JEE Mains · Maths · STD 12 - 11. three dimension geometry
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 to
- A \(\sqrt{\frac{15}{2}}\)
- B \(\frac{5 \sqrt{3}}{2}\)
- C \(2 \sqrt{2}\)
- D \(\sqrt{\frac{14}{3}}\)
Answer & Solution
Correct Answer
(B) \(\frac{5 \sqrt{3}}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(1+x^2\right) \frac{d y}{d x}+x y=5 x^2 \sqrt{1+x^2} \\ & \frac{d y}{d x}+\frac{x y}{1+x^2}=\frac{5 x^2}{\sqrt{1+x^2}} \\ & \therefore \text { I.F. }=\mathrm{e}^{\int \frac{\mathrm{x}}{1+x^2} \mathrm{dx}}=\mathrm{e}^{\frac{\ln…
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 integral \(\int {\cos \,\left( {{{\log }_e}\,x} \right)dx} \) is equal to: (where \(C\) is a constant of integration)JEE Mains 2019 Medium
- Number of integral terms in the expansion of \(\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824}\) is equal to ...........JEE Mains 2024 Hard
- The number of values of \(\alpha\) for which the system of equations: \(x+y+z=\alpha\) ; \(\alpha x+2 \alpha y+3 z=-1\) ; \(x+3 \alpha y+5 z=4\) is inconsistent, isJEE Mains 2022 Medium
- Let \(\mathrm{M}\) and \(\mathrm{m}\) respectively be the maximum and minimum values of the function \(f(x)=\tan ^{-1}(\sin x+\cos x)\) in \(\left[0, \frac{\pi}{2}\right]\), Then the value of \(\tan (\mathrm{M}-\mathrm{m})\) is equal to:JEE Mains 2021 Hard
- The distance, of the point \((7,-2,11)\) from the line \(\frac{x-6}{1}=\frac{y-4}{0}=\frac{z-8}{3}\) along the line \(\frac{x-5}{2}=\frac{y-1}{-3}=\frac{z-5}{6}\), is :JEE Mains 2024 Hard
- If \(\beta \) is one of the angles between the normals to the ellipse, \(x^2 + 3y^2 = 9\) at the points \(\left( {3\cos \theta ,\sqrt {3\,} \sin \theta } \right)\) and \(\left( { - 3\sin \,\theta ,\sqrt 3 \,\cos \theta } \right); \in \left( {0,\frac{\pi }{2}} \right)\); then \(\frac{{2\,\cot \beta }}{{\sin \,2\theta }}\) is equal toJEE Mains 2018 Hard
More PYQs from JEE Mains
- Let \(A=\{-3,-2,-1,0,1,2,3\),\(\} . Let R\) be a relation on A defined by \(x R y\) if and only if \(0 \leq x^2+2 y \leq 4\).
Let \(l\) be the number of elements in R and \(m\) be the minimum number of elements required to be added in R to make it a reflexive relation. then \(l+m\) is equal toJEE Mains 2025 Medium - If the orthocentre of the triangle formed by the lines \(y=x+1, y=4 x-8\) and \(y=m x+c\) is at \((3,-1)\), then \(\mathrm{m}-\mathrm{c}\) is :JEE Mains 2025 Medium
- Let \(f(x)=3 \sqrt{x-2}+\sqrt{4-x}\) be a real valued function. If \(\alpha\) and \(\beta\) are respectively the minimum and the maximum values of \(\mathrm{f}\), then \(\alpha^2+2 \beta^2\) is equal toJEE Mains 2024 Hard
- The angle of elevation of the top \(P\) of a vertical tower \(PQ\) of height \(10\) from a point \(A\) on the horizontal ground is \(45^{\circ}\). Let \(R\) be a point on \(AQ\) and from a point \(B\), vertically above \(R\), the angle of elevation of \(P\) is \(60^{\circ}\). If \(\angle BAQ =30^{\circ}, AB = d\) and the area of the trapezium \(PQRB\) is \(\alpha\), then the ordered pair \(( d , \alpha)\) is.JEE Mains 2022 Hard
- Let the tangents at the points \(P\) and \(Q\) on the ellipse \(\frac{x^{2}}{2}+\frac{y^{2}}{4}=1\) meet at the point \(R(\sqrt{2}, 2 \sqrt{2}-2)\). If \(S\) is the focus of the ellipse on its negative major axis, then \(SP ^{2}+ SQ ^{2}\) is equal to.JEE Mains 2022 Hard
- The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[ x ]+4}\right) dx\), where \([\bullet]\) denotes the greatest integer function, isJEE Mains 2026 Easy