#### 12th Standard Maths Ordinary Differential Equations English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

Answer all the questions

10 x 1 = 10
1. The order and degree of the differential equation $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0$are respectively

(a)

2, 3

(b)

3, 3

(c)

2, 6

(d)

2, 4

2. The differential equation of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

(a)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0$

(b)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0$

(c)

$\frac { { d }y }{ { dx } } +y=0$

(d)

$\frac { { d }y }{ { dx } } -y=0$

3. The solution of the differential equation 2x$\frac{dy}{dx}-y=3$represents

(a)

straight lines

(b)

circles

(c)

parabola

(d)

ellipse

4. The degree of the differential equation y $y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....$ is

(a)

2

(b)

3

(c)

1

(d)

4

5. The solution of the differential equation $\frac { dy }{ dx } +\frac { 1 }{ \sqrt { 1-{ x }^{ 2 } } } =0$

(a)

y + sin-1 x = c

(b)

x + sin-1 y = 0

(c)

y2+ 2 sin-1 x = c

(d)

x2+ 2 sin-1y= c

6. The number of arbitrary constants in the general solutions of order n and n +1are respectively

(a)

n-1,n

(b)

n,n+1

(c)

n+1,n+2

(d)

n+1,n

7. The slope at any point of a curve y = f (x) is given by $\frac{dy}{dx}=3x^2$ and it passes through (-1,1). Then the equation of the curve is

(a)

y=x3+2

(b)

y=3x2+4

(c)

y=3x4+4

(d)

y=3x2+5

8. The order and degree of the differential equation ${ \left[ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +\left( \frac { dy }{ dx } \right) \right] }^{ \frac { 1 }{ 2 } }=\frac { { d }^{ 3 }y }{ { dx }^{ 3 } }$are

(a)

1,2

(b)

2,1

(c)

3,2

(d)

2,3

9. The solution of sec2x tan y dx+sec2y tan x dy=0 is

(a)

tan x+tan y =c

(b)

sec x+sec y=c

(c)

tan x tan y=c

(d)

sec x-sec y =c

10. The transformation y=vx reduces $\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x }$

(a)

$\frac { 3av }{ 4v+1 } =\frac { dx }{ x }$

(b)

$\frac { 3dv }{ v+1 } =\frac { dx }{ x }$

(c)

$2x\frac { dv }{ dx } =v$

(d)

$\frac { 3dv }{ 1-2v } ==\frac { dx }{ x }$