10 distinct points are taken on a circle. The | vedclass

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

Question

(D) Step $1$: The number of triangles formed by $n$ points on a circle is given by $^{n}C_3$. For $n=10$, number of triangles = $^{10}C_3 = \frac{10 \

Vedclass · Accepted Answer

Statement $I$ is false and statement $II$ is true

Vedclass · Answer

(D) Step $1$: The number of triangles formed by $n$ points on a circle is given by $^{n}C_3$. For $n=10$, number of triangles = $^{10}C_3 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$. Thus, Statement $I$ is false.Step $2$: The number of chords formed by $n$ points on a circle is given by $^{n}C_2$. For $n=10$, number of chords = $^{10}C_2 = \frac{10 	imes 9}{2} = 45$. Thus, Statement $II$ is true.Step $3$: Comparing the results, Statement $I$ is false and Statement $II$ is true.

$10$ distinct points are taken on a circle. Then using these points:
Statement $I$: The number of triangles that can be formed is $100$
Statement $II$: The number of chords that can be formed is $45$
Which of the following is correct?

Similar Questions

The number of diagonals in an octagon is

If $3$ squares are chosen at random from the $64$ squares of a chess board,then the probability that all of them lie along the same diagonal line is

$A$ polygon has $54$ diagonals. Then,the number of its sides is

There are $16$ points in a plane out of which $6$ are collinear. How many lines can be drawn by joining these points?

How many triangles can be formed using $5$ points on a line and $3$ points on a parallel line?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$10$ distinct points are taken on a circle. Then using these points:Statement $I$: The number of triangles that can be formed is $100$Statement $II$: The number of chords that can be formed is $45$Which of the following is correct?