Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Permutations and Combinations question

2018 · Shift 0 · Q27
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Permutations and Combinations
  5. /2018 · Shift 0 · Q27

Permutations and Combinations question

2018 · Shift 0 · Q27

JEE MainMathematicsPermutations and CombinationsMCQ+4 / −1
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :
  1. A
    at least 750 but less than 1000
  2. B
    at least 1000
  3. C
    less than 500
  4. D
    at least 500 but less than 750
View written solutionFree

Correct answer: B

  1. Choose the books

We need to select:

  • 444 novels out of 666
  • 111 dictionary out of 333

Number of ways: (64)(31)=15⋅3=45\binom{6}{4}\binom{3}{1} = 15 \cdot 3 = 45(46​)(13​)=15⋅3=45

  1. Arrange them in a row

There are 555 books total: 444 novels and 111 dictionary.

The dictionary must always be in the middle position. Since there are 555 positions in a row, the middle is the 3rd3^{\text{rd}}3rd position.

So the dictionary is fixed in position 333.

Now arrange the 444 selected novels in the remaining 444 positions: 4!=244! = 244!=24

  1. Total number of arrangements

(64)(31)⋅4!=15⋅3⋅24\binom{6}{4}\binom{3}{1}\cdot 4! = 15 \cdot 3 \cdot 24(46​)(13​)⋅4!=15⋅3⋅24

=45⋅24=1080= 45 \cdot 24 = 1080=45⋅24=1080

  1. Match with the options

Since 1080≥10001080 \ge 10001080≥1000 we get the correct option as B.

  1. Comparison with stored answer

Stored correct answer: B

Our derived answer: B

So they agree.

PreviousNext

More from Permutations and Combinations

  • If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :2017 · MCQ
  • The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is :2017 · MCQ
  • A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party…2017 · MCQ
  • If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :2016 · MCQ
  • The value of r=1∑15​r2(15Cr−1​15Cr​​) is equal to :2016 · MCQ
  • If n−2P2​n+2C6​​ = 11, then n satisfies the equation :2016 · MCQ
  • The sum r=1∑10​(r2+1)×(r!) is equal to :2016 · MCQ
  • If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :2016 · MCQ