Download App

STD 12 - 9. differential equations — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 9. differential equations1 Mark
MCQ
Let $y=y(x)$ satisfies the equation $\frac{d y}{d x}-|A|=0$, for all $x>0$, where $A=\left[\begin{array}{ccc}y & \sin x & 1 \\ 0 & -1 & 1 \\ 2 & 0 & \frac{1}{x}\end{array}\right] .$

If $y(\pi)=\pi+2$, then the value of $y\left(\frac{\pi}{2}\right)$ is:

  • A
    $\frac{\pi}{2}-\frac{4}{\pi}$
  • B
    $\frac{\pi}{2}-\frac{4}{\pi}$
  • C
    $\frac{\pi}{2}-\frac{1}{\pi}$
  • ✓
    $\frac{\pi}{2}+\frac{4}{\pi}$
✓

Answer

Correct option: D.
$\frac{\pi}{2}+\frac{4}{\pi}$
d
$|\mathrm{A}|=\frac{-\mathrm{y}}{\mathrm{x}}+2 \sin x+2$

$\frac{\mathrm{dy}}{\mathrm{dx}}=|\mathrm{A}|$

$\frac{\mathrm{d} y}{\mathrm{~d} \mathrm{x}}=\frac{\mathrm{y}}{\mathrm{x}}+2 \sin \mathrm{x}+2$

$\frac{\mathrm{d} y}{\mathrm{~d} \mathrm{x}}+\frac{-\mathrm{y}}{\mathrm{x}}=2 \sin x+2$

$\text { I.F. }=\mathrm{e}^{\int \frac{1}{\mathrm{x}} \mathrm{dx}}=\mathrm{x}$

$\Rightarrow \mathrm{yx}=\int \mathrm{x}(2 \sin \mathrm{x}+2) \mathrm{d} \mathrm{x}$

$\mathrm{xy}=\mathrm{x}^{2}-2 \mathrm{x} \cos x+2 \sin x+\mathrm{c}.....(i)$

Now $x=\pi, y=\pi+2$

Use in $(i)$

$c=0$

Now $(i)$ be comes

$x y=x^{2}-2 x \cos x+2 \sin x$

put $x=\frac{\pi}{2}$

$\frac{\pi}{2} y=\frac{\pi^{2}}{4}+2$

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

More "M.C.Q (1 Marks)" from STD 12 - 9. differential equations→STD 12 - 9. differential equations — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Bag $A$ contains $2$ white, $1$ black and $3$ red balls and bag $B$ contains $3$ black, $2$ red and $n$ white balls. One bag is chosen at random and $2$ balls drawn from it at random, are found to be $1$ red and $1$ black. If the probability that both balls come from Bag $A$ is $\frac{6}{11}$, then $n$ is equal to
→
If the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda}$ and $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$, then the sum of all possible values of $\lambda$ is
→
If $\begin{vmatrix}\text{a}&\text{p}&\text{x}\\\text{b}&\text{q}&\text{y}\\\text{c}&\text{r}&\text{z}\end{vmatrix}=16,$ then the value of $\begin{vmatrix}\text{p}+\text{x}&\text{a}+\text{x}&\text{a}+\text{p}\\\text{q}+\text{y}&\text{b}+\text{y}&\text{b}+\text{q}\\\text{r}+\text{z}&\text{c}+\text{z}&\text{c}+\text{r}\end{vmatrix}$ is:
→
The line $y = mx$ bisects the area enclosed by lines $\text{x}=0,\text{y}=0$ and $\text{x}=\frac{3}{2}$ and the curve $\text{y}=1+4\text{x}-\text{x}^2.$ Then the value of m is:
→
Choose the correct answer from the given four options.
If $\text{P}(\text{A})=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$ is equal to:
→
If $y = {\tan ^{ - 1}}\left( {{{\sqrt x - x} \over {1 + {x^{3/2}}}}} \right),$ then $y'(1)$ is
→
The value of $ \cos^{-1}\left (\cot \left (\dfrac {\pi}{2}\right )\right ) + \cos^{-1} \left (\sin \left (\dfrac {2\pi}{3}\right )\right )$ is:
→
$\begin{bmatrix}2\text{x}&5\\8&\text{x}\end{bmatrix}=\begin{bmatrix}6\text{x}&-2\\7&3\end{bmatrix},$ then the value of $\text{x}$ is:
→
The area of the region bounded by the line $y = | x - 2 |, x = 1, x = 3$ and $x-$ axis is :
→
Let $f(x) = (x^2 - 1)^n (x^2 + x + 1)$ then $f(x)$ has local extremum at $x = 1$ when
→