Deemed University 2009 A.M.I.E.T.E Electronics

(C) 0 (D) ¼

i. Eliminating function from we find the partial differential formula

(A) (B)
(C) (D)

j. If , then value of div F is

(A) (B)
(C) (D)



ans any 5 ques. out of 8 ques..
every ques. carries 16 marks.


Q.2 a. A tightly stretched string of length l with fixed ends is initially in an equilibrium position. It is set vibrating by giving every point a velocity . obtain the Displacement (8)

b. An infinitely long plane uniform plate is bounded by 2 parallel edges and an end at right angles to them. The breadth of the plate is This end is maintained at a temperature at all points and other edges are at zero temperature. Determine the temperature at any point of the plate in the steady state. (8)

Q.3 a. A random variable X have the density function . If and zero otherwise obtain
(i) its distribution function.
(ii) probabilities and . (8)

b. In a production of iron rods, let the diameter X be normally distributed
(i) What percentage of defectives can we expect? If the tolerance limits are set at in.
(ii) How should we set the tolerance limits to allow for 4% defectives?
presume
(8)

Q.4 a. A continuous random variable X has a pdf obtain K. Also obtain mean and variance of this random variable. (8)

b. Prove that where and (8)
Q.5 a. obtain the directional derivative of in the direction of a unit vector which makes an angle of with x-axis. (8)

b. Use the Divergence theorem to evaluate where and S is the boundary of the region bounded by the paraboloid and the plane z = 4y. (8)

Q.6 a. Show that is independent of the path of integration from (1,1,2) to (2,3,4) and hence evaluate it. (8)

b. Verify the Greens theorem for and C is the square with vertices at (0,0), (8)

Q.7 a. Show that the function
(8)
satisfies Cauchy-Riemann equations at z = 0, but does not exist.
b. obtain the image of the region under the mapping (8)

Q.8 a. find the Taylor series expansion of about z = 0. Also obtain its radius of convergence. (8)

b. Evaluate the integral a > 0 by using contour integration. (8)

Q.9 a. Using the method of separation of variables, solve where u(x,0)=6e–3x. (8)

b. Evaluate by using Stokess theorem where c is the boundary the rectangle . (8)

Earning:   Approval pending.