Let n(A) = 3, ,n(B) = 3 (where n(S) denotes number of elements in set S ), then number of

English

Gujarati

Hindi

6.Permutation and Combination

normal

Let $n(A) = 3, \,n(B) = 3$ (where $n(S)$ denotes number of elements in set $S$), then number of subsets of $(A \times B)$ having odd number of elements, is-

A

$64$

B

$128$

C

$256$

D

$512$

Solution

$\mathrm{n}(\mathrm{A} \times \mathrm{B})=9$

${\,^9}{{\rm{C}}_1} + {\,^9}{{\rm{C}}_3} + \ldots \ldots + {\,^9}{{\rm{C}}_9} = {2^8} = 256$

Standard 11

Mathematics

Share

Similar Questions

Find the number of words with or without meaning which can be made using all the letters of the word $AGAIN$. If these words are written as in a dictionary, what will be the $50^{\text {th }}$ word?

medium

If all the letters of the word $'GANGARAM'$ be arranged, then number of words in which exactly two vowels are together but no two $'G'$ occur together is-

normal

The number of ways, in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together, is

medium

(JEE MAIN-2023)

How many $6 -$ digit numbers can be formed from the digits, $0,1,3,5,7$ and $9$ which are divisible by $10$ and no digit is repeated?

medium

A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at most $n$ elements is :-

normal