JEE MATHEMATICS MCQ: COMBINATIONS

1 Easy

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Consider the following statements :
The product of

r

consecutive natural numbers is always divisible by

r

.
The total number of proper positive divisors of 115500 is 94
A pack of 52 cards can be divided equally among four players order in

\frac{{52!}}{{{{\left( {13!} \right)}^4}}}

ways.
Which of the statement given above is/are correct?

View answer and explanation

Correct option: D

All of (1), (2) and (3)

Option D (All of (1), (2) and (3)) is correct because each of the statements is individually true based on number theory and combinatorics principles.

More Questions from COMBINATIONS

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A rectangle of dimension

m \times n

(

m

and

n

being odd) is divided into square of unit length by drawing horizontal and vertical lines. The number of rectangles having side of odd unit length is The number of ways selecting three numbers from 1 to 30, so as to exclude every selection of three consecutive number is: Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams, when a boy plays against a boy and a girl plays against a girl, then n is equal to The number of ways choosing a committee of 4 woman and 5 men from 10 women and 9 men, if Mr.

A

refuses to serve on the committee when Ms.

B

is a member of the committee, is A man has 7 friends. In how many ways he can invite one or more of them for a tea party? If

{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

, then

n

is equal to