Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Differential Equations

Multiple Choice Questions

221.

The order and power of differential equation

$\frac{d^{2} y}{{dx}^{2}} + 7 \frac{dy}{dx} + \int ydx = \sin (x)$ is

1, 3
3, 1
1, 2
2, 1

222.

The solution of differential equation ${xcos}^{2} (y) dx = {ycos}^{2} (x) dx$ is

$xtan (x) - ytan (y) - \log (\sec (x) / \sec (y)) = c$
$ytan (x) - xtan (x) - \log (\sec (x) . \sec (y)) = c$
$xtan (x) - ytan (y) + \log (\sec (x) . \sec (y)) = c$
None of the above

223.
Differential equation of those circles which passes through origin and their centres lie on y-axis will be

$(x^{2} - y^{2}) \frac{dy}{dx} + 2 xy = 0$

$(x^{2} - y^{2}) \frac{dy}{dx} = 2 xy$

$(x^{2} - y^{2}) \frac{dy}{dx} = xy$

$(x^{2} - y^{2}) \frac{dy}{dx} + xy = 0$

$(x^{2} - y^{2}) \frac{dy}{dx} = 2 xy$

Equation of circle whose centre is (0, f) and radius f, is

$\Rightarrow {(x - 0)}^{2} + {(y - 0)}^{2} = f^{2} \Rightarrow x^{2} + y^{2} - 2 fy = 0 . . . (i) On differentiating w . r . t . x, we get \Rightarrow 2 x + 2 y \frac{dy}{dx} - 2 f \frac{dy}{dx} = 0 \Rightarrow x + \frac{dy}{dx} (y - f) = 0 \Rightarrow x + \frac{dy}{dx} (y - \frac{x^{2} + y^{2}}{2 y}) = 0 [∵ from Eq . (i)] \Rightarrow x + \frac{dy}{dx} (\frac{y^{2} - x^{2}}{2 y}) = 0 \Rightarrow (x^{2} - y^{2}) \frac{dy}{dx} = 2 xy$

Equation of circle passing through origin and centre lies on x-axis is x² + y² - 2gx = 0

224.

The differential equation of all circles touching the axis of y at origin and centre on the x-axis is given by

$xy \frac{dy}{dx} - x^{2} + y^{2} = 0$
$2 xy \frac{dy}{dx} - x^{2} - y^{2} = 0$
$(x^{2} + y^{2}) \frac{dy}{dx} - 2 xy = 0$
None of these

225.

The solution of the differential equation

$(e^{- 2 \sqrt{x}} - \frac{y}{\sqrt{x}}) \frac{dx}{dy} = 1$ is given by

$e^{2 \sqrt{x}} = 2 \sqrt{x} + c$
${ye}^{- 2 \sqrt{x}} = \sqrt{x} + c$
$y = \sqrt{x}$
None of these

226.

The solution of the differential equation

$\frac{dy}{dx} = \sqrt{\frac{1 - y^{2}}{1 - x^{2}}}$ is

$\sin^{- 1} (y) - \sin^{- 1} (x) = c$
$\sin^{- 1} (y) + \sin^{- 1} (x) = c$
$\sin^{- 1} (xy) = 2$
None of these

227.

The solution of differential equation (1 + x)ydx + (1 - y)x dy = 0 is

$\log_{e} (xy) + x - y = c$
$\log_{e} (\frac{x}{y}) + x + y = c$
$\log_{e} (\frac{x}{y}) - x + y = c$
$\log_{e} (xy) - x + y = c$

228.

The differential equation of all circles which passes through the origin and whose centre lies on y-axis is

$(x^{2} - y^{2}) \frac{dy}{dx} - 2 xy = 0$
$(x^{2} - y^{2}) \frac{dy}{dx} + 2 xy = 0$
$(x^{2} - y^{2}) \frac{dy}{dx} - xy = 0$
$(x^{2} - y^{2}) \frac{dy}{dx} + xy = 0$

229.

The general solution of y²dx + (x² - xy + y²)dy = 0 is

$\tan^{- 1} (\frac{x}{y}) + \log (y) + c = 0$
$2 \tan^{- 1} (\frac{x}{y}) + \log (x) + c = 0$
$\log (y + \sqrt{x^{2} + y^{2}}) + \log (y) + c = 0$
$\sinh^{- 1} (\frac{x}{y}) + \log (y) + c = 0$

230.

The solution of the equation $\frac{d^{2} y}{{dx}^{2}} = e^{- 2 x}$ is

$y = \frac{1}{4} e^{- 2 x} + \frac{cx}{2} + d$
$y = \frac{1}{4} e^{- 2 x} + cx + d$
$y = \frac{1}{4} e^{- 2 x} + {cx}^{2} + d$
$y = \frac{1}{4} e^{- 2 x} + {cx}^{3} + d$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

223. Differential equation of those circles which passes through origin and their centres lie on y-axis will be x2 - y2dydx + 2xy = 0 x2 - y2dydx = 2xy x2 - y2dydx = xy x2 - y2dydx + xy = 0

223.
Differential equation of those circles which passes through origin and their centres lie on y-axis will be

$(x^{2} - y^{2}) \frac{dy}{dx} + 2 xy = 0$

$(x^{2} - y^{2}) \frac{dy}{dx} = 2 xy$

$(x^{2} - y^{2}) \frac{dy}{dx} = xy$

$(x^{2} - y^{2}) \frac{dy}{dx} + xy = 0$