=x*2-y*2>
C:u=x*2+y%2>
D:-‘u = log 02232)
Correct Answer:- Option-C
Question82:-A partial differential equation of the form ലയി रपय ‏لا‎
‎elliptic if :
ac-b*2=0°
ac-b*2 > 0°
C:ac-b*2 < 0°
D:-a+c=2b
Correct Answer:- Option-B
Question83:-General Integral of *yzz_x+xzz_y=xy" is :
AF (x*2-y%2, 2*2-y*2) =

ह 0 ५ ۰
8: ಆ 3

C:-F *(yz, xz)=0°

[3-3 இ -0
ഉ മ

Correct Answer:- Option-A
Question84:-Which of the following function is nowhere analytic
=3xty+i> (30
= 29/41 ` (^ 2-/^2)
©: (र) =^2-#^24+1) ` 2309
0: 2) =605॥)` *x* ‘cosy+i ‘sinh’ *x* ‏الامو"‎
‎Correct Answer:- Option-B

*=F(x, y, U, U_X, U_y)” is said to be

=o?
Question85:-Let ‏قا © نينا‎ be the one-dimensional wave equation with boundary conditions
u(0, t) = 0, u(L, t)=0 for all t and initial conditions

u(x, 0)=f(x), “u_t (x, 0) = g(x) for all x.

If u (x, t) = “sum_(n=1)*00° *(a_n cos lambda_n t+b_nsinlambda_n t) sin’ *(npix)/(L)’, then ‘a_n =*

2 eos ध
cdf

na

کربت
‎പ പം‏

೧೯೯೩

ela) cos dx

ന്ന

dx

Fix) sin

2 पा

dx

[മി sin
L 3
D:-
Correct Answer:- Option-C
Question86:-Two-dimensional heat equation is :

वि ॥ 1

~~.
8 വം
C:u_t=c%2 (யய

putt =e? (ag tty)

Correct Answer:- Option-A

Question87:-Let * phi’ (x)=x be an iteration function for solving the equation f(x)=0 by fixed point iteration method. The
iterations converges to a root, if :

A:-[ phi ` (८ <` |>1, for k=0, 1, 2,..