AP EAMCET · Maths · Differential Equations
If \(m\) and \(n\) are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and \(X\)-axis as its axis, then \(m n-m+n=\)
- A 1
- B 4
- C 3
- D 2
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
The equation of the family of parabolas with focus at the origin and \(X\)-axis as its axis is given by \[ \begin{array}{rlrl} y^2 & =4 a(x+a)=4 a x+4 a^2 \\ \therefore & & 2 y \frac{d y}{d x} & =4 a \\ \Rightarrow & & a & =\frac{1}{2} y \frac{d y}{d x} \end{array} \]…
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
- A kind of bacteria grows by \(t^3\) in \(t \mathrm{~s}\). Time taken for the rate of growth of the bacteria to become 1200 per \(s\) isAP EAMCET 2020 Easy
- If \(-2, \frac{4}{3}, \frac{-4}{5}\) are the intercepts made by a plane on \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\)-axes respectively then the direction cosines of a normal to this plane areAP EAMCET 2022 Easy
- If two of the lines represented by \(2 x^3+x^2 y+y^3=0\) are mutually perpendicular, then the slope of the third line isAP EAMCET 2017 Easy
- The equation of the pair of straight lines perpendicular to the pair and passing though the origin is______AP EAMCET 2021 Medium
- If and are two opposite vertices of a square, then find the equation of a side passing throughAP EAMCET 2021 Hard
- Let \(y=Y(x)\) be the solution of the differential equation \(\frac{d y}{d x}+y \tan x=2 x+x^2 \tan x\), \(x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)\), such that \(Y(0)=1\), thenAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- The paramagnetic complex ion which has no unpaired electrons in \(t_2 g\) orbitals isAP EAMCET 2024 Hard
- The minimum horizontal speed with which a body must be projected, so that it goes around a smooth vertical circular track of radius \(4 \mathrm{~m}\) is \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\)AP EAMCET 2020 Easy
- What will be the product \(A\) in the reaction given below?
AP EAMCET 2020 Easy - Find the sum of the order and degree of the differential equation \(y=x\left(\frac{d y}{d x}\right)^3+\frac{d^2 y}{d x^2}\)AP EAMCET 2020 Easy
- In \(\triangle A B C\), if \(\mathrm{A}=60^{\circ}\) and \(\mathrm{B}=105^{\circ}\) then
\[
\begin{aligned}
& \frac{2 \mathrm{R}^2(b-c) \sin \mathrm{A} \sin \mathrm{B} \sin \mathrm{C}}{(b+c)(s-a \cos \mathrm{C}-c \cos \mathrm{A})(\mathrm{s}-a \cos \mathrm{B}-b \cos \mathrm{A})}= \\
\end{aligned}
\]AP EAMCET 2018 Hard - \(\mathrm{BF}_3\) reacts with \(\mathrm{NaH}\) at \(450 \mathrm{~K}\) to form \(\mathrm{NaF}\) and \(X\). When \(X\) reacts with \(\mathrm{LiH}\) in diethyl ether, \(Y\) is formed. What is \(Y\) ?AP EAMCET 2018 Medium