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Permutations and Combinations

JEE Main 2024 (Online) 29th January Morning ShiftNumericalEasy📈 Topic in 17% papers+4
Ques. 1JEE 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 .

Answer

553

Solution

Letters in dictionary order: E, G, N, T, T, W, Y (T twice)

Starting with E: 6!2!=360

Starting with GE: 5!2!=60; with GN: 60

Starting with GTE, GTN, GTT: 3 4!=72 (remaining letters distinct)

Starting with GTW: the first word is GTWENTY itself (E, N, T, Y in order): 1

Serial number =360+60+60+72+1=553

Answer: 553

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Ques. 2JEE 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
Ques. 3JEE 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. 4JEE 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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