Practice Questions on Permutation-Combination
Aptitude Questions and Answers

Difficult Permutation-Combination Question - 1

Q1.

The number of ways of arranging $n$ students in a row such that no two boys sit together and no two girls sit together is $m(m > 100)$.

If one more student is added, then number of ways of arranging as above increases by $200\%$, The value of $n$ is:

A.

$12$

B.

$8$

C.

$9$

D.

$10$

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Difficult Permutation-Combination Question - 2

Q2.

How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?

A.

499

B.

500

C.

375

D.

376

E.

501

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Difficult Permutation-Combination Question - 3

Q3.

How many five digit positive integers that are divisible by 3 can be formed using the digits $0, 1, 2, 3, 4$ and $5$, without any of the digits getting repeating?

A.

15

B.

96

C.

216

D.

120

E.

625

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Difficult Permutation-Combination Question - 4

Q4.

There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man.

If $P$ and $Q$ denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then $P : Q$ equals,

A.

$9 : 1$

B.

$72 : 1$

C.

$10 : 1$

D.

$8 : 1$

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Difficult Permutation-Combination Question - 5

Q5.

How many factors of $2^5 × 3^6 × 5^2$ are perfect squares?

A.

$20$

B.

$24$

C.

$30$

D.

$36$

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