Class 11th maths Permutations and Combinations JEE MAIN PYQ
Class 11th maths Permutations and Combinations JEE MAIN PYQ
1. All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is [JEE Main 2019, 8 April Shift-I]
(a) 180 (b) 175 (c) 160 (d) 162
2. 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 [JEE Main 2019, 8 April Shift-II]
(a) 306 (b) 310 (c) 360 (d) 288
3. 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, then
[JEE Main 2019, 9 April Shift-I]
(a) m = n = 68 (b) m + n = 68 (c) m = n = 78 (d) n =m – 8
4. 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 [JEE Main 2019, 10 April Shift-I]
(a) 60 (b) 72 (c) 48 (d) 36
5. 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 number of beams is
[JEE Main 2019, 10 April Shift-II]
(a) 180 (b) 210 (c) 170 (d) 190
6. The number of ways of choosing 10 objects out of 31 objects ofwhich 10 are identical and the remaining 21 are distinct, is [JEE Main 2019, 12 April Shift-I]
(a) 2 20 −1 (b) 221 (c) 220 (d) 2 20 +1
7. 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, is 1750, then n is equal to
[JEE Main 2019, 12 April Shift-II]
(a) 28 (b) 27 (c) 25 (d) 24
8. 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 team, is
[JEE Main 2019, 9 Jan Shift-I]
(a) 350 (b) 500 (c) 200 (d) 300
9. 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 [JEE Main 2019, 9 Jan Shift-II]
(a) 374 (b) 375 (c) 372 (d) 250
10. Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni , the label of the ball drawn from the ith box, (i = 1,2,3). Then, the number of ways in which the balls can be chosen such that n1 <n2 <n3 is [JEE Main 2019, 12 Jan Shift-I]
(a) 82 (b) 120 (c) 240 (d) 164
11. 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 played between the men and the women by 84, then the value of m is [JEE Main 2019, 12 Jan Shift-II]
(a) 12 (b) 11 (c) 9 (d) 7
12. 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 [JEE Main 2018]
(a) atleast 1000 (b) less than 500
(c) atleast 500 but less than 750 (d) atleast 750 but less than 1000
13. 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 andY together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X andY are in this party, is [JEE Main 2017 (Offline)]
(a) 485 (b) 468 (c) 469 (d) 484
14. 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 [JEE Main 2016 (Offline)]
(a) 46th (b) 59th (c) 52nd (d) 58th
15. Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A × B, each having atleast three elements are [JEE Main 2015]
(a) 219 (b) 256 (c) 275 (d) 510
16. The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8 without repetition, is
[JEE Main 2015]
(a) 216 (b) 192 (c) 120 (d) 72
17. Let A and B be two sets containing 2 elements and 4 elements, respectively. The number of subsets of AX B having 3 or more elements is [JEE Main 2013]
(a) 256 (b) 220 (c) 219 (d) 211
18. LetTn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1 –Tn =10, then the value of n is [JEE Main 2013]
(a) 7 (b) 5 (c) 10 (d) 8
19. Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is [AIEEE 2012]
(a) 880 (b) 629 (c) 630 (d) 879
20. Statement I The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty, is 9C3.
Statement II The number of ways of choosing any 3 places from 9 different places is 9C3
(a) Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I
(b) Statement I is true, Statement II is false
(c) Statement I is false, Statement II is true
(d) Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I [AIEEE 2011]
21. There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then [AIEEE 2011]
(a) N >190 (b) N <=100 (c)100< N <=140 (d)140< N <=190
22. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is [AIEEE 2009]
(a) atleast 500 but less than 750 (b) atleast 750 but less than 1000
(c) atleast 1000 (d) less than 500
23. In a shop, there are five types of ice-creams available. A child buy six ice-creams.
Statement I The number of different ways the child can buy the six ice-creams is 10C5. [AIEEE 2008]
Statement II The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row.
(a) Statement I is false, Statement II is true
(b) Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I
(c) Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I
(d) Statement I is true, Statement II is false
24. How many different words can be formed by jumbling the letters in the word ‘MISSISSIPPI’ in which no two S are adjacent? [AIEEE 2008]
25. At an election, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for atleast one candidate, then the number of ways in which he can vote, is [AIEEE 2006]
(a) 6210 (b) 385 (c) 1110 (d) 5040
26. If the letters of the word ‘SACHIN’ are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number [AIEEE 2005]
(a) 602 (b) 603 (c) 600 (d) 601
27. The range of the function f(x)=7-xPx-3 [AIEEE 2004]
(a) {1, 2, 3} (b) {1, 2, 3, 4, 5, 6} (c) {1, 2, 3, 4} (d) {1, 2, 3, 4, 5}
28. How many ways are there to arrange the letters in the word ‘GARDEN’ with the vowels in alphabetical order?
[AIEEE 2004]
(a) 120 (b) 240 (c) 360 (d) 480
29. The number of ways of distributing 8 identical balls in 3 distinct boxes, so that none of the boxes is empty, is
[AIEEE 2004]
(a) 5 (b) 21 (c) 38 (d) 8c3
30. A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is [AIEEE 2003]
(a) 140 (b) 196 (c) 280 (d) 346
31. The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by [AIEEE 2003]
(a) 6! × 5! (b) 30 (c) 5! × 4! (d) 7! × 5!