Here are model questions from the topic permutations and combinations. These questions are useful for JEE Main appearing candidates. Answers are also given at the end of the questions.

3. If there are 2 flights, 5 trains and 20 buses from A to B, then no. of ways going from A to B is

1) 27 2) 200 3) 20P7 4) 20P2.

4. There are 6 doors in a class room. The no. of ways in which a student can enter the room and leave it by a different room is

1) 36 2) 30 3) 6P5 4) 6C5

5. When 4 letter words are written using letters of the word “ATHEISM” then no. of times 'S' is written is

1) 840 2) 360 3) 420 4) 480

6. When 5 boys and 5 girls are arranged in a row at random, then no. of possible arrangements in which boys and girls sit alternatively is

1) 2 × (5!)2 2) (5!)2 3) 3.5!6! 4) 2 × 5! × 6!

7. No. of ways of giving away 4 prizes to 5 students is

1) 45 2) 54 3) 5P4 4) 5C4

8. When letters of the word LABOUR are used to form 4 letter words allowing repetition then, out of them, no. of arrangements in

which at least one letter is repeated is

1) 46 2) 64 3) 6P4 4) 64-6P4

9. The sum of all the 5 digit numbers formed by using the digits {2, 3, 4, 5, 6} is

1) 5333280 2) 53280 3) 342980 4) 432880

10. The sum of all the 4 digit numbers formed by {0, 2, 3, 5} is

1) 66660 2) 64440 3) 2220 4) 688880

11. When 5 letters are arranged in 5 addressed envelopes, without looking at the address, then no. of possible arrangements in which

all the letters enter into right envelopes is

1) 76 2) 1 3) 44 4) 119

12. A number lock has 5 rings each marked with the digits 0 to 9. Then the no. of all possible unsuccessful attempts to open the lock

is

1) 100000 2) 99999 3) 1 4) 9999

14. When 4 dice are thrown together, then no. of possible ways in which at least one die shows '2' is

1) 625 2) 1296 3) 671 4) 670

15. 9 balls are to be arranged one in each of 9 boxes. But 5 of the balls are too big for 3 boxes. Then no. of ways of arranging them

is

1) 17280 2) 120 3) 720 4) 9!

16. If the letters of the word “GARDEN” are arranged in all possible ways and the resulting words are arranged as in dictionary then

rank of the word “DANGER” is

1) 379 2) 375 3) 135 4) 175

17. Total no. of arrangements by taking any no. of letters from letters of the word KANPUR is

1) 120 2) 720 3) 1956 4) 1695

18. When all the letters of the word RANDOM are arranged in all possible ways then no. of arrangements in which there are exactly 2

letters between R and D is

1) 720 2) 120 3) 72 4) 144

19. While listing the natural numbers 1 to 1000, number of times the digit '7' is used is

1) 200 2) 300 3) 700 4) 350

20. The number of ways in which 5 beads of different colours can form a necklace is

1) 120 2) 60 3) 24 4) 12

21. The number of ways of arranging 6 objects around a circle taking any 4 at a time is

1) 90 2) 60 3) 72 4) 36

22. The number of ways in which 7 ladies and 7 gentlemen sit around a circular table, so that no two ladies sit together is

1) 6!8! 2) 6!7! 3) 7!8! 4) 7!

23. Number of way of arranging 6 men and 3 ladies in a round table so that each man has a lady adjacent to them is

1) 0 2) 720 3) 1440 4) 8!

27. The ratio of 24Cr to 25Cr when each of them has the greatest value possible is

1) 12:25 2) 13:25 3) 13:24 4) 1:2

28. A father takes 8 children, 3 at a time to the zoo, as often as he can take without the same three together more than once. If the

number of times each children can go is x and the number of times he can go is y, then (x, y) =

1) (21, 53) 2) (20, 56) 3) (20, 53) 4) (21, 56)

29. The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is

1) 16C11 2) 16C5 3) 16C9 4) 20C9

30. There are two cars of which one holds not more than 5 and the other not more than 4. In how many ways can a party of 8 people

go for excursion in the two cars?

1) 8400 2) 126 3) 124 4) 6400

31. Out of 8 gentlemen and 5 ladies a committee of 5 is to be formed. The number of ways in which this can be done so as to

always include atleast 2 ladies is

1) 321 2) 881 3) 1234 4) 1785

33. A man has 7 relatives, 4 women and 3 men. His wife also has 7 relatives, 3 women and 4 men. The number of ways in which they

can invite 3 women and 3 men so that 3 of them are the man's relatives and 3 his wife's is

1) 485 2) 584 3) 720 4) 1024

34. There are 12 points in a plane, 5 only of which are collinear. The number of triangles which can be formed by joining the points is

1) 210 2) 220 3) 35 4) 105

35. The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using points as vertices is

1) 220 2) 205 3) 235 4) 325

KEY:

1) 3 2) 1 3) 1 4) 2 5) 4 6) 1 7) 2 8) 4 9) 1 10) 2 11) 2 12) 2 13) 4

14) 3 15) 1 16) 3 17) 3 18) 4 19) 2 20) 4 21) 1 22) 2 23) 3 24) 2 25) 3 26) 3 27) 2 28) 4 29) 3 30) 2 31) 2 32) 3 33) 1 34) 1 35) 2 36) 1.