Question:
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are
Show Hint
Total triangles sharing NO sides $= \binom{n}{3} - n - n(n-4)$.
Updated On: May 14, 2026
- $1140$
- $800$
- $340$
- $20$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
The total number of triangles from $n$ vertices is $\binom{n}{3}$. We must subtract triangles that use one side or two sides of the polygon.
Step 2: Meaning
For an $n$-sided polygon, the number of triangles with no sides shared is given by the formula: $\frac{n(n-4)(n-5)}{6}$.
Step 3: Analysis
Here $n = 20$. Triangles sharing no sides $= \frac{20(20-4)(20-5)}{6}$. $= \frac{20 \times 16 \times 15}{6} = \frac{4800}{6} = 800$.
Step 4: Conclusion
There are 800 such triangles. Final Answer: (B)
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Combinations Questions
- A committee of 11 members is to be formed out of 8 males and 5 females. If \( m \) is the number of ways the committee is formed with at least 6 males and \( n \) is the number of ways with at least 3 females, then:
- If $^{11}\text{C}_4 + {^{11}\text{C}_5} + {^{12}\text{C}_6} + {^{13}\text{C}_7} = {^{14}\text{C}_r}$, then the value of $r$ is
- The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is ______.
- There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is ______.
- If \( n^+ C_{n+1} - n^3 C_n = 15(n + 2) \), then \( n = \)
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions