KCET · Maths · Permutation Combination
\(10\) 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?
- A Both Statement I and Statement II are true
- B Both Statement I and Statement II are false
- C Statement I is true and Statement II is false
- D Statement I is false and Statement II is true
Answer & Solution
Correct Answer
(D) Statement I is false and Statement II is true
Step-by-step Solution
Detailed explanation
Number of points on the circle is \(10\).
To form a triangle, \(3\) points are required. Since all points are on a circle, no three points are collinear.
Number of triangles \(= ^{10}C_{3} = \dfrac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120\)
Statement I is false.
To form a chord, \(2\) points are required.
Number of chords \(= ^{10}C_{2} = \dfrac{10 \times 9}{2 \times 1} = 45\)
Statement II is true.
Answer: Statement I is false and Statement II is true
To form a triangle, \(3\) points are required. Since all points are on a circle, no three points are collinear.
Number of triangles \(= ^{10}C_{3} = \dfrac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120\)
Statement I is false.
To form a chord, \(2\) points are required.
Number of chords \(= ^{10}C_{2} = \dfrac{10 \times 9}{2 \times 1} = 45\)
Statement II is true.
Answer: Statement I is false and Statement II is true
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int \sqrt{\operatorname{cosec} x-\sin x} d x\) is equals toKCET 2023 Medium
- The function \(f(x)=\left\{\begin{array}{ll}e^x+a x & , x \lt 0 \\ b(x-1)^2 & , \quad x \geq 0\end{array}\right.\) is differentiable at \(x=0\). ThenKCET 2025 Medium
- The vectors \(\mathbf{A B}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}\) and \(\mathbf{A C}=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) are the sides of a \(\triangle A B C\), The length of the median through \(A\) isKCET 2024 Easy
- If \([x]\) is the greatest integer function not greater than \(x\), then \(\int_{0}^{11}[x] d x\) is equal toKCET 2012 Medium
- \(\int \frac{\cos ^{n-1} x}{\sin ^{n+1} x} d x(\) where, \(n \neq 0)\) is equal toKCET 2013 Medium
- If \(x^{x}=y^{y}\), then \(\frac{d y}{d x}\) isKCET 2007 Medium
More PYQs from KCET
- The area of the region bounded by \(y=-\sqrt{16-x^{2}}\) and \(X\)-axis isKCET 2021 Medium
- If \(\mathbf{i}+\mathbf{j}-\mathbf{k}\) and \(2 \mathbf{i}-3 \mathbf{j}+\mathbf{k}\) are adjacent sides of a parallelogram, then the lengths of its diagonals areKCET 2012 Easy
- The carbonyl compound that does not undergo aldol condensation isKCET 2020 Medium
- \( \int_{0}^{\frac{\pi}{2}} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x \) is equal toKCET 2017 Hard
- If lines \(\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}\) and \(\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}\) are mutually perpendicular, then \(k\) is equal toKCET 2024 Easy
- In the given transcription unit, identify the regions the regions I and II respectively.
KCET 2018 Hard