AP EAMCET · Maths · Permutation Combination
There are 10 points in a plane, out of these 6 are collinear. If \(N\) is the total number of triangles formed by joining these points, then \(N=\)
- A \(120\)
- B \(850\)
- C \(100\)
- D \(150\)
Answer & Solution
Correct Answer
(C) \(100\)
Step-by-step Solution
Detailed explanation
If all 10 points are collinear, then number of triangles formed \({ }^{10} C_3=\frac{10 !}{3 ! 7 !}=\frac{10 \times 9 \times 8}{3 \times 2}=120\) Triangles formed using 6 collinear points \({ }^6 C_3=20\) Therefore, required number of triangles \(120-20=100\)
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 \(f(2)=4\) and \(f^{\prime}(2)=1\), then
\[
\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}
\]
is equal toAP EAMCET 2008 Medium - If the chord of the ellipse \(\frac{x^2}{4}+\frac{y^2}{9}=1\) having \((1,1)\) as its middle point is \(\dot{x}+\alpha y=\beta\), thenAP EAMCET 2024 Easy
- The equation of the base of an equilateral triangle is \(x+y=2\) and its opposite vertex is \((2,1)\). If \(m_1, m_2\) are the slopes of the other two sides and the length of its side is a, then \(\left|m_1-m_2\right|+a \sqrt{2}=\)AP EAMCET 2025 Hard
- Let \(A=\{1,2,3,4,5,6\}\) number of functions \(f\) from \(A\) to \(A\) such that \(f(m)+f(n)=7\), whenever \(m+n=7\) isAP EAMCET 2021 Hard
- A vector of magnitude \(\sqrt{51}\) which makes equal angles with the vectors \(\bar{a}=\frac{1}{3}(\bar{i}-2 \bar{j}+2 \bar{k})\), \(\bar{b}=\frac{1}{5}(-4 \bar{i}-3 \bar{k})\) and \(\bar{c}=\bar{j}\), isAP EAMCET 2017 Medium
- If the roots of the equation \(4 x^3-12 x^2+11 x+m=0\) are ir arithmetic progression, then \(m=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- If the system of simultaneous linear equations \(x+y-z=6,4 x+y+z=2\) and \(x+k y+z=-8\) has a unique solution \(x=2\), \(y=\beta, z=\gamma\), then the value of \(k\) satisfies the following quadratic equationAP EAMCET 2022 Easy
- The magnetic induction and the intensity of magnetic field inside an iron core of an electromagnet are \(1 \mathrm{~Wb} \mathrm{~m}^{-2}\) and \(150 \mathrm{Am}^{-1}\), respectively. The relative permeability of iron is
\(\left(\mu_0=4 \pi \times 10^{-7}\right.\) henry \(\left./ \mathrm{m}\right)\)AP EAMCET 2004 Easy - A body is projected at an angle other than \(90^{\circ}\) with the horizontal with same velocity. If the time of ascent of the body is ls, then the maximum height it can reach is (Take, \(g=10 \mathrm{~ms}^{-2}\) )AP EAMCET 2019 Easy
- The \(\mathrm{p} K_a\) values of four carboxylic acids are \(4.76,4.19,0.23\) and 3.41 respectively. The \(\mathrm{p} K_a\) value of strongest carboxylic acid among them isAP EAMCET 2011 Easy
- In \(I_n=\int \frac{\sin n x}{\sin x} d x\) for \(n=1,2,3, \ldots\), then \(I_6=\)AP EAMCET 2019 Hard
- Let \([t]\) represents the greatest integer not exceeding \(t\) and \(\mathrm{C}=1-2 \mathrm{e}^2\). If the function
\(f(x)=\left\{\begin{array}{cc}
{\left[e^x\right],} & x < 0 \\
a e^x+[x-2], & 0 \leq x < 2 \\
{\left[e^{-x}\right]-C,} & x \geq 2
\end{array}\right.\)
is continuous at \(\mathrm{x}=2\), then \(\mathrm{f}(\mathrm{x})\) is discontinuous atAP EAMCET 2023 Easy