A number x is chosen at random from the set { | vedclass

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

Question

(A) We are given the inequality $\frac{(x-10)(x-50)}{(x-30)} \ge 0$. Using the wavy curve method (sign scheme) for the expression $f(x) = \frac{(x-10)

Vedclass · Accepted Answer

$0.71$

Vedclass · Answer

(A) We are given the inequality $\frac{(x-10)(x-50)}{(x-30)} \ge 0$. Using the wavy curve method (sign scheme) for the expression $f(x) = \frac{(x-10)(x-50)}{(x-30)}$,the critical points are $x = 10, 30, 50$. The sign of $f(x)$ in different intervals is: - For $x - For $10 \le x - For $30 - For $x \ge 50$: $f(x) \ge 0$ Since $x \in \{1, 2, \dots, 100\}$,we look for integers $x$ in the intervals $[10, 30)$ and $[50, 100]$. In the interval $[10, 30)$,the integers are $\{10, 11, \dots, 29\}$. The number of such integers is $29 - 10 + 1 = 20$. In the interval $[50, 100]$,the integers are $\{50, 51, \dots, 100\}$. The number of such integers is $100 - 50 + 1 = 51$. The total number of favorable outcomes is $20 + 51 = 71$. The total number of possible outcomes is $100$. Therefore,$P(A) = \frac{71}{100} = 0.71$.

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, \dots, 100\}$. Define the event: $A =$ the chosen number $x$ satisfies $\frac{(x - 10)(x - 50)}{(x - 30)} \ge 0$. Then $P(A)$ is

Similar Questions

The probability of getting a total of $5$ or $6$ in a single throw of $2$ dice is

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is

$A$ pair of dice is thrown twice in succession. The probability of getting prime numbers on both the dice in the first throw and composite numbers on both the dice in the second throw is

Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random,the probability that $A$ and $B$ have the same number of elements is:

$A$ die is thrown. Find the probability of the following event: $A$ number less than or equal to $1$ will appear.

Vedclass Test Series

Exam Paper Generator

Online Exam Module