The solution of dy dx = ( ax + b cy + d ) represents a parabola i… - Vidyadip

MCQ

The solution of $\frac{{dy}}{{dx}} = \left( {\frac{{ax + b}}{{cy + d}}} \right)$ represents a parabola if

A
$a = 0, c = 0$
B
$a = 1, c = 2$
✓
$a = 0,c \ne 0$
D
$a = 1, c = 1$

✓

Answer

Correct option: C.

$a = 0,c \ne 0$

c
$(c y+d) d y=(a x+b) d x$

$\frac{\mathrm{cy}^{2}}{2}+\mathrm{dy}=\frac{\mathrm{ax}^{2}}{2}+\mathrm{bx}+\mathrm{K}$ ($K$ being the constant of integration)

The equation represents a parabola

If $\mathrm{c}=0, \mathrm{a} \neq 0$ or $\mathrm{a}=0, \mathrm{c} \neq 0$

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

If $f : A \rightarrow B$ is surjective then:

Statement $-1 :$ The point $A(1, 0, 7)$ is the mirror image of the point $B( 1, 6, 3)$ in the line: $\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}$

Statement $-2 :$ The line $\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}$ bisects the line joining $A(1, 0, 7)$ and $B( 1, 6, 3)$

The taxi fare in a city is as follows. For the first km the fare is Rs.10 and subsequent distance is Rs.6/ km.Taking the distance covered as x km and fare as Rs y, write a linear equation.

Choose the correct answer from the given four options.
If $\cos\Big(\sin^{-1}\frac{2}{5}+\cos^{-1}\text{x}\Big)=0$ then x is equal to:

If $\mathrm{R}$ is the smallest equivalence relation on the set $\{1,2,3,4\}$ such that $\{(1,2),(1,3)\} \subset R$, then the number of elements in $\mathrm{R}$ is

If $C$ and $D$ are two events such that $P\left( D \right) \ne 0$ then the correct statement among the following is

The derivative of $f(x) = x|x|$ is

Let $f:(-1,1) \rightarrow R$ be a differentiable function satisfying $\left(f^{\prime}(x)\right)^4=16(f(x))^2$ for all $x \in(-1,1)$ $f(0)=0$ The number of such functions is

In linear programming, objective function and objective constraints are:

The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.

	Number of cars manufactured
Colour	Vento	Creta	Wagonr
Red	$65$	$88$	$93$
White	$54$	$42$	$80$
Black	$66$	$52$	$88$
Sliver	$37$	$49$	$74$

Which car was twice the number of silver Vento?