Download App

STD 12 - 9. differential equations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 9. differential equations4 Marks
MCQ
If $y\cos x + x\cos y = \pi $, then $y''(0)$ is
  • A
    $1$
  • ✓
    $\pi$
  • C
    $0$
  • D
    $-\pi$
✓

Answer

Correct option: B.
$\pi$
b
(b) $y\cos x + x\cos y = \pi $

Differentiate both sides with respect to $x$, we get

$ - y\sin x + \cos x.y' + x( - \sin y)y' + \cos y$

Again differentiate with respect to $x$

$ - y''\sin x - y\cos x + \cos x.y'' + \sin x.y' - \sin y.y'$

$ - x[\cos y.{(y')^2} + \sin y.y''] - \sin y.y'$

Putting $x = 0$, we get $ - y + y'' - 2\sin y\,y' = 0$

$y'' = y + 2y'\sin y$

Since at $x = 0$, $y = \pi $; ${(y'')_0} = \pi $.
 

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

The extremities of a diagonal of a parallelogram are the points $(3, - 4)$ and $( - 6,5)$. If third vertex is $( - 2,1)$, then fourth vertex is
→
If $\beta=\lim _{x \rightarrow 0} \frac{e^{x^3}-\left(1-x^3\right)^{\frac{1}{3}}+\left(\left(1-x^2\right)^{\frac{1}{2}}-1\right) \sin x}{x \sin ^2 x}$

then the value of $6 \beta$ is $\qquad$

→
Let $\alpha =\sum_{n=101}^{200} 2^n \sum_{k=101}^n \frac{1}{k !}$ and $b=\sum_{n=101}^{200} \frac{2^{201}-2^n}{n !}$ Then, $\frac{a}{b}$ is
→
The number of common terms in the progressions $4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and $3,6,9,12$, ......., up to $37^{\text {th }}$ term is:
→
The region represented by $\left| {x - y} \right| \leq 2$ and $\left| {x + y} \right| \leq 2$ is bounded by a
→
If $a,\;b,\;c$ are in $A.P.$, then ${10^{ax + 10}},\;{10^{bx + 10}},\;{10^{cx + 10}}$ will be in
→
The number of ways in which $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by
→
Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on A $\times$ B by $\left(a_1, b_1\right) R\left(a_2, b_2\right)$ is and only if $a_1+a_2=b_1+b_2$. Then the number of elements in $\mathrm{R}$ is ...........
→
Let $f$ be a continuous, periodic even function defined on $R$ such that $f(0) = 1$, $f(2) = -1$ and period of $f$ is $4$. Minimum number of roots of equation $f(x) = 0$ in $[-10, 10]$ will be
→
The number of real solutions of the equation $x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0$ is
→