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Permutations and Combinations

JEE Main 2024 (Online) 29th January Evening ShiftMCQMedium📈 Topic in 21% papers+4−1
Ques. 1JEE Main 2024, 29 January (Evening Shift)

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

  1. 18
  2. 16
  3. 12
  4. 15

Answer

(4) 15

Solution

∵ Books and shelves are both identical ⇒ only the set of numbers on the shelves matters (partitions of 8 into at most 4 parts).

1 shelf used: (8) → 1 way

2 shelves used: (7,1),(6,2),(5,3),(4,4) → 4 ways

3 shelves used: (6,1,1),(5,2,1),(4,3,1),(4,2,2),(3,3,2) → 5 ways

4 shelves used: (5,1,1,1),(4,2,1,1),(3,3,1,1),(3,2,2,1),(2,2,2,2) → 5 ways

Total =1+4+5+5=15

Answer: (4)

Keep practising — Permutations and Combinations

Ques. 2JEE Main 2024, 27 January (Morning Shift)

n-1Cr= (k2-8 )nCr+1 if and only if :

  1. 2 2<k<2 3
  2. 2 2<k 3
  3. 2 3<k<3 3
  4. 2 3<k 3 2
Ques. 3JEE Main 2024, 27 January (Evening Shift)

Let = (4!)!(4!)3! and = (5!)!(5!)4!. Then :

  1. and
  2. and
  3. and
  4. and

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