Download 1. has real and distinct roots when a) b) c) d) 2. has real and

1.
a)
b)
c)
d)
has real and distinct roots when
2.
a)
b)
c)
d)
has real and repeated roots when
3.
a)
b)
c)
d)
has complex roots when
)
(
)
4. The system (
then which one is true?
)
a) (
)
b) (
)
c) (
)
d) (
5. The differential equation in terms of
(
)
(
)
a) (
)
b) (
c) (
)
d) (
)
(
(
)
when represented in terms of
corresponding to the system
) is
(
)
)
6. The differential equation in terms of
using elimination of , corresponding to the system
(
)
(
)
(
) is
a) Linear homogeneous Differential equation
b) Non-linear Differential equation
c) Linear non homogeneous Differential equation
d) Linear non homogeneous Differential equation with constant coefficients
7. The general solution of the system
, then a and b are
*
+ is given by
a)
b)
c)
d)
1, 4
-1, 4
1, -4
-1, -4
8. Complementary solution of the system
given by
a) 1, 5
b) -1, 5
c) 1, -5
d) -1, -5
a) *
+
*
+ is
*
+
*
+ is
*
+
*
+ is
*
+
*
+ is
, then a and b are
9. Complementary solution of the system
given by
*
, then
is
+
b) * +
c) * +
d) * +
10. Complementary solution of the system
given by
e) *
f)
, then
is
+
* +
g) * +
h) * +
11. Complementary solution of the system
given by
, what will be the characteristic equation for the matrix?
a)
b)
c)
d)
12. The auxiliary equation of
is
a)
b)
c)
d)
13. The auxiliary equation of
has double root
then
has double root
then
is given by
a)
b)
c)
d)
14. The auxiliary equation of
is given by
a)
b)
c)
d) None of these
15. The auxiliary equation of
a) √ √
has double root ½ then its LI solutions are
b) √ √
c) cos(x/2), sin(x/2)
d) cos(lnx/2), sin(lnx/2)
16. Particular integral of
is
a)
b)
c) 6e2x
d)
17. The lowest order of a differential equation having 3 + cosh2x + 2sinh2x as its particular solution
is
a) 2
b) 3
c) 4
d) 5
18. If cosbx is one of the linearly independent solutions of
a) 3
then b can have the value
b) -3
c) 3, -3
d) None of these
19. For the non homogeneous linear system
to be chosen as [it is given that
[
a)
]
[
d)
are the eigen values of ]
]
[
c)
the particular integral
]
[
b)
( )
where
]
20. For the homogeneous linear system
where has the eigen values
corresponding eigen vectors , . Then it’s general solution becomes
a)
b)
c)
d)
*
21. Complementary solution of the system
by
[
]
b)
[
]
d)
(
)
[
[
]
* +
is given
+
( )
, the
]
particular integral is chosen as
2
3
-2
-3
+
* +
22. For the non-homogeneous linear system
a)
b)
c)
d)
and
, what will be the choice of Yp(x)?
a)
c)
,
where
[
], find
*
23. For the non homogeneous linear system
particular integral is chosen as
a)
b)
c)
d)
where
[
*
+
( )
, the
*
+
( )
, the
], find
2
3
-2
-3
24. For the non homogeneous linear system
particular integral is chosen as
where
[
], find d.
a) * +
b) *
+
c) * +
d) *
+
25. Characteristic equation of
a)
b)
c)
d)
is
26. If
is an auxiliary equation of a homogeneous Euler Cauchy equation,
then its general solution is given by
a)
b)
c)
d)