JEE MATHEMATICS MCQ: COMBINATIONS

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The packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 26 cards so that he does not get two cards of the same suit and same denomination, is

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Correct option: A

{\;^{52}}{C_{26}}{.2^{26}}

The correct answer is A (

{\;^{52}}{C_{26}}{.2^{26}}

) because it accounts for choosing 26 cards out of 52 and then considering that each card can come from either of the two packs.

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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