Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?
Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?
- [KVPY 2012]
- A
$10$
- B
$13$
- C
$17$
- D
$20$
Similar Questions
State whether each of the following set is finite or infinite :
The set of lines which are parallel to the $x\,-$ axis
State whether each of the following set is finite or infinite :
The set of lines which are parallel to the $x\,-$ axis
Which of the following are sets ? Justify your answer.
The collection of all natural numbers less than $100 .$
Which of the following are sets ? Justify your answer.
The collection of all natural numbers less than $100 .$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,5\}\in A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,5\}\in A$
Write the following sets in the set-builder form :
$\{ 2,4,6 \ldots \} $
Write the following sets in the set-builder form :
$\{ 2,4,6 \ldots \} $
State whether each of the following set is finite or infinite :
The set of letters in the English alphabet
State whether each of the following set is finite or infinite :
The set of letters in the English alphabet