JEE Mains · Maths · STD 11 - 6. permutation and combination
There are \(5\) points \(\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \mathrm{P}_4, \mathrm{P}_5\) on the side \(\mathrm{AB}\), excluding \(\mathrm{A}\) and \(\mathrm{B}\), of a triangle \(\mathrm{ABC}\). Similarly there are \(6\) points \(\mathrm{P}_6, \mathrm{P}_7, \ldots, \mathrm{P}_{11}\) on the side \(\mathrm{BC}\) and \(7\) points \(\mathrm{P}_{12}, \mathrm{P}_{13}, \ldots, \mathrm{P}_{18}\) on the side \(\mathrm{CA}\) of the triangle. The number of triangles, that can be formed using the points \(\mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{18}\) as vertices, is :
- A \(776\)
- B \(751\)
- C \(796\)
- D \(771\)
Answer & Solution
Correct Answer
(B) \(751\)
Step-by-step Solution
Detailed explanation
\( { }^{18} \mathrm{C}_3-{ }^5 \mathrm{C}_3-{ }^6 \mathrm{C}_3-{ }^7 \mathrm{C}_3 \) \( =751\)
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 \(f( x + y )=f( x ) f( y )\) and \(\sum \limits_{ x =1}^{\infty} f( x )=2, x , y \in N\) where \(N\) is the set of all natural numbers, then the value of \(\frac{f(4)}{f(2)}\) isJEE Mains 2020 Hard
- The sum of all the \(4 -\) digit distinct numbers that can be formed with the digits \(1,2,2\) and \(3\) isJEE Mains 2021 Medium
- The domain of the function \(f(x)=\frac{\cos ^{-1}\left(\frac{x^{2}-5 x+6}{x^{2}-9}\right)}{\log _{e}\left(x^{2}-3 x+2\right)} \text { is }\)JEE Mains 2022 Hard
- Let the plane \(ax \,\,+\,\,by \,\,+c z=d\) pass through \((2,3,-5)\) and is perpendicular to the planes \(2 x + y -5 z =10\) and \(3 x+5 y-7 z=12\). If \(a, b, c, d\) are integers \(d>0\) and gcd \((lal, |b|,|c|, d)\) \(=1\), then the value of \(a+7 b+c+20 \,d\) is equal toJEE Mains 2022 Hard
- The height of a right circular cylinder of maximum volume inscribed in a sphere of radius \(3\) isJEE Mains 2019 Hard
- Let the lines \( L_1: \vec{r}=\hat{i}+2\hat{j}+3\hat{k}+\lambda(2\hat{i}+3\hat{j}+4\hat{k}) \), \( \lambda \in R \) and \( L_{2}:\vec{r}=(4\hat{i}+\hat{j})+\mu(5\hat{i}+2\hat{j}+\hat{k}) \), \( \mu\in\mathbb{R} \), intersect at the point R. Let P and Q be the points lying on lines \( L_{1} \) and \( L_{2} \), respectively, such that \({|\overrightarrow{ PR }|}=\sqrt{29}\) and \({|\overrightarrow{ PQ }|}=\sqrt{\frac{47}{3}}\). If the point P lies in the first octant, then \( 27(QR)^{2} \) is equal toJEE Mains 2026 Medium
More PYQs from JEE Mains
- In the expansion of \(\left(9x-\dfrac{1}{3\sqrt{x}}\right)^{18}\), \(x>0\), if the term independent of \(x\) is \((221)k\), then \(k\) is equal to:JEE Mains 2026 Medium
- If the tangent at a point on the ellipse \(\frac{{{x^2}}}{{27}} + \frac{{{y^2}}}{3} = 1\) meets the coordinate axes at \(A\) and \(B,\) and \(O\) is the origin, then the minimum area (in sq. units) of the triangle \(OAB\) isJEE Mains 2016 Hard
- Let \(P (3\, sec\,\theta , 2\, tan\,\theta )\) and \(Q\, (3\, sec\,\phi , 2\, tan\,\phi )\) where \(\theta + \phi \, = \frac{\pi}{2}\) , be two distinct points on the hyperbola \(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1\) . Then the ordinate of the point of intersection of the normals at \(P\) and \(Q\) isJEE Mains 2014 Hard
- Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B =\left[\begin{array}{rr}1 & - i \\ 0 & 1\end{array}\right]\), where \(i =\sqrt{-1}\). If \(M = A ^{ T } BA\), then the inverse of the matrix \(AM ^{2023} A ^{ T }\) is \(.........\)JEE Mains 2023 Hard
- If the curve \(y=y(x)\) is the solution of the differential equation \(2\left(x^{2}+x^{5 / 4}\right) d y-y\left(x+x^{1 / 4}\right) d x=2 x^{9 / 4} d x, x > 0\) which passes through the point \(\left(1,1-\frac{4}{3} \log _{e} 2\right),\) then the value of \(y(16)\) is equal to :JEE Mains 2021 Hard
- Let the equation of the plane \(P\) containing the line \(x+10=\frac{8-y}{2}=z\) be \(a x+b y+3 z=2(a+b)\) and the distance of the plane \(P\) from the point \((1,27,7)\) be c. Then \(a^2+b^2+c^2\) is equal to \(.............\).JEE Mains 2023 Hard