Andhra University 2008 B.E MATHEMATICS - II - Question Paper
Wednesday, 01 May 2013 03:00Web
I Year B.E./B.Tech Degree exams
MATHEMATICS - II
(Common to All Branches)
Time : 3 hours Maximum : 75 Marks
ques. one is compulsory
ans any 4 from ques. two to 8
8
3. a) Using elementary row operations obtain the inverse of
1 one 3
1 three 3
2 four 4
é ù
êê -úú
êë- - -úû
b) decrease the quadratic form 2xy+2yz+2zx into canonical
form.
4. a) Using Gauss elimination method.
Solve 2x1+4x2+x3=3,3x1+2x2-2x3=-2
x1-x2+x3=6
b) Using iteration method obtain the largest eigen value and eigen
vector of the matrix
1 2
3 4
A
é ù
=ê ú
ë û
5. a) Solve (2x+y-3) dx=(x+2y-3)dy
b) Solve (x3dx-y3dy)=3xy ( y dx-x dy)
c) Solve x p2+p-y=0
6. a) Solve
2 2
2
3 two 2 x sin two d y d y dy
e x
dx dx dx
+ + = +
b) Solve five , 4
dx dy
x y y x
dt dt
= + = -
9
7. a) obtain the Laplace transform of f(t) provided
i) f(t) = t e’ sin t
ii) f(t) = sin t 0
= 0 t >p
b) obtain the inverse transform of
i)
1
log
s
s
æ + ö
çè ÷ø
ii) ( 1)( 2)
es
s s
-
- -
8. a) Using convolution theorem obtain the inverse transform of
( )( )2
1
s-1 s-9
b) Using transform method solve || | four three t y y y e- + + +
y(0)=y|(0)=1
10
1. a) State and discuss entropy.
b) Write the difference ranging from Diffraction and Interference
phenomena.
c) discuss Hall effect.
d) Write applications of optical fibers.
e) discuss Type-I and Type-II superconductors.
2. a) State and discuss 1st legal regulations of thermodynamics.
b) define different operations of Cannot’s cycle and derive
an expression for its efficiency.
3. a) State and discuss Gauss legal regulations and explain the application
b) explain the growth and decay of current in an LR circuit.
4. a) explain the construction and working of Michelson’s
interferometer and write applications of Michelson’s
interferometer.
b) discuss the construction and working of Nicol’s prism.
5. a) What is population inversion? define the construction and
working of He-Ne laser.
b) Write applications of lasers
| Earning: Approval pending. |
