" /> -->

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

12th Standard EM

Reg.No. :
•
•
•
•
•
•

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

10 x 1 = 10
1. The order and degree of the differential equation $\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 }$ are respectively

(a)

2 and 3

(b)

3 and 2

(c)

2 and 1

(d)

2 and 2

2. The integrating factor of the differential equation $\frac{dx}{dy}+Px=Q$

(a)

eഽPdx

(b)

eഽPdx

(c)

ഽPdy

(d)

eഽPdy

3. The complementary function of (D2+ 4)y = e2x is

(a)

(Ax +B)e2x

(b)

(Ax +B)e−2x

(c)

A cos 2x + B sin 2x

(d)

Ae−2x+ Be2x

4. The particular integral of the differential equation f(D)y = eax where f(D) = (D−a)2

(a)

$\frac { { x }^{ 2 } }{ 2 } { e }^{ ax }$

(b)

xeax

(c)

$\frac { x }{ 2 }$eax

(d)

x2eax

5. The differential equation of all circles with centre at the origin is

(a)

xdy +ydx = 0

(b)

xdy - ydx = 0

(c)

xdx + ydy = 0

(d)

xdx - ydy = 0

6. The differential equation obtained by eliminating a and b from y = a e3x + b e-3x is

(a)

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

(b)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } }$-9y=0

(c)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } } -9\frac { dy }{ dx }$

(d)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } }$+9x=0

7. The degree and order of $\frac { { d }^{ 2 }y }{ dx^{ 2 } } -6\sqrt { \frac { dy }{ dx } }$=0 are

(a)

2,1

(b)

1,2

(c)

2,2

(d)

1,1

8. The integrating factor of (1+x2)$\frac { dy }{ dx }$+xy = (1+x2)3 is

(a)

$\sqrt { 1+{ x }^{ 2 } }$

(b)

log(1+x2)

(c)

etan-1x

(d)

log(tan-1x)

9. The complementary function of the differential equations (D2-D)y=ex is

(a)

A+Bex

(b)

(Ax+B)ex

(c)

A+Be-x

(d)

(A+Bx)e-x

10. The P.I. of $\frac { d^{ 2 }y }{ { dx }^{ 2 } } -6\frac { dy }{ dx } +9y$=e3x is ______

(a)

$\frac { { e }^{ 3x } }{ 2! }$

(b)

$\frac { { x }^{ 2 }e^{ 3x } }{ 2! }$

(c)

$\frac { xe^{ 3x } }{ 2! }$

(d)

9e3x