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Permutations and Combinations

JEE Main 2024 (Online) 30th January Evening ShiftNumericalMedium📈 Topic in 34% papers+4
Ques. 1JEE 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 .

Answer

11376

Solution

4 from each section =12; the other 3 questions are shared out (B and C can take at most 2 more each).

(A, B, C) =(7, 4, 4): 8C7 6C4 6C4=8 15 15=1800

(6, 5, 4), (6, 4, 5): 2 28 6 15=5040

(5, 5, 5): 8C5 6C5 6C5=56 6 6=2016

(5, 6, 4), (5, 4, 6): 2 56 1 15=1680

(4, 5, 6), (4, 6, 5): 2 70 6 1=840

total =1800+5040+2016+1680+840

=11376

Answer: 11376

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Ques. 2JEE 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 .

Ques. 3JEE 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. 4JEE 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. 5JEE 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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All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
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