Fy)

ന്ന
[ न न
Correct Answer:- Option-8

‘Question8:-For the second order linear homogeneous equation, L(y) = y” + 2y’ + 2y = 0, which one is true ?

Asthe solutions are ‏)رف‎

ह 17

Solutions are linearly independent
C:Wronskian of the solutions is 0
D:-The equation has no solution

Correct Answer:- Option-B

Question:-Consider a second order nonhomogeneous linear differential equation described by, L(y) = y""-+a,(x)y!-bag(-c)y=b(sr) where @,09 and b are continuous functions

defined on an interval I. The general solution of the equation by using method of variation of parameter is dependent on.
L. Complementary function

॥. Particular integral

11. ೫೯೦೧೮ 2೧.

IV. None of the above

‘Which one is true from the following ?
AsOnly Lis correct
B:-Only Il and Ill are correct
Ce-All are correct except IV
D:-Only IV is correct
Correct Answer:- Option-C

Questiont0;-For an auxiliary equation of an Euler-Cauchy equation L(y) =
bis a continuous function on an interval |, which possiblity is not true ?

ரரி தாடி. .+०,,_129५/+०%9 - 0(2), 800) कलर 00/01 ಡಿ are constants and

A=Roots ate real and distinct
B:-Roots are real and equal

CRoots are complex and conjugate

Roots must be always real
Correct Answer:- Option-D
Question11 Fourier Sine Series of a function f(x) is defined

(1 When f(x) is odd
(ii) When f(x) is even,

|
പയ) a2
=

0
(iv) f(x) is an odd periodic function of period 2L in the interval = L< x ‘Which one is false from the following ?

AsOnly (ii) is comect
B:Both (i) and (iv) are correct
C=Only (ii) is correct
Dealll are correct except (ii)
Correct Answer:-Question Cancelled
Question12:-The Cauchy Integral Theorem for f(z) has the following conditions
AsThe domain Dis simply connected

8:12) is analytic

:-J!(2) Is continuous in D

-The domain D is multiply connected
Correct Answer:-Question Cancelled

Question 3:-Which of the folowing condition is not true for Taylor Series Expansion of a function f(z)
Asif f(z) is not analytic, then it can not be expanded in Taylor Series about the point 2 = 2

B:-The radius of convergence of the Taylor series is the distance between 2g and the nearest point at which the function is not analytic if f(z) is analytic ina domain D except at
the points 23,29, --2n,

CTaylor Series is unique
‏كته‎ series is divergent also
Correct Answer:- Option-D
Question14:-Gradient of f(x,y) = ௧2-42 ௭1, 2) ௩.
‏آ6 -جھ‎ - 4(
७6 -१
‏امل‎ +
D~6i + 4)
Correct Answer:- Option-A
Question15 fa force field Fis conservative then

५५५६) =

B:-There exists a scalar potential function f such that F # grad f