JEE MATHEMATICS MCQ: COMBINATIONS

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A binary sequence is an array of 0's and 1's. The number of

n -

digit binary sequence which contain even number of 0's is

View answer and explanation

Correct option: A

{2^{n - 1}}

Option A (

{2^{n - 1}}

) is correct because the number of n-digit binary sequences with an even number of 0's is given by the sum of binomial coefficients corresponding to even numbers, which simplifies to

{2^{n - 1}}

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

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

, then

n

is equal to