JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The urns \(A, B\) and \(C\) contain \(4\) red, \(6\) black;\(5\) red,\(5\) black and \(\lambda\) red,\(4\) black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn \(C\) is \(0.4\) then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola \(y^2=\lambda x\) with one vertex at the vertex of the parabola is
- A \(431\)
- B \(430\)
- C \(433\)
- D \(432\)
Answer & Solution
Correct Answer
(D) \(432\)
Step-by-step Solution
Detailed explanation
\(P\left(\frac{C}{R}\right)=\frac{P(C) P\left(\frac{R}{C}\right)}{P(A) P\left(\frac{R}{A}\right)+P(B) P\left(\frac{R}{B}\right)+P(C) P\left(\frac{R}{C}\right)}\)…
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
- Let \(z\) be those complex numbers which satisfy \(|z+5| \leq 4\) and \(z(1+i)+\bar{z}(1-i) \geq-10, i=\sqrt{-1}\) If the maximum value of \(Iz +\left.1\right|^{2}\) is \(\alpha+\beta \sqrt{2}\), then the value of \((\alpha+\beta)\) is ...... .JEE Mains 2021 Hard
- Let \(v\) be the solution of the differential equation \(\left(1-x^{2}\right) d y=\left(xy+\left(x^{3}+2\right) \sqrt{1-x^{2}}\right) d x,-1 < x < 1\) and \(y(0)=0\) if \(\int\limits_{-\frac{1}{2}}^{\frac{1}{2}} \sqrt{1-x^{2}} y(x) d x=k\) then \(k^{-1}\) is equal to:JEE Mains 2022 Hard
- Let \(a_1,a_2,a_3,....,a_{10}\) be in \(G.P.\) with \(a_i > 0\) for \(i = 1, 2,....,10\) and \(S\) be the set of pairs \((r,k), r, k \in N\) (the set of natural numbers) for which \(\left| {\begin{array}{*{20}{c}}
{{{\log }_e}\,a_1^ra_2^k}&{{{\log }_e}\,a_2^ra_3^k}&{{{\log }_e}\,a_3^ra_4^k} \\
{{{\log }_e}\,a_4^ra_5^k}&{{{\log }_e}\,a_5^ra_6^k}&{{{\log }_e}\,a_6^ra_7^k} \\
{{{\log }_e}\,a_7^ra_8^k}&{{{\log }_e}\,a_8^ra_9^k}&{{{\log }_e}\,a_9^ra_{10}^k}
\end{array}} \right| = 0\) Then the number of elements in \(S\), isJEE Mains 2019 Hard - 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 :JEE Mains 2024 Medium
- A group of students comprises of \(5\) boys and \(n\) girls. If the number of ways, in which a team of \(3\) students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is \(1750\), then \(n\) is equal toJEE Mains 2019 Hard
- Let \(A = \begin{bmatrix} -1 & 1 & -1 \\ 1 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix}\) satisfy \(A^2 + \alpha(adj(adj(A))) + \beta(adj(A)(adj(adj(A)))) = \begin{bmatrix} 2 & -2 & 2 \\ -2 & 0 & -1 \\ 0 & 0 & -1 \end{bmatrix}\) for some \(\alpha, \beta \in \mathbb{R}\). Then \((\alpha - \beta)^2\) is equal to _______JEE Mains 2026 Medium
More PYQs from JEE Mains
- A line, with the slope greater than one, passes through the point \(A (4,3)\) and intersects the line \(x -\) \(y-2=0\) at the point \(B\). If the length of the line segment \(AB\) is \(\frac{\sqrt{29}}{3}\), then \(B\) also lies on the line..JEE Mains 2022 Medium
- Two sides of a rhombus are along the lines, \(x -y+ 1 = 0\) and \(7x-y-5 =0.\) If its diagonals intersect at \((-1,-2),\) then which one of the following is a vertex of this rhombus?JEE Mains 2016 Hard
- Let the system of equations \(x+2 y+3 z=5\), \(2 x+3 y+z=9,4 x+3 y+\lambda z=\mu\) have infinite number of solutions. Then \(\lambda+2 \mu\) is equal to :JEE Mains 2024 Hard
- If \(\alpha=\lim _{x \rightarrow \pi / 4} \frac{\tan ^{3} x-\tan x}{\cos \left(x+\frac{\pi}{4}\right)}\) and \(\beta=\lim _{x \rightarrow 0}(\cos x)^{\operatorname{cotx}}\) are the roots of the equation, \(a x^{2}+b x-4=0\), then the ordered pair \((\mathrm{a}, \mathrm{b})\) is :JEE Mains 2021 Hard
- Let \(\mathrm{C}\) be the set of all complex numbers. Let \(\mathrm{S}_{1} =\left\{\mathrm{z} \in \mathrm{C}|| \mathrm{z}-3-\left.2 \mathrm{i}\right|^{2}=8\right\}\) \(\mathrm{S}_{2} =\{\mathrm{z} \in \mathrm{C} \mid \operatorname{Re}(\mathrm{z}) \geq 5\} \text { and }\) \(\mathrm{S}_{3} =\{\mathrm{z} \in \mathrm{C} \| \mathrm{z}-\bar{z} \mid \geq 8\}\) Then the number of elements in \(\mathrm{S}_{1} \cap \mathrm{S}_{2} \cap \mathrm{S}_{3}\) is equal to:JEE Mains 2021 Hard
- Let the system of linear equations \(x+y+\alpha z=2\) \(3 x+y+z=4\) \(x+2 z=1\) have a unique solution \(\left(x^{*}, y^{*}, z^{*}\right)\). If \(\left(\alpha, x^{*}\right),\left(y^{*}, \alpha\right)\) and \(\left(x^{*},-y^{*}\right)\) are collinear points, then the sum of absolute values of all possible values of \(\alpha\) isJEE Mains 2022 Hard