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JEE Main Permutations and Combinations questions

48 Mathematics questions on Permutations and Combinations as asked in JEE Main, newest first. 25 come with a worked solution.

  1. The value of sum_r=0^22 ^22C_r \ ^23C_r is

    2023 · with solution

  2. The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

    2023 · with solution

  3. The number of integers, greater than 7000 that can be formed, using the digits 3,5,6,7,8 without repetition, is

    2023 · with solution

  4. The number of square matrices of order 5 with entries from the set \0, 1\, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is

    2023 · with solution

  5. Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5, is __________.

    2023

  6. If all the six digit numbers x_1 x_2 x_3 x_4 x_5 x_6 with 0 < x_1 < x_2 < x_3 < x_4 < x_5 < x_6 are arranged in the increasing order, then the sum of the digits in the 72^nd number is ________.

    2023 · with solution

  7. A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is __________

    2023 · with solution

  8. The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is __________

    2023

  9. Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white…

    2023 · with solution

  10. Let S = \1, 2, 3, 5, 7, 10, 11\. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _________.

    2023

  11. Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is

    2023 · with solution

  12. The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is

    2019 · with solution

  13. A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team,…

    2019 · with solution

  14. The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is

    2019 · with solution

  15. The number of 6 digits numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is

    2019

  16. Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the…

    2019 · with solution

  17. Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total…

    2019

  18. A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with atleast 3 females,…

    2019

  19. Consider three boxes, each containing 10 balls labelled 1, 2, ..., 10. Suppose one ball is randomly drawn from each of the boxes. Denote by n_i, the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the…

    2019 · with solution

  20. Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of…

    2019

  21. The number of functions f from \1, 2, 3, …, 20\ onto \1, 2, 3, …, 20\ such that f(k) is a multiple of 3, whenever k is a multiple of 4, is

    2019

  22. The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to

    2019

  23. There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games…

    2019

  24. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same…

    2019 · with solution

  25. If ^nC_4, ^nC_5 and ^nC_6 are in AP, then n can be

    2019 · with solution

  26. If sum_r=1^25 \^50C_r · ^50-rC_25-r\ = K(^50C_25), then, K is equal to

    2019

  27. If sum_i=1^20 ( frac^20C_i-1^20C_i + ^20C_i-1 )^3 = k/21, then k equals

    2019 · with solution

  28. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf, so that the dictionary is always in the middle. The number of such arrangements is

    2018

  29. How many 3 × 3 matrices M with entries from \0, 1, 2\ are there, for which the sum of the diagonal entries of M^T M is 5?

    2017 · with solution

  30. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then, the total number of ways in which X and Y…

    2017

  31. Let S = \1, 2, 3, …, 9\. For k = 1, 2, …, 5, let N_k be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N_1 + N_2 + N_3 + N_4 + N_5 =

    2017

  32. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is

    2016

  33. A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include atmost one…

    2016

  34. The number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is

    2015 · with solution

  35. Let T_n be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_n+1 - T_n = 10, then the value of n is

    2013

  36. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball, is

    2012 · with solution

  37. The number of seven-digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

    2009 · with solution

  38. The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN, is

    2007 · with solution

  39. If r, s, t are prime numbers and p, q are the positive integers such that LCM of p, q is r^2 s^4 t^2, then the number of ordered pairs (p, q) is

    2006 · with solution

  40. The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is

    2002 · with solution

  41. How many different nine-digit numbers can be formed from the number 22 33 55 888 by rearranging its digits so that the odd digits occupy even positions?

    2000

  42. An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible, is

    1998

  43. In a collage of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

    1998

  44. If a_n = sum_r=0^n frac1^nC_r, then sum_r=0^n fracr^nC_r equals

    1998

  45. A five digits number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is

    1989

  46. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the…

    1982

  47. The different letters of an alphabet are given. Words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated, is

    1980 · with solution

  48. The value of the expression ^47C_4 + sum_j=1^5 ^52-jC_3 is

    1980 · with solution

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