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← IIT-JEE 2008 · Paper 2
MathematicsMatrix match+6Question 22 of 66

IIT-JEE 2008 · Paper 2, Mathematics question 22

Consider all possible permutations of the letters of the word ENDEANOEL.

Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I

  • A
    The number of permutations containing the word ENDEA is
  • B
    The number of permutations in which the letter E occurs in the first and the last positions is
  • C
    The number of permutations in which none of the letters D, L, N occurs in the last five positions is
  • D
    The number of permutations in which the letters A, E, O occur only in odd positions is

Column II

  • P
    5!
  • Q
    2 × 5!
  • R
    7 × 5!
  • S
    21 × 5!
Mark every match for each entry
PQRS
A
B
C
D
Answer and worked solution

Official answer: A → P; B → S; C → Q; D → Q

The word ENDEANOEL has 9 letters: E ×3, N ×2, D, A, O, L.

  • A. Treat ENDEA as one block; the remaining letters N, O, E, L are all different. Five distinct units: 5!5!. → P.
  • B. E first and last; the middle seven are N, D, E, A, N, O, L: 7!2!=2520=21×5!\dfrac{7!}{2!}=2520=21\times5!. → S.
  • C. D, L, N, N fill the first four places (4!2!=12\frac{4!}{2!}=12 ways) and E, E, E, A, O the last five (5!3!=20\frac{5!}{3!}=20): 240=2×5!240=2\times5!. → Q.
  • D. A, E, E, E, O fill the five odd places (20 ways) and N, N, D, L the four even places (12 ways): 240=2×5!240=2\times5!. → Q.

Answer: A → P; B → S; C → Q; D → Q

Topics:Permutations
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