Question:
How many chords can be drawn through \(21\) points on a circle?
How many chords can be drawn through \(21\) points on a circle?
Show Hint
Whenever two points are selected on a circle, they determine exactly one chord. Thus, the number of chords from \(n\) points is always \(^{n}C_2\).
Updated On: Jun 15, 2026
- \(105\)
- \(210\)
- \(420\)
- \(840\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Recall the definition of a chord.
A chord of a circle is formed by joining any two distinct points on the circle.
Therefore, the number of chords formed from \(21\) points is equal to the number of ways of choosing \(2\) points from \(21\) points.
Step 2: Use combinations.
The required number of chords is
\[ ^{21}C_2 \]
Using the formula,
\[ ^{n}C_2=\frac{n(n-1)}{2} \]
we get
\[ ^{21}C_2=\frac{21\cdot20}{2} \]
\[ =21\cdot10 \]
\[ =210 \]
Step 3: Final conclusion.
Hence, the number of chords that can be drawn is
\[ \boxed{210} \]
A chord of a circle is formed by joining any two distinct points on the circle.
Therefore, the number of chords formed from \(21\) points is equal to the number of ways of choosing \(2\) points from \(21\) points.
Step 2: Use combinations.
The required number of chords is
\[ ^{21}C_2 \]
Using the formula,
\[ ^{n}C_2=\frac{n(n-1)}{2} \]
we get
\[ ^{21}C_2=\frac{21\cdot20}{2} \]
\[ =21\cdot10 \]
\[ =210 \]
Step 3: Final conclusion.
Hence, the number of chords that can be drawn is
\[ \boxed{210} \]
Was this answer helpful?
0
0
Top AP EAMCET Mathematics Questions
- If $\int \cos x . \cos 2x . \cos 5x dx = A \; \sin 2x + B \sin 4x + C \sin 6x + D \sin 8x + k $ (where $k$ is the arbitrary constant of integration), then $\frac{1}{B} + \frac{1}{C} = $
- If $k$ is one of the roots of the equation $x^2 - 25x + 24 = 0 $ such that $A = \begin{bmatrix}1&2&1\\ 3&2&3\\ 1&1&k\end{bmatrix} $ is a non-singular matrix, then $A^{-1}$ =
- If $p$ and $q$ are respectively the global maximum and global minimum of the function $f(x) = x^2 e^{2x}$ on the interval $[-2, 2]$ , then $pe^{-4} + qe^4 = $
- If $\displaystyle\sum^n_{k - 1} \tan^{-1} \left( \frac{1}{k^2 + k + 1} \right) = \tan^{-1} (\theta) $ , then $\theta$ =
- If the line joining the points $A(\alpha)$ and $B(\beta)$ on the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$ is a focal chord, then one possible values of $\cot \frac{\alpha}{2} . \cot \frac{\beta}{2}$ is
View More Questions
Top AP EAMCET Combinatorics Questions
- If there are 6 alike fruits, 7 alike vegetables, and 8 alike biscuits, then the number of ways of selecting any number of things out of them such that at least one from each category is selected, is:
- A person writes letters to \(6\) friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?
\[ \text{Notation: } D_n=n!\left(\sum_{i=0}^{n}\frac{(-1)^i}{i!}\right) \]
Top AP EAMCET Questions
- If $\int \cos x . \cos 2x . \cos 5x dx = A \; \sin 2x + B \sin 4x + C \sin 6x + D \sin 8x + k $ (where $k$ is the arbitrary constant of integration), then $\frac{1}{B} + \frac{1}{C} = $
- If $k$ is one of the roots of the equation $x^2 - 25x + 24 = 0 $ such that $A = \begin{bmatrix}1&2&1\\ 3&2&3\\ 1&1&k\end{bmatrix} $ is a non-singular matrix, then $A^{-1}$ =
- If only $\frac{1}{51}^{th}$ ot the main current is to be passed through a galvanometer then the shunt required is $R_1$ and if only $\frac{1}{11}^{th}$ of the main voltage is to be developed across the galvanometer, then the resistance required is $R_2$. Then $\frac{R_2}{R_1} =$
- If $p$ and $q$ are respectively the global maximum and global minimum of the function $f(x) = x^2 e^{2x}$ on the interval $[-2, 2]$ , then $pe^{-4} + qe^4 = $
- If $\displaystyle\sum^n_{k - 1} \tan^{-1} \left( \frac{1}{k^2 + k + 1} \right) = \tan^{-1} (\theta) $ , then $\theta$ =
View More Questions