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M.Sc. Maths (Finsl)
Max Marks
-
Min Marks-l2
30
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I
ed 30
31.F E
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Advqnced Calculus and Matrix
sin x in power of
1.
2.
I
(Assignment Work of each paper carries 30 Marks. All questions carry equal marks. Attempt all questions.)
(a) Evaluate I#;
(b)
a*-V*
Evatuate
f
\t7=7
a*
(x-d' rj
-t
59
Verify whether the following system of linear equation are consistent, if so find there solution
x*y*z=3
x*2y--32=4
Functional
^S
: H
(b)
1.
(a)
show that 0@,b)
2.
(a)
Discuss the asymptotic expansions
(b)
3"
(a)
(b)
(a)
(b)
2"
3.
prove
that
, e) = {"
- 4f Afle
*
^* O / -'
Find the general Solution of
(1 - x2)# - .# n2y
=
Show that T, (\) = 1, T*(-7) = (-1)" - Sg/*
Express x+ as asum of chebyohev polynomials of first kind. :-+€.
for larger
Msthemuticsl
1.
.- 3l Q
^,
(^ rn.l)
1
ZS
f tS A
ramm
*qg
Distinguish between artificial and slack variables.
Describe the simplex method for solving linear programming.
- t{J'
(a)
Write down the important features associated with out pat specifications. - [Q
(n)
Write short notes on Tactical and operational decision.
(a)
Discuss the strategic moAet:-
l6(n;
-.
t 3Y
Describe the basic findings in planning.
I
*lqa
Fluid Mechqnics
1.
(a)
Derive Euler's dynamical equation in Cartesian Co-ordinates"
Derive Helmholtz vorticity
2.
(b)
(a)
(U)
3.
equation.
*
G
o
ql
Find the necessary and sufficient condition that the vortex lines may be at right angles to the
stream lines.
rtr
Discuss the case of two vortex filaments in the same
(b) oerive
general equation of large
(c) ffre cross section of a canal
,1
.
waves is
; ./raq
waves
sense. t t7
?
2OS
is semi-circle of radius a" Prove that the velocity of propagation of long
the banks of the canal being supposed vertical.
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