JEE (Main) Mathematics - Permutations and Combinations MCQs

16. How many ways can 5 distinct objects be arranged in a row?
    a) 120
    b) 60
    c) 24
    d) 12
    Answer: a) 120
17. In how many ways can 4 men and 3 women be arranged in a row such that all the men are together?
    a) 168
    b) 5040
    c) 5760
    d) 720
    Answer: c) 5760
18. How many ways can 3 books be chosen from 8 distinct books?
    a) 56
    b) 56
    c) 56
    d) 56
    Answer: a) 56
19. From a group of 5 men and 6 women, how many different ways can a committee of 4 people be selected such that the committee consists of exactly 2 men and 2 women?
    a) 300
    b) 150
    c) 100
    d) 200
    Answer: a) 300
20. How many ways can 4 identical red balls and 3 identical green balls be arranged in a row?
    a) 210
    b) 120
    c) 35
    d) 70
    Answer: d) 70
21. A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if repetition is allowed and the letters must be in uppercase?
    a) 17576
    b) 456
    c) 175760
    d) 26000
    Answer: c) 175760
22. How many different ways can a team of 3 men and 2 women be selected from a group of 7 men and 8 women?
    a) 280
    b) 300
    c) 2800
    d) 3500
    Answer: a) 280
23. How many ways can 3 letters be selected from the word “COMPUTER”?
    a) 56
    b) 120
    c) 60
    d) 35
    Answer: c) 60
24. How many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?
    a) 120
    b) 24
    c) 5
    d) 60
    Answer: a) 120
25. In how many ways can a set of 6 people be divided into two groups of 3 people each?
    a) 100
    b) 200
    c) 80
    d) 10
    Answer: d) 10
26. How many different words can be formed using the letters of the word “STATISTICS”?
    a) 5040
    b) 2520
    c) 362880
    d) 15120
    Answer: b) 2520
27. How many different words can be formed using the letters of the word "EQUATION" if the vowels must come together?
    a) 5040
    b) 360
    c) 840
    d) 720
    Answer: c) 840
28. How many ways can 2 cards be drawn from a deck of 52 cards if repetition is allowed?
    a) 52
    b) 2704
    c) 1024
    d) 270
    Answer: b) 2704
29. In how many ways can a committee of 4 members be formed from a group of 5 men and 6 women, such that at least one woman is included?
    a) 230
    b) 250
    c) 300
    d) 350
    Answer: a) 230
30. How many ways can 5 people sit around a circular table?
    a) 120
    b) 24
    c) 60
    d) 120
    Answer: a) 120

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