Linear Permutations

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JEE Main 2016

LEVELJEE Main

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 :

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

(A)

8 \cdot ^6C_4 \cdot ^7C_4

(B)

6 \cdot 7 \cdot ^8C_4

(C)

6 \cdot 8 \cdot ^7C_4

(D)

7 \cdot ^6C_4 \cdot ^8C_4

JEE Main 2009

LEVELJEE Main

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. Then the number of such arrangement is:

(A)

at least 500 but less than 750

(B)

at least 750 but less than 1000

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

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ?

A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

(A)

^{6} C_{3} \times^{4} C_{2}

(B)

^{4} P_{2} \times^{6} P_{3}

(C)

^{4} C_{2} +^{4} P_{3}

Let $n$ be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is

JEE Advanced 1988

LEVELBoard

Total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs occur together is .........

JEE Advanced 2004

LEVELJEE Main

Prove by permutation or otherwise $\frac{( n ^{2} )!}{( n ! ) ^{n}}$ is an integer ( $n \in I^{+}$ ).

JEE Advanced 1983

LEVELJEE Main

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$ , then show that the number of ways in which they can be seated is $\frac{m ! ( m + 1 )!}{( m - n + 1 )!}$

JEE Advanced 2008

LEVELJEE Main

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 $4 \times 4$ matrix given in the ORS.

List-I

(P)

The number of permutations containing the word ENDEA is

(Q)

The number of permutations in which the letter E occurs in the first and the last positions is

(R)

The number of permutations in which none of the letters D, L, N occurs in the last five positions is

(S)

The number of permutations in which the letters A, E, O occur only in odd positions is

List-II

(1)

5!

(2)

2 \times 5!

(3)

7 \times 5!

(4)

21 \times 5!

JEE Main 2018 (Paper 1)

LEVELJEE Main

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 :

(A)

at least 750 but less than 1000

at least 500 but less than 750

JEE Main 2018 (15 April Evening)

LEVELJEE Main

The number of four letter words that can be formed using the letters of the word BARRACK is :-

JEE Main 2019 (8 April Shift 1)

LEVELJEE Main

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is :

(A)

175

(B)

162

(C)

160

(D)

180

JEE Main 2020 (7 January Shift 1)

LEVELJEE Main

Total number of six-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is

(A)

5^{6}

(B)

\frac{1}{2} (6!)

(C)

6!

(D)

\frac{5}{2} (6!)

JEE Main 2020 (9 January Shift 1)

LEVELBoard

If the number of five digit numbers with distinct digits and 2 at the 10th place is $336 k$ , then $k$ is equal to:

JEE Main 2020 - 7 Jan (Morning)

LEVELBoard

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is

(A)

5^{6}

(B)

\frac{1}{2} (6!)

(C)

6!

(D)

\frac{5}{2} (6!)

JEE Main 2020 - 8 Jan (Evening)

LEVELJEE Main

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

JEE Main 2020 - 2 Sep (Morning)

LEVELJEE Main

If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is

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 :

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

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. Then the number of such arrangement is:

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

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ?

A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs occur together is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Prove by permutation or otherwise (n!)n(n2)!​ is an integer (n∈I+).

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } m men and n women are to be seated in a row so that no two women sit together. If m>n, then show that the number of ways in which they can be seated is (m−n+1)!m!(m+1)!​

List-I

List-II

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 :

The number of four letter words that can be formed using the letters of the word BARRACK is :-

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is :

Total number of six-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the number of five digit numbers with distinct digits and 2 at the 10th place is 336k, then k is equal to:

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is

Prove by permutation or otherwise $\frac{( n ^{2} )!}{( n ! ) ^{n}}$ is an integer ( $n \in I^{+}$ ).

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$ , then show that the number of ways in which they can be seated is $\frac{m ! ( m + 1 )!}{( m - n + 1 )!}$

If the number of five digit numbers with distinct digits and 2 at the 10th place is $336 k$ , then $k$ is equal to: