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GS Prelims Paper II Permutation & Combination, Probability up to 2019

Civil Services Examination 2019


1. Each face of a cube can be painted in black or white colours. In how many different ways can the cube be painted?

  1. 9
  2. 10
  3. 11
  4. 12


2. How many triplets (x, y, z) satisfy the equation x + y + z = 6, where x, y and z are natural numbers?

  1. 4
  2. 5
  3. 9
  4. 10


3. Suppose you have sufficient amount of rupee currency in three denominations: Rs. 1, Rs. 10 and Rs. 50. In how many different ways can you pay a bill of Rs. 107?

  1. 16
  2. 17
  3. 18
  4. 19


Civil Services Examination 2018


1. For a sports meet, a winners' stand comprising three wooden blocks is in the following form:

There are six different colours available to choose from and each of the three wooden blocks is to be painted such that no two of them has the same colour. In how many different ways can the winners' stand be painted?

  1. 120
  2. 81
  3. 66
  4. 36


2. A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces?

  1. 12
  2. 8
  3. 6
  4. 4


3. 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% arc 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?

  1. 1/2
  2. 4/7
  3. 5/9
  4. 12 /13


Civil Services Examination 2017


1. Certain 3-digit numbers following characteristics:

  1. All the three digits are different.
  2. The number is divisible by 7.
  3. The number on reversing the digits is also divisible by 7.

How many such 3-digit numbers are there?

  1. 2
  2. 4
  3. 6
  4. 8


2. A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is Hie 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?

  1. 17
  2. 16
  3. 13
  4. 11


3. 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?

  1. 3
  2. 6
  3. 12
  4. 24


4. There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?

  1. 16
  2. 24
  3. 36
  4. 42


Civil Services Examination 2016


1. 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?

  1. 6
  2. 8
  3. 9
  4. None of the above


Civil Services Examination 2015


1. 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

  1. 4
  2. 12
  3. 18
  4. None of the above


2. 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

  1. 5
  2. 6
  3. 7
  4. 8