HARD

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Let $a_{n}$ denote the number of all $n$ digit positive integers formed by the digits $0, 1$ or both such that no consecutive digits in them are $0 .$ Let $b_{n} =$ the number of such $n$ digit integers ending with digit $1$ and $c_{n} =$ the number of such $n$ digit integers ending with digit $0 .$

Which of the following is correct?

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Important Questions on Permutation and Combination

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

If all the words (with or without meaning) having five letters, formed using the letters of the word

S M A L L

and arranged as in a dictionary; then the position of the word

S M A L L

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of four-digit numbers strictly greater than

4321

that can be formed using the digit

0,1, 2,3, 4,5

(repetition of digits is allowed) is:

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

{}^{56}{P_{r + 6}} : {}^{54}{P_{r + 3} = 30800 : 1}

,

then

r

is equal to

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of

4

letter words (with or without meaning) that can be formed from the eleven letters of the word

EXAMINATION

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The sum of the digits in the unit's place of all the

4

- digit numbers formed by using the numbers

3, 4, 5

and

6

, without repetition is :

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of

4

digit numbers without repetition that can be formed using the digits

1, 2, 3, 4, 5, 6, 7

in which each number has two odd digits and two even digits is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of distinct primes dividing

12! + 13! + 14!

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

How many ways are there to arrange the letters of the word

EDUCATION

so that all the following three conditions hold?
- the vowels occur in the same order

(EUAIO),

- the consonants occur in the same order

(DCTN),

- no two consonants are next to each other.

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of

6

digit number that can be formed using the digits

0, 1, 2, 5, 7

and

9

which are divisible by

11

and no digit is repeated is:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

How many natural numbers

n

are there such that

n! + 10

is a perfect square ?

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

How many numbers of four digits can be made by using the digits $3, 5, 6, 7,$ and $9$ ? (Repetition of digits is not allowed)

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

In how many ways the letters of word 'MACHINE' can be arranged so that vowels will always be together?

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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.....

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

{}^{n}P_{r} = 840

and

{}^{n}C_{r} = 35

, then the value of

r

is equal to

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The largest non-negative integer

k

such that

24^{k}

divides

13!

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of all

3 -

digits numbers

a b c

(in base

10

) for which

10

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

Two girls and four boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?

Important Questions on Permutation and Combination

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