Question

If all the arrangements formed using all the letters of the following words are arragned in the order
of dictionary then what will be the rank of that word ?
(1) PINTU
(2) NURI
(3) NIRAL
(4) SUMAN​

Answer 1

Answer:

83Q:

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number :

A) 601

B) 600

C) 603

D) 602

Answer: A) 601

Answer 2

PINTU

1) PINTU

: There are 5 words P.,I,N, T, U in the letter PINTU

The five letters Can be arranged in 5p5 =120

Now In alphabatic order it is INPTU

Number of word I at a first Place

= 1p1 × 4p4 = 24

Number of word N at a first place = 1p1 x 4p4 = 24

Number of word P at a first place I at a second place N at a third Place are PINTU, PINUT

.:: Dictionary order of the word PINTU = 24+24+1 = 49

(2) NURI

There are four word N,U.R.I in the Lettere NURI

The four letters Can be arranged In=4P4

• Now. In alphabatic order it is INRU

Number of word I at a first place = 1px 3p3 = 6

Number of word N at a First Place I at a second place

= 1p₁ x 1ps x 2p₂ = 2

Number of word N at first place R at second place

= 1p1 × 1p1 × 2p2 = 2

Number of word N at a first place U at a second place I at a third place

1p1 x 1p1 x 1p1 x 1p1 = 1

Number of word N at a first place U at a second R at a third I at fourth place are NURI

Dictionary order of word NURI = 6+2+2+1+ 1 = 12

(3) NIRAL

There are 5 letters N, I, R, A, L in the word NIRAL.

These 5 letters can be arranged in 5P5 = 5! = 120 ways.

Now, we have to obtain the order of the word NIRAL from all 120 arrangements as per the dictionary order.

The alphabetical order of all letters of the word NIRAL is A, I, L, N, R.

Number of words with A at the first place = 1P1 × 4P4 = 1 × 4! = 24

Number of words with I at the first place = 1P1 × 4P4 = 1 × 4! = 24

Number of words with L at the first place = 1P1 × 4P4 = 1 × 4! = 24

Number of words with N at the first place and A at the second place = 1P1 ×1P1 × 3P3 = 1 × 1 × 3! = 1 × 6 = 6.

Number of words with N at the first place, I at the second place and A at the third place = 1P1 × 1P1 × 1P1 × 2P2 = 1 × 2! = 2

Number of words with N at the first place, I at the second place and L at the third place = 1P1 × 1P1 × 1P1 × 2P2 = 1 × 2! = 2

Now, the words with N at the first place, I at the second place, and R at the third place are NIRAL, NIRLA,

∴ Dictionary order of the word NIRAL = 24+ 24+ 24 + 6 + 2 + 2 + 1 = 83

(4). SUMAN

There are 5 letters S, U, M, A, N in the word SUMAN.

These 5 letters can be arrange in 5P5 = 5! = 120 ways.

Now, we have to obtain the order of the word SUMAN from all 120 arrangements as per the dictionary order.

The alphabetical order of all letters of the word SUMAN is A, M, N, S, U.

Number of words with A at the first place = 1P1 × 4P4 = 1 × 4! = 24

Number of words with M at the first place = 1P1 × 4P4 = 1 × 4! = 24

Number of words with N at the first place = 1P1 × 4P4 = 1 × 4! = 24

Number of words with S at the first place and A at the second place = 1P1 × 3P3 = 1 × 3! = 6

Number of words with S at the first place and M at the second place = 1P1 × 3P3 = 1 × 3! = 6

Number of words with S at the place and N at the second place = 1P1 × 3P3 = 1 × 3! = 6

Number of words with S at the first place, U at the second place and A at the third place = 1P1 × 1P1 × 1P1 × 2P2 = 1 × 2! = 2

Now, the words with S at the first place, U at the second place and M at the third place are SUMAN and SUMNA.

∴ Dictionary order of the word SUMAN is = 24+ 24+ 24 + 6 + 6 + 6 + 2+1 = 93