JEE Advanced (Matrix Match): Permutations & Combinations | Chapter-wise Tests for JEE Main & Advanced PDF Download

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Each question contains statements given in two columns, which have to be matched. The statements in Column-I are labelled A, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in ColumnII. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example :

If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s then the correct darkening of bubbles will look like the given.

Q.1. 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.             (2008)
Column I                                                                                                      Column II 

(A) The number of permutations containing the word ENDEA is           (p) 5!
 (B) The number of permutations in which the letter E occurs in           (q) 2 × 5!
 the first and the last positions is
 (C) The number of permutations in which none of the letters                (r) 7 × 5!
 D, L, N occurs in the last five positions is
 (D) The number of permutations in which the letters A, E, O                (s) 21 × 5!
 occur only in odd positions is

Ans.  (A)-p; (B)-s; (C)-q; (D)-q (A) 

Sol.
(A) For the permutations containing the word ENDEA we consider 'ENDEA' as single letter. Then we have total ENDEA, N, O, E, L i.e. 5 letters which can be arranged in 5! ways. ∴ (A) → (p)

(B) If E occupies the first and last position, the middle 7 positions can be filled by N, D, E, A, N, O, L.
These can be arranged in = 21 x 5! ways.

∴ (B) → (s)

(C) If none of the letters D, L, N occur in the last five positions then we should arrange D, D, L, N at first four positions and rest five i.e. E, E, E, A,O at last five positions. This can be done in

 ways . (C) → (q)

(D) As per question A, E, E, E, O can be arranged at 1st, 3rd, 5th, 7th  and 9th positions and rest N, D, N, L at rest 4 positions. This can be done in

ways = 2 x 5! ways (D) → (q)