JEE Mains · Maths · STD 11 - 6. permutation and combination
There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is
- A 230
- B 220
- C 200
- D 210
Answer & Solution
Correct Answer
(D) 210
Step-by-step Solution
Detailed explanation
\({ }^{12} \mathrm{C}_3-{ }^5 \mathrm{C}_3=210\)
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
- If the area enclosed between the curves \(y = kx^2\) and \(x = ky^2, (k > 0)\), is \(1\) square unit. Then \(k\) isJEE Mains 2019 Hard
- If \(\alpha > \beta > 0\) are the roots of the equation \(ax ^2+ bx +\) \(1=0\), and \(\lim _{x \rightarrow \frac{1}{\alpha}}\left(\frac{1-\cos \left(x^2+b x+a\right)}{2(1-\alpha x)^2}\right)^{\frac{1}{2}}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right)\), then \(k\) is equal toJEE Mains 2023 Hard
- The number of distinct real roots of the equation \(x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0\) isJEE Mains 2022 Hard
- The value of \(\lim _{x \rightarrow 0^{+}} \frac{\cos ^{-1}\left(x-[x]^{2}\right) \cdot \sin ^{-1}\left(x-[x]^{2}\right)}{x-x^{3}},\) where \([ x ]\) denotes the greatest integer \(\leq x\) isJEE Mains 2021 Hard
- If the shortest distance between the lines \(\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}\) and \(\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}\) is \(1 ,\) then the sum of all possible values of \(\lambda\) is :JEE Mains 2024 Hard
- A straight the through a fixed point \((2, 3)\) intersects the coordinate axes at distinct points \(P\) and \(Q.\) If \(O\) is the origin and the rectangle \(OPRQ\) is completed, then the locus of \(R\) is:JEE Mains 2018 Hard
More PYQs from JEE Mains
- \(96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}\) is equal to\(......\).JEE Mains 2023 Medium
- For which of the following ordered pairs \((\mu, \delta)\) the system of linear equations \(x+2 y+3 z=1\) ; \(3 x+4 y+5 z=\mu\) ; \(4 x+4 y+4 z=\delta\) is inconsistent?JEE Mains 2020 Hard
- Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than \(99\%\) isJEE Mains 2019 Hard
- Let the locus of the centre \((\alpha, \beta), \beta>0\), of the circle which touches the circle \(x ^{2}+( y -1)^{2}=1\) externally and also touches the \(x\)-axis be \(L\). Then the area bounded by \(L\) and the line \(y =4\) is.JEE Mains 2022 Hard
- If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{ll}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}\), and \(\mathrm{Q}=\mathrm{A}^{\mathrm{T}} \mathrm{BA}\), then the inverse of the matrix \(\mathrm{A} \mathrm{Q}^{2021} \mathrm{~A}^{\mathrm{T}}\) is equal to :JEE Mains 2021 Hard
- If the mean deviation about the median of the numbers \( k, 2k, 3k, \dots, 1000k \) is 500, then \( k^{2} \) is equal to :JEE Mains 2026 Hard