Download App

Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
Choose the correct answer from the given four option. Solution of differential equation $x\ dy - y \ dx = 0$ represents :
  • A
    A rectangular hyperbola.
  • B
    Parabola whose vertex is at origin.
  • ✓
    Straight line passing through origin.
  • D
    A circle whose centre is at origin.
✓

Answer

Correct option: C.
Straight line passing through origin.
Given that, $\text{x dy}-\text{y dx}=0$
$\Rightarrow\text{x dy}=\text{y dx}$
$\Rightarrow\frac{\text{dy}}{\text{y}}=\frac{\text{dx}}{\text{x}}$
On integrating both sides, we get
$\Rightarrow\int\frac{\text{dy}}{\text{y}}=\int\frac{\text{dx}}{\text{x}}$
$\Rightarrow\log\text{y}=\log\text{x}+\log\text{C}$
$\Rightarrow\log\text{y}=\log\text{Cx}$
$\Rightarrow\text{y}=\text{Cx}$
Which is a straight line passing through origin.

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 Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\int_{ - \pi /2}^{\,\pi /2} {(3\sin x + {{\sin }^3}x)\,dx} $ is
→
If $x\left[\begin{array}{l}1 \\ 2\end{array}\right]+y\left[\begin{array}{l}2 \\ 5\end{array}\right]=\left[\begin{array}{l}4 \\ 9\end{array}\right],$ then
→
$\int_{}^{} {x\cos x\;dx = } $
→
If $y = {\sec ^{ - 1}}{{2x} \over {1 + {x^2}}} + {\sin ^{ - 1}}{{x - 1} \over {x + 1}}$, then ${{dy} \over {dx}}$ is equal to
→
Find the principal value of $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)$
→
For the function $\text{f}(\text{x})=\text{x}+\frac{1}{\text{x}}$
→
If $a, b, c $ are position vector of vertices of a triangle $ABC$, then unit vector perpendicular to its plane is
→
For matrix $A=\left[\begin{array}{cc}2 & 5 \\ -11 & 7\end{array}\right],(\operatorname{adj} A)^{\prime}$ is equal to
→
$\int {\frac{{xdx}}{{\sqrt {1 + {x^2} + \sqrt {{{\left( {1 + {x^2}} \right)}^3}} } }}} $ is equal to (where $C$ denotes constant of integration)
→
$\sin[\cot^{-1}\{\cos(\tan^{-1}\text{x})\}]=$
→