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Permutations and Combinations

JEE Main 2024 (Online) 5th April Evening ShiftMCQEasy📈 Topic in 17% papers+4−1
Ques. 1JEE Main 2024, 5 April (Evening Shift)

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50th word is:

  1. OBBJH
  2. HBBJO
  3. OBBHJ
  4. JBBOH

Answer

(1) OBBJH

Solution

Letters in dictionary order: B, B, H, J, O

Starting with B: 4! = 24 words 24

Starting with H: 4!2! = 12 words 36

Starting with J: 4!2! = 12 words 48

Starting with O: 49th word OBBHJ, 50th word OBBJH

Answer: (1)

Keep practising — Permutations and Combinations

Ques. 2JEE Main 2024, 4 April (Morning Shift)

There are 5 points P1, P2, P3, P4, P5 on the side AB, excluding A and B, of a triangle ABC. Similarly there are 6 points P6, P7, , P11 on the side BC and 7 points P12, P13, , P18 on the side CA of the triangle. The number of triangles, that can be formed using the points P1, P2, , P18 as vertices, is:

  1. 751
  2. 776
  3. 796
  4. 771
Ques. 3JEE Main 2024, 4 April (Evening Shift)

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is .

Ques. 4JEE Main 2024, 1 February (Morning Shift)

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to :

  1. 47
  2. 53
  3. 51
  4. 43
Ques. 5JEE Main 2024, 1 February (Morning Shift)

The number of elements in the set S=\(x, y, z): x, y, z , x+2y+3z=42, x, y, z 0\ equals .

Ques. 6JEE Main 2024, 1 February (Evening Shift)

The lines L1, L2, ,L20 are distinct. For n=1,2,3, ,10 all the lines L2n-1 are parallel to each other and all the lines L2n pass through a given point P. The maximum number of points of intersection of pairs of lines from the set \L1, L2, ,L20\ is equal to .

Ques. 7JEE Main 2024, 31 January (Morning Shift)

The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to .

Ques. 8JEE Main 2024, 31 January (Evening Shift)

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

  1. 130
  2. 136
  3. 142
  4. 406
Ques. 9JEE Main 2024, 31 January (Evening Shift)

If for some m, n; 6Cm+2 (6Cm+1 )+6Cm+2>8C3 and n-1P3:nP4=1:8, then nPm+1+n+1Cm is equal to

  1. 380
  2. 376
  3. 372
  4. 384
Ques. 10JEE Main 2024, 30 January (Evening Shift)

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is .

Ques. 11JEE Main 2024, 29 January (Morning Shift)

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is .

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