### MCQ's collected from all Engineering Entrance Examinations (Click here)

### Important Formulas :

1.The number of permutations of dissimilar objects taken at a time is denoted by or .

2.The number of permutations of dissimilar objects taken at a time is denoted by

3.The number of permutations of dissimilar objects taken at a time is denoted by

4.The number of permutations of dissimilar objects taken at a time is denoted by

5.The number of permutations of dissimilar objects taken at a time is denoted by

6.Permutations when repetitions are allowed Let and be positive integers such that .Then the number of permutations of dissimilar things taken at a time, when repetition of things is allowed any number of time, is .

7.Permutations when repetitions are allowed The number of permutations of dissimilar things taken at a time with at least one repetition is

8.Circular permutations : The number of circular permutations of dissimilar things taken all at a time is *( n-1 )!*

9.Circular permutations : In case of hanging type circular permutations like garlands of flowers, chains of beads etc., the number of circular permutations of things is .

10.Permutations of objects in which some are like and the rest are different : The number of linear permutations of things in which P things are similar and the rest are dissimilar is

11.Permutations of objects in which some are like and the rest are different : The number of linear permutations of things in which there are similar things of one kind, similar things of second kind and the rest are dissimilar is

12.Combinations The number of combinations of dissimilar things taken at a time is denoted by

13.Combinations

14.Combinations

15.Combinations For

16.Combinations For

17.Combinations If .

18.Combinations If .

19.If similar things are of one kind , similar things are of second kind and similar things are of third kind, then the number of ways of selecting any number of things ( one or more) out of them is

20.The number of ways of dividing dissimilar things into two groups containing and thing is

21.The number of ways of dividing , dissimilar things ( are ditinct) into three groups of ( things is

22.The number ways of dividing dissimilar things into equal groups is .

23.The number ways of distributing dissimilar things equally to persons is .

24.The number of ways that different things of one type and different things of a second type where can be arranged in a row so that no two things of the second type come together is .

25.If are distinct primes and are non-negative integers, then the number of positive integral divisors of (this includes 1 and n.)

26.If are distinct primes and are positive integers, then the sum of distinct positive integral divisors of is .

27.Highest power of a prime in *n*! is where denotes the integral part.

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