 5 sets of balls while there are 3 balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed?

3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?

Refer to the three figures I, II and III in which numbers are arranged in squares. What is the value of X in figure III?

Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. This cube is shown in its four different positions in the figures I, II, III and IV. Consider the following statements:

1. Figures II and III are sufficient to know as to which face is opposite to the face numbered 6.
2. Figures II and III are sufficient to know as to which face is opposite to the face numbered 4.
3. Figures I and IV are sufficient to know as to which face is opposite to the face numbered 4.

Which of the statements given above are correct? The original figure is not available for this question.

In a question paper, there are four multiple-choice questions. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

Each of the persons A, B, C, D and E possesses unequal number (<10) of similar items. A, B and C possess 21 items in all, while C, D and E possess 7 items in all. How many items do A and B possess in all?

There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line, and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. Consider the following statements:

1. The minimum number of triangles that can be formed by joining these points is zero.
2. The maximum number of triangles that can be formed by joining these points is twenty.

Which of the statements given above is/are correct?

A mixed doubles tennis game is to be played between two teams (each team consists of one male and one female). There are 4 married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

In an office, the number of persons who take tea is twice the number of persons who take only coffee. The number of persons who take coffee is twice the number of persons who take only tea. Consider the following statements:

1. The sum of the number of persons who take either tea or coffee or both is four times the number of persons who take both coffee and tea.
2. The sum of the number of persons who take only coffee and those who take only tea is twice the number of persons who take both coffee and tea.

Which of the statements given above is/are correct?

How many numbers are there in all 6000 to 6999 (both 6000 and 6999 included) having at least one of their digits repeated?

Each of 2 women and 3 men is to occupy one chair out of 8 chairs, each of which is numbered from 1 to 8. First, women are to occupy any two chairs from those numbered 1 to 4; and then 3 men would occupy any three chairs out of the remaining 6 chairs. What is the maximum number of different ways in which this can be done?

Which is Krishnan’s hometown?

Which College is situated in Inder’s hometown?

Who studies in Bhopal?

If Inder studies in Ahmedabad, then

which one of the following is the correct combination of Person–Hometown–Place of Study?

Left pan of a faulty balance weighs 100 gram more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is his gain?

On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?

Aryan runs at a speed of 40 metre/minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahul’s dog runs at a speed of 60 metre/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog?

A big rectangular plot of area 4320 m² is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot?

2 men and 1 woman board a bus in which 5 seats are vacant. One of these five seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies but a man can not sit on the seat reserved for ladies. In how many different ways can the five seats be occupied by these three passengers?

A square is divided into 9 identical smaller squares. Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball (one ball in one square only). In how many different ways can this be done?

There are 6 persons – A, B, C, D, E and F. They are to be seated in a row such that B never sits anywhere ahead of A. In how many different ways can this be done?

300 persons are participating in a meeting, out of which 120 are foreigners and the rest are Indians. Out of the Indians there are 110 men who are not judges; 160 are men judges, and 35 are women judges. There are no foreign judges. How many Indian women attended the meeting?

Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all ten particles will be lying in the same half of the box?

An equilateral triangular plate is to be cut into a number of identical small equilateral triangular plates.

Which one of the following can be a possible value of n?

There are 10 identical coins and each one of them has ‘H’ engraved on one face and ‘T’ engraved on the other face. These 10 coins are lying on a table and each one of them has the ‘H’ face as the upper face. In one attempt, exactly four (neither more nor less) coins can be turned upside down. What is the minimum number of attempts in which the ‘T’ faces of all the 10 coins can be brought to be the upper faces?

Two cars X and Y start from two places A and B respectively which are 700 km apart at 9 a.m. Both the cars run at an average speed of 60 km/hr. Car X stops at 10 a.m. and again starts at 11 a.m. while the other car Y continues to run without stopping. When do the two cars cross each other?

In a question of a test paper, there are five items each under List-A and List-B. The examinees are required to match each item under List-A with its corresponding correct item under List-B. Further, it is given that

1. No examinee has given the correct answer
2. Answers of no two examinees are identical

What is the maximum number of examinees who took this test?

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