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

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

i. The value of is

(A) (B)
(C) (D)
j. Value of

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


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


Q.2 a. If u is a homogeneous function in x, y of degree n. Prove the subsequent outcomes.

(i)
(ii) (8)

b. A rectangular box open at the top is to have quantity of 32 cubic feet. obtain the dimension of the box requiring lowest material for its construction. (8)

Q.3 a. By changing the order of integration evaluate
(8)
b. Using triple integration obtain the quantity of the sphere x2+y2+z2=a2 (8)

Q.4 a. obtain all the eigen values and the eigen vector corresponding to the dominant eigen value of the matrix
A= (8)

b. Investigate for consistency of the subsequent equations and if possible obtain the solutions
4x-2y+6z=8
x+y-3z=-1
15x-3y+9z=21 (8)

Q.5 a. Solve the subsequent equations by Gauss-Siedal Method
2x+15y+6z=72
54x+y+z=110
–x+6y+27z=85 (8)

b. Solve x sin x+cos x=0, near x= using Newton-Raphson method. Carry out 3 iterations. (8)

Q.6 a. Solve the differential formula (8)

b. A body of mass m, falling from rest is subject to the force of gravity and an air resistance proportional to the square of the velocity (v2). If it falls through a distance x and possesses a velocity v at that instant, prove that where mg=ka2. Mention 1 important observation. (8)

Q.7 a. Solve by the method of variation of parameter. (6)


b. Solve the simultaneous equations


being provided x=y=0, when t=0 (10)

Q.8 a. Solve in series the formula . (10)

b. Prove that (6)

Q.9 a. If are 2 distinct roots of Jn(x)=0. Prove that
(8)

b. Prove that (8)

Earning:   Approval pending.