JEE Mains · Maths · STD 11 - 9. straight line
The straight lines \(l_1\) and \(l_2\) pass through the origin and trisect the line segment of the line \(L: 9 x+5 y=\) 45 between the axes. If \(m_1\) and \(m_2\) are the slopes of the lines \(l_1\) and \(1_2\),then the point of intersection of the line \(y =\left( m _1+ m _2\right) x\) with \(L\) lies on
- A \(6 x + y =10\)
- B \(6 x-y=15\)
- C \(y-x=5\)
- D \(y-2 x=5\)
Answer & Solution
Correct Answer
(C) \(y-x=5\)
Step-by-step Solution
Detailed explanation
\(m _{ L _1}=\frac{3.3}{10}=\frac{9}{10}\) \(m _{ L _2}=\frac{6.3}{5}=\frac{18}{5}\) \(y =\left( m _1+ m _2\right) x\) \(y =\frac{9}{2} x\) Point of intersection with \(L\) is \(\left(\frac{10}{7}, \frac{45}{7}\right)\)
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
- The value of \(\sum_{n=1}^{100} \int_{n-1}^{n} e^{x-[x]} d x,\) where \([x]\) is the greatest integer \(\leq x ,\) isJEE Mains 2021 Medium
- Let the point \(P\) be the vertex of the parabola \(y = x^2 - 6x + 12\). If a line passing through the point \(P\) intersects the circle \(x^2 + y^2 - 2x - 4y + 3 = 0\) at the points \(R\) and \(S\), then the maximum value of \((PR + PS)^2\) is :JEE Mains 2026 Medium
- Let \(\beta=\lim _{x \rightarrow 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x}-1\right)}\) for some \(\alpha \in R\). Then the value of \(\alpha+\beta\) is.JEE Mains 2022 Hard
- If one real root of the quadratic equation \(81x^2 + kx + 256 = 0\) is cube of the other root, then a value of \(k\) isJEE Mains 2019 Hard
- If \((a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^{2}-b^{2}\) where \(a>b>0,\) then \(\frac{d x}{d y}\) at \(\left(\frac{\pi}{4}, \frac{\pi}{4}\right)\) isJEE Mains 2020 Hard
- Let \(\left|z_1-8-2 i\right| \leq 1\) and \(\left|z_2-2+6 i\right| \leq 2, z_1, z_2 \in \mathbf{C}\). Then the minimum value of \(\left|z_1-z_2\right|\) is :JEE Mains 2025 Easy
More PYQs from JEE Mains
- If the perpendicular bisector of the line segment joining the points \(P (1,4)\) and \(Q ( k , 3)\) has \(y\)- intercept equal to \(-4,\) then a value of \(k\) isJEE Mains 2020 Medium
- The plane containing the line \(\frac{{x - 3}}{2} = \frac{{y + 2}}{{ - 1}} = \frac{{z - 1}}{3}\) and also containing its projection on the plane \(2x + 3y -z = 5,\) contains which one of the following points?JEE Mains 2019 Hard
- Let \(p(x)\) be a quadratic polynomial such that \(p(0)= 1\) . If \(p(x)\) leaves remainder \(4\) when divided by \(x-1\) and it leaves remainder \(6\) when divided by \(x+ 1\) ; thenJEE Mains 2017 Hard
- If \(\left| {\vec a} \right| = 2,\left| {\vec b} \right| = 3\) and \(\left| {2\,\vec a - \vec b} \right| = 5\), then \(\left| {2\,\vec a + \vec b} \right|\) equalsJEE Mains 2014 Hard
- If \(n (2 n +1) \int_{0}^{1}\left(1- x ^{ n }\right)^{2 n } dx =1177 \int_{0}^{1}\left(1- x ^{ n }\right)^{2 n +1} dx\), then \(n \in N\) is equal to \(\dots\dots\)JEE Mains 2022 Hard
- Let \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) be the solution of the differential equation \(\left(x y-5 x^2 \sqrt{1+x^2}\right) d x+\left(1+x^2\right) d y=0, y(0)=0\). Then \(y(\sqrt{3})\) is equal toJEE Mains 2025 Medium