Fundamental counting principle: filling the boxes 4 PYQs

• How many 3-digit numbers can be formed using digits 1, 2, 3, 4 without repeating any digit?Other exams 2026 · 21 Jan 2026
• In a class of 10 students, in how many ways can a president, a vice-president and a secretary be selected (all different)?Other exams 2026 · 20 Jan 2026
• Consider the set of digits 1, 2, 3, 4, 5, 6. If repetition of digits is allowed, how many 4-digit numbers formed from this set will be even?Other exams 2026 · 21 Jan 2026
• A lock requires a 4-character password formed using digits 0 – 9 and letters A – F, with no repetition. How many such passwords are possible?UP Police Constable 2026 · 09 Jun 2026

Permutations: arrangements, words, together/apart and circular 10 PYQs

• A code is formed using all the letters of the word "MAGIC", with no repetition. How many such codes can be made such that 'A' is never at the…Other exams 2026 · 20 Jan 2026
• In how many ways can the letters of the word "BANANA" be arranged?Other exams 2026 · 16 Jan 2026
• In how many ways can the letters of the word SCHOOL be arranged such that the vowels always come together?Other exams 2026 · 16 Jan 2026
• There are 8 different symbols. A code is formed by selecting 5 symbols such that each symbol can be used only once (that is, no symbol is repeated…UP Police Constable 2026 · 09 Jun 2026
• From the letters of the word BRIGHT, how many 3-letter arrangements can be formed without repeating any letter?UP Police Constable 2026 · 08 Jun 2026
• Consider a group of 5 boys and 3 girls. If they are to be seated in a single row, how many seating arrangements are possible if the girls must be…Other exams 2026 · 21 Jan 2026
• A chef has 4 identical red plates, 3 identical blue plates, and 2 identical green plates. In how many distinct ways can he arrange all the 9 plates…Other exams 2026 · 16 Jan 2026
• From the letters of the word ALGORITHM, how many 5-letter words (not necessarily meaningful) can be formed if the word must begin with a vowel and…Other exams 2026 · 20 Jan 2026
• A box contains 6 identical red balls and 5 identical blue balls. How many distinct ways can these balls be arranged in a row?UP Police Constable 2026 · 10 Jun 2026
• A photographer arranges 6 people in a row, but two persons refuse to stand next to each other. In how many ways can the arrangement be made?UP Police Constable 2026 · 08 Jun 2026

Combinations: selections, committees and geometry counts 6 PYQs

• There are 10 points in a plane, and no three of them are in a straight line. What is the total number of triangles that can be constructed by…Other exams 2026 · 20 Jan 2026
• A vendor has 9 different fruits. In how many ways can he select 3 fruits?UP Police Constable 2026 · 10 Jun 2026
• Consider a bag with 7 red and 5 blue balls. What is the number of ways to pick 4 balls such that a minimum of 3 of them are red?Other exams 2026 · 21 Jan 2026
• A magician has 6 different tricks. He wants to perform 4 of them in a show, but two specific tricks should never be together. In how many ways can…Other exams 2026 · 20 Jan 2026
• From a group of 8 males and 6 females, how many different 5-person committees can be assembled if there must be a minimum of 3 females on each…Other exams 2026 · 20 Jan 2026
• A club has 5 painters, 4 dancers, and 3 singers. A committee of 5 people is to be formed such that it includes at least 2 painters and at least 1…Other exams 2026 · 16 Jan 2026

Probability basics: coins, dice, cards and balls 2 PYQs

• A basket has 6 apples, 3 mangoes and 5 oranges. One fruit is selected at random. What is the probability that it is neither an apple nor a mango?UP Police Constable 2026 · 10 Jun 2026
• A student randomly picks a day from the days of a week. What is the probability that the selected day starts with the letter 'W' or 'S'?UP Police Constable 2026 · 09 Jun 2026