Download App

STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If $\cos ^{-1}\left(\frac{y}{2}\right)=\log _{e}\left(\frac{x}{5}\right)^{5},|y|<2$, then
  • A
    $x^{2} y^{\prime \prime}+x y^{\prime}-25 y=0$
  • B
    $x^{2} y^{\prime \prime}+x y^{\prime}-25 y=0$
  • C
    $x^{2} y^{\prime \prime}-x y^{\prime}+25 y=0$
  • ✓
    $x^{2} y^{\prime \prime}+x y^{\prime \prime}+25 y=0$
✓

Answer

Correct option: D.
$x^{2} y^{\prime \prime}+x y^{\prime \prime}+25 y=0$
d
$\cos ^{-1}\left(\frac{y}{2}\right)=\log _{e}\left(\frac{x}{5}\right)^{5}$

$\cos ^{-1}\left(\frac{y}{2}\right)=5 \log _{e}\left(\frac{x}{5}\right)$

$\frac{-1}{\sqrt{1-\frac{y^{2}}{4}}} \cdot \frac{y^{\prime}}{2}=5 \cdot \frac{1}{\frac{x}{5}} \times \frac{1}{5}$

$\Rightarrow \frac{-y^{\prime}}{\sqrt{4-y^{2}}}=\frac{5}{x}$

$-x y^{\prime}=5 \sqrt{4-y^{2}}$

$-x y^{\prime \prime}-y^{\prime}=5 \cdot \frac{1}{2 \sqrt{4-y^{2}}}\left(-2 y y^{\prime}\right)$

$\Rightarrow x y^{\prime \prime}+y^{\prime}=\frac{5 y^{\prime} \cdot y}{\sqrt{4-y^{2}}}$

$x y^{\prime \prime}+y^{\prime}=5 \cdot\left(\frac{-5}{x}\right) y$

$x^{2} y^{\prime \prime}+x y^{\prime}=-25 y$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A (h, k), \,B(1, 1)$ and $C (2, 1)$ be the vertices of a right angled triangle with $AC$ as its hypotenuse. If the area of the triangle is $1$ square unit, then the set of values which $'k'$ can take is given by
→
If $f$ and $g$ are continuous functions on $[0,\,\,a]$ satisfying $f(x) = f(a - x)$ and $g(x) + g(a - x) = 2,$ then $\int_0^a {f(x)g(x)\,dx = } $
→
Let $A=\left[a_{i j}\right]$ be a square matrix of order $3$ such that $a_{i j}=2^{j-i}$, for all $i, j=1,2,3$. Then, the matrix $A ^{2}+ A ^{3}+\ldots+ A ^{10}$ is equal to
→
$\mathop {\lim }\limits_{x \to \pi /6} \frac{{{{\cot }^2}\theta - 3}}{{{\rm{cosec}}\theta - 2}} = $
→
The tangent to the parabola ${y^2} = 4ax$ at the point $(a, 2a)$ makes with $x$ - axis an angle equal to
→
Let $f: R \rightarrow R$ be a twice differentiable function such that $(\sin x \cos y)(f(2 x+2 y)-f(2 x-2 y))=(\cos x$ $\sin y )(f(2 x +2 y )+f(2 x -2 y ))$, for all $x , y \in R$.
If $f^{\prime}(0)=\frac{1}{2}$, then the value of $24 f^{\prime \prime}\left(\frac{5 \pi}{3}\right)$ is:
→
The greater of $\int_0^{\pi /2} {\frac{{\sin x}}{x}\,dx} $ and $\frac{\pi }{2},$ is
→
If a tangent having slope of $ - \frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to .................. $\mathrm{sq. \, units}$ ($O$ is centre of the ellipse)
→
The total number of $5$-digit numbers, formed by using the digits $1,2,3,5,6,7$ without repetition, which are multiple of $6$, is
→
A bag contains, $7$ different Black balls .and $10$ different Red balls, if one by one ball are randomely drawn untill all black balls are not drawn, then probability that this process is completed in $12 ^{th}$ draw, is equal to 
→