Let S = {0, 1, 2, 3, ldots, 100}. The number | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the set $S = \{0, 1, 2, \ldots, 100\}$.We need to find the number of ordered pairs $(x, y)$ such that $x, y \in S$,$x 
eq y$,and $x + y = 1

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(D) Given the set $S = \{0, 1, 2, \ldots, 100\}$.We need to find the number of ordered pairs $(x, y)$ such that $x, y \in S$,$x 
eq y$,and $x + y = 100$.The possible pairs $(x, y)$ are:$(0, 100), (1, 99), (2, 98), \ldots, (49, 51)$.Note that the pair $(50, 50)$ is excluded because the condition $x 
eq y$ must be satisfied.Also,the pairs $(51, 49), (52, 48), \ldots, (100, 0)$ are distinct from the first set because the order matters in selecting $x$ and $y$.Counting the pairs from $x = 0$ to $x = 49$,we have $50$ pairs.Counting the pairs from $x = 51$ to $x = 100$,we have $50$ pairs.Total number of ways = $50 + 50 = 100$.

Let $S = \{0, 1, 2, 3, \ldots, 100\}$. The number of ways of selecting $x, y \in S$ such that $x \neq y$ and $x + y = 100$ is

Similar Questions

The smallest positive integer $n$,for which $n! < {\left( {\frac{{n + 1}}{2}} \right)^n}$ holds is

The number of five-digit numbers that are divisible by $6$ which can be formed by choosing digits from $\{0, 1, 2, 3, 4, 5\}$,when repetition is allowed,is

The sum of all the $4$-digit numbers formed by taking all the digits from ${2, 3, 5, 7}$ without repetition is:

Words with or without meaning are to be formed using all the letters of the word $EXAMINATION$. The probability that the letter $M$ appears at the fourth position in any such word is:

If $f(n) = n! (31-n)!$,where $n \in \{0, 1, 2, \ldots, 31\}$,then the minimum value of $f(n)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module