C=)
REFERENCE

Module - IV

232 032 _ ८०३० _ ‏2ہ‎
‎(19) (a)Solve 2 ‏و‎ 56 7%“). (6)
(b)Solve(x + y)zp + (x -—y)zq=x*+y? (5)

OR
(20) (७) Solve $3 - 4 + 4 त = 2sin (3x + 2y). (6)
(b)Solve aa a = cos2x cos3y. (5)

Module -

(21) ‏ىم‎ tightly stretched string with fixed end points x = Oand x = 1 is
initially in ೩ position given by ‏پر‎ = ೫5171 ( ) If it is released from rest from this
position, find the displacement y(x, ಐ. (10)

۱ OR

(22) A tightly stretched string with fixed end points x = 0andx = lis
initially at rest in its equilibrium position. If it is vibrating by giving to each of its points a
velocity Ax(l— ൧, find the displacement of the string at any distance x from one end

at any time ர்‌. (10)
Module -

(23) A bar 10 cm long with insulated sides has its ends A and B maintained at
30% and 100° 0 respectively until steady state conditions prevail. The temperature at A is
suddenly raised to 20° c and at the same time that of B is lowered to 40° C. Find the
temperature distribution in the bar at time ர்‌. (10)
OR
(24) A rod of 30cm long has its ends A and 8 kept at 30° c and 90° c respectively
until steady state temperature prevails. The temperature at each end is then suddenly
reduced to zero temperature and kept so. Find the resulting temperature function u(x, y)
taking x = 0 ‏ذاه‎ (10)