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

12th Standard

Reg.No. :
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Maths

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

10 x 1 = 10
1. The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

(a)

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

(b)

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

(c)

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

(d)

$\frac { { d }^{ 2 }x }{ { dy }^{ 2 } }=0$

2. The general solution of the differential equation $\frac { dy }{ dx } =\frac { y }{ x }$ is

(a)

xy = k

(b)

y = k log x

(c)

y = kx

(d)

log y = kx

3. The solution of $\frac{dy}{dx}+$p(x)y=0 is

(a)

$y={ ce }^{ \int { pdx } }$

(b)

$y={ ce }^{ -\int { pdx } }$

(c)

$x={ ce }^{ -\int { pdy } }$

(d)

$x={ce }^{ \int { pdy } }$

4. If p and q are the order and degree of the differential equation $y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,$When

(a)

p < q

(b)

p = q

(c)

p>q

(d)

p exists and q does not exist

5. If sin x is the integrating factor of the linear differential equation $\frac { dy }{ dx } +Pt=Q,$Then P is

(a)

log sin x

(b)

cos x

(c)

tan x

(d)

cot x

6. The solution of (x2-ay)dx=(ax-y2)dy is

(a)

y=x2+y2-a(x+y)

(b)

y=x2+y2-a(x+y)

(c)

x3+y2=3ayx+c

(d)

(x2-ay)(ax-y2)=0

7. The general solution of $4\frac{d^2 y}{dx^2}$+y=0 is

(a)

$y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } +B\quad sin\frac { x }{ 2 } \right]$

(b)

$y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } -B\quad sin\frac { x }{ 2 } \right]$

(c)

$y=Acos\frac { x }{ 2 } +Bsin\frac { x }{ 2 }$

(d)

$t={ Ae }^{ \frac { x }{ 2 } }+B{ e }^{ \frac { -x }{ 2 } }$

8. The population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

(a)

$\frac{dp}{dt}=\frac{k}{p}$

(b)

$\frac{dp}{dt}=kt$

(c)

$\frac{dp}{dt}=kp$

(d)

$\frac{dp}{dt}=-kp$

9. Using y = vx, the differential equation $\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } }$ is reduced to ________.

(a)

x(1+$\sqrt{v}$)dv=v$\sqrt{v}$dx

(b)

x(1-$\sqrt{v}$)dv=v$\sqrt{v}$dx

(c)

x(1+$\sqrt{v}$)dv=-v$\sqrt{v}$dx

(d)

v(1+$\sqrt{v}$)dx-v$\sqrt{v}$dv=0

10. The differential equation associated with the family of concentric circles having their centres at the origin is _________.

(a)

$\frac { dy }{ dx } =\frac { -x }{ y }$

(b)

$\frac { dy }{ dx } =\frac { -y }{ x }$

(c)

$\frac { dy }{ dx } =\frac { x }{ y }$

(d)

$\frac { dy }{ dx } =\frac { y }{ x }$