UPSC CSE Prelims CSAT (Paper II) previous year questions on Permutation Combination and Probability (Quantitative Ability), asked from 2011–2026, with answers. There are 37 questions in this post. Attempt each question, then click Show Answer to check.
← All Quantitative Ability topics | CSAT PYQs home
1] How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning. [2026/9]
(a) 6
(b) 8
(c) 10
(d) 12
Show Answer
Ans: (d) 12
2] There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring? [2026/23]
(a) 7
(b) 8
(c) 9
(d) 10
Show Answer
Ans: (b) 8
3] Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make? [2023/4]
(a) 27
(b) 36
(c) 44
(d) 45
Show Answer
Ans: (d) 45
4] In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots? [2023/5]
(a) 18
(b) 19
(c) 20
(d) 21
Show Answer
Ans: (b) 19
5] There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:
1. It is possible that exactly one letter goes into an incorrect envelope.
2. There are only six ways in which only two letters can go into the correct envelopes.
Which of the statements given above is/are correct? [2023/6]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Show Answer
Ans: (b) 2 only
6] A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements:
1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.
2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.
Which of the above statements is/are correct? [2023/36]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Show Answer
Ans: (c) Both 1 and 2
7] What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated? [2023/47]
(a) 7998
(b) 8028
(c) 8878
(d) 9238
Show Answer
Ans: (a) 7998
8] What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction? [2023/48]
(a) 3
(b) 11
(c) 12
(d) 66
Show Answer
Ans: (c) 12
9] A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour? [2023/66]
(a) 12
(b) 18
(c) 24
(d) 36
Show Answer
Ans: (c) 24
10] There are five persons P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1 Task-2 must be assigned to either R or S. In how many ways can the assignment be done? [2023/68]
(a) 6
(b) 12
(c) 18
(d) 24
Show Answer
Ans: (d) 24
11] The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows? [2022/10]
(a) 4
(b) 3
(c) 2
(d) 1
Show Answer
Ans: (c) 2
12] In a tournament of chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that, no match results in a tie/draw. How many matches are played in the entire tournament? [2022/17]
(a) 151
(b) 150
(c) 149
(d) 148
Show Answer
Ans: (c) 149
13] How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5? [2022/18]
(a) 8
(b) 12
(c) 16
(d) 24
Show Answer
Ans: (b) 12
14] The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible? [2022/24]
(a) 12
(b) 18
(c) 24
(d) 36
Show Answer
Ans: (c) 24
15] A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C In how many different ways can one travel from A to C using these roads? [2022/27]
(a) 10
(b) 13
(c) 15
(d) 36
Show Answer
Ans: (c) 15
16] There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty? [2022/55]
(a) 6
(b) 8
(c) 10
(d) 12
Show Answer
Ans: (c) 10
17] One non-zero-digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated? [2022/76]
(a) 105
(b) 525
(c) 945
(d) 1050
Show Answer
Ans: (c) 945
18] There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee? [2022/77]
(a) 18
(b) 27
(c) 54
(d) 81
Show Answer
Ans: (d) 81
19] The sum of three consecutive integers is equal to their product. How many such possibilities are there? [2022/78]
(a) Only one
(b) Only two
(c) Only three
(d) No such possibility is there
Show Answer
Ans: (c) Only three
20] What is the number of numbers of the form 0•XY, where X and Y are distinct non-zero digits? [2022/79]
(a) 72
(b) 81
(c) 90
(d) 100
Show Answer
Ans: (a) 72
21] On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path? [2021/64]
(a) 4
(b) 6
(c) 8
(d) 12
Show Answer
Ans: (b) 6
22] Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed? [2021/66]
(a) 3
(b) 6
(c) 9
(d) 12
Show Answer
Ans: (b) 6
23] There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place? [2021/69]
(a) 3
(b) 4
(c) 5
(d) 6
Show Answer
Ans: (b) 4
24] How many different 5-letter words (with or without meaning) can be constructed using all the letters of the word ‘DELHI’ so that each word has to start with D and end with I ? [2020/67]
(a) 24
(b) 18
(c) 12
(d) 6
Show Answer
Ans: (d) 6
25] A bag contains 15 red balls and 20 black balls. Each ball is numbered either 1 or 2 or 3. 20% of the red balls are numbered 1 and 40% of them are numbered 3. Similarly, among the black balls, 45% are numbered 2 and 30% are numbered 3. A boy picks a ball at random. He wins if the ball is red and numbered 3 or if it is black and numbered 1 or 2. What are the chances of his winning? [2018/39]
(a) 1/2
(b) 4/7
(c) 5/9
(d) 12 /13
Show Answer
Ans: (b) 4/7
26] A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour? [2017/56]
(a) 17
(b) 16
(c) 13
(d) 11
Show Answer
Ans: (b) 16
27] If 2 boys and 2 girls are to be arranged in a row so that the girls are not next to each other, how many possible arrangements are there? [2017/57]
(a) 3
(b) 6
(c) 12
(d) 24
Show Answer
Ans: (c) 12
28] In a question paper there are five questions to be attempted and answer to each question has two choices – True (T) or False (F). It is given that no two candidates have given the answers to the five questions in an identical sequence. For this to happen the maximum number of candidates is: [2016/40]
(a) 10
(b) 18
(c) 26
(d) 32
Show Answer
Ans: (d) 32
29] Four-digit numbers are to be formed using the digits 1, 2, 3 and 4; and none of these four digits are repeated in any manner. Further,
1. 2 and 3 are not to immediately follow each other
2. 1 is not to be immediately followed by 3
3. 4 is not to appear at the last place
4. 1 is not to appear at the first place
How many different numbers can be formed? [2016/72]
(a) 6
(b) 8
(c) 9
(d) None of the above
Show Answer
Ans: (a) 6
30] A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow, and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability, that the arrows fall in the red region of the archery target? [2016/79]
(a) 0.40
(b) 0.20
(c) 0.16
(d) 0.04
Show Answer
Ans: (c) 0.16
31] Twelve people form a club. By picking lots, one of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is [2015/9]
(a) One
(b) Zero
(c) Three
(d) Cannot be predicted
Show Answer
Ans: (d) Cannot be predicted
32] A selection is to be made for one post of Principal and two posts of Vice-Principal. Amongst the six candidates called for the interview, only two are eligible for the post of Principal while they all are eligible for the post of Vice-Principal. The number of possible combinations of selectees is [2015/48]
(a) 4
(b) 12
(c) 18
(d) None of the above
Show Answer
Ans: (d) None of the above
33] A student has to opt for 2 subjects out of 5 subjects for a course, namely, Commerce, Economics, Statistics, Mathematics I and Mathematics II. Mathematics II can be offered only if Mathematics I is also opted. The number of different combinations of two subjects which can be opted is [2015/49]
(a) 5
(b) 6
(c) 7
(d) 8
Show Answer
Ans: (c) 7
34] There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1 or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done? [2015/69]
(a) 6
(b) 12
(c) 24
(d) 144
Show Answer
Ans: (c) 24
35] In a society it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met in a party and there were 24 handshakes.
Which one among the following numbers indicates the possible number of hugs? [2015/74]
(a) 39
(b) 30
(c) 21
(d) 20
Show Answer
Ans: (c) 21
36] Six identical cards are placed on a table. Each card has number ‘1’ marked on one side and number 2’ marked on its other side. All the six cards are placed in such a manner that the number ‘1’ is on the upper side. In one try, exactly four (neither more nor less) cards are turned upside down. In how many least number of tries can the cards be turned upside down such that all the six cards show number ‘2’ on the upper side? [2014/25]
(a) 3
(b) 5
(c) 7
(d) This cannot be achieved
Show Answer
Ans: (a) 3
37] There are four routes to travel from city A to city B and six routes from city B to city C. How many routes are possible to travel from the city A to city C? [2011/34]
(a) 24
(b) 12
(c) 10
(d) 8
Show Answer
Ans: (a) 24
← 2H) Sets (CSAT PYQs) | Quantitative Ability index | 2J) Data Interpretation (CSAT PYQs) →