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

12th Standard EM

Reg.No. :
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Time : 00:10:00 Hrs
Total Marks : 10

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

(a)

1

(b)

2

(c)

3

(d)

4

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

(a)

2 and 6

(b)

3 and 6

(c)

1 and 4

(d)

2 and 4

3. If y=cx + c− c3 then its differential equation is

(a)

$y=\frac { dy }{ dx } +\frac { dy }{ dx } -{ \left( \frac { dy }{ dx } \right) }^{ 3 }$

(b)

$y={ \left( \frac { dy }{ dx } \right) }^{ 3 }=x\frac { dy }{ dx } -\frac { dy }{ dx }$

(c)

$\frac { dy }{ dx } +y={ \left( \frac { dy }{ dx } \right) }^{ 3 }-x\frac { dy }{ dx }$

(d)

$\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0$

4. The differential equation of y = mx + c is (m and c are arbitrary constants)

(a)

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

(b)

y = x $\frac { dy }{ dx }$ + c

(c)

xdy + ydx = 0

(d)

ydx − xdy = 0

5. Solution of $\frac { dy }{ dx }$ + Px = 0

(a)

x=cepy

(b)

x=ce−py

(c)

x = py + c

(d)

x = cy

6. The differential equation formed by eliminating A and B from y = e−2x(A cos x + B sin x) is

(a)

y− 4y+ 5 = 0

(b)

y2+ 4y – 5 = 0

(c)

y2−4y1−5= 0

(d)

y+ 4y+ 5 = 0

7. A homogeneous differential equation of the form $\frac { dy }{ dx }$ = f$\left( \frac { y }{ x } \right)$ can be solved by making substitution,

(a)

y = v x

(b)

v = y x

(c)

x = v y

(d)

x = v

8. The solution of the differential equation $\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) }$ is

(a)

$f\left( \frac { y }{ x } \right) =k.x$

(b)

$xf\left( \frac { y }{ x } \right) =k$

(c)

$f\left( \frac { y }{ x } \right) =ky$

(d)

$yf\left( \frac { y }{ x } \right) =k$

9. The differential equation $\left( \frac { dx }{ dy } \right) ^{ 2 }+5y^{ \frac { 1 }{ 3 } }$=x is

(a)

order 2 degree

(b)

order 1 degree 2

(c)

order 1 degree 6

(d)

order 1 degree 3

10. The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is (k is negative).

(a)

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

(b)

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

(c)

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

(d)

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