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All the letters of the word animal are permutated in all possible ways and the permutations these formed are arranged in dictionary order. If the Rank of the word ANIMAL is x, then the permutation with rank x, among the permutations obtained by permurting theletters of the word PERSON and arranging the permutations thus formed in dictionary order is

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NOSPRE

ENOPRS

NOEPRS

ESORNP

answer is D.

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Detailed Solution

Alphabetical order of ANIMAL is

A, A, I, L, M, N

No of words begin with AA=4!

No of words begin with AI=4!

No of words begin with AL=4!

No of words begin with AM=4!

No of words begin with ANA=3!

No of words begin with ANIA=2!

No of words begin with ANIL=2!

No of words begin with ANIMAL=1

Rank of ANIMAL = x = 4(4!)+3!+(2!)2+1

X = 96++4+1=107

Alphabetical order of the word PERSON 1,

E, N, O, P, R, W

No of words begin with EN=4!

No of words begin with EO=4!

No of words begin with EP=4!

No of words begin with ER=4!

No of words begin with ESN=3!

No of words begin with ESON=2!

No of words begin with ESOP=2!

No of words begin with ESORNP=1

∴ Required word = ESORNP

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