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Consider the boundary value problem 
If and are continuous on 10, Il, then 
b

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Answer : 
Explanation : 
Auxiliary equation: 
4&#8226; Sin 
Using initial conditions 
u COS 
hence (a) is correct 
hence (b) is true

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Consider the boundary value problem 
X If u are 
continuous on 10,11 then 
b 
(x)dx

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Answer : (b),(c),(d) 
Explanation : 
Auxiliary equation: 
COS (&#39;LAO Sin 
is arbitrary 
u&#39;2(X) &#8212;C; 
Therefore, (b)(c) are true 
R.H.S

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The boundary value problem 
has non-trivial 
solution for 
b 
All negative value of k 
All the values of

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Answer : (c) 
Explanation : 
Case (i) : b0,The eigen values are 
Case (ii) eco , The eigen value are 
Case (iii) 
(Non trivial)

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(11) 
The Sturm-Liouville problem: 
has its eigenvectors 
given by 
cos&#8222;x; where 
&#39;I-OX

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(12) 
The eigen values of the Sturm Liouville 
system are 
b 
&quot;2 
None of these

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Answer : (d) 
Explanation : 
cos Sin 
and 
2 c, COS x

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Answer : (b) 
Explanation : 
Regular SLP 
Case (i): Let 
J ; (n-N) are eigen values 
Case (ii) 
is not an eigen value. 
Case (iii) 
Let

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(13) 
Let n be a nonnegative integer. The 
eigen values of the Sturm-Liouville 
problemQY4kY20, With boundary 
are 
conditions 
nr2 
n2

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(14) 
Consider the Sturm Liouville 
problems: with Y&#39;(O-O 
and then the set eigen-valuesk, 
satisfy

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(15) 
The set of all eigen values of the Sturm 
Liouville problem 
is given by

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Answer : (d) 
Explanation : 
For 
COS Sin 
1&#8212;4n2 ; 
trivialsolution) 
is also eigen value. 
Eigen values :

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(17) 
The difference between the least two 
eigenvalues of the boundary value 
problem 
such that 
is 
Enter Your Response

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Answer : 
Explanation : 
The eigen values of this system are 
(2n-l)&#39; 
For k,-1/4 
For n-2, 
Hence

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(19) 
The eigen values of the strum Liouville 
problem ogxgr, are 
&quot;2

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Answer : 
Explanation : 
This is periodic SLP and a, b, c, d are 
true by direct properties.

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Answer : (c) 
Explanation : 
Regular SLP 
Case (i): Let 
&#8226; (&#8222;eN) are eigen values

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(20) 
The boundary value problem 
b 
has 
Unique eigen value 
Two eigen value 
No eigen value 
Infinite number of eigen value

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Answer : (d) 
Explanation : 
4 C2 Sin 
cos ga tan 
Which holds for infinite values of

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Answer : 
Explanation : 
This is periodic SLP and by its 
properties a, b, c, d are true