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l=h; dk;[email protected] Work – 2014-15
M.Sc. Maths (Final)
Max Marks – 30
Min Marks-12
funsZ'k %&
l=h; dk;Z ds izR;sd fo"k; esa dqy 30 vad gSaA lHkh iz'uksa ds
vad leku gksaxsA lHkh iz'u gy dhft,A (Assignment Work of each paper carries 30 Marks. All
questions carry equal marks. Attempt all questions.)
Advanced Calculus and Matrix - I
1.
If y=sin−1 x, then show that (1+x 2 ) y2 -xy =0
2.
∫ (x2+5x+6) dx
3.
∫ cos x+sin x+3
x2 +1
dx
π
4.
sin x−cos x
∫02 1+sin x cos x dx = 0
5. Define Differential Equations Reducible to exact differential equations.
Special Functional - II
1. We can generalize the Euler definition of the gamma function by defining the incomplete gamma
function ã(z,x) and its compliment ⌈(z, x).
2. What do you mean by the σ Gaussian function.
3. Define Orthogonal Series of Chebyshev Polynomials with example?
4. Define the Concept of Bessel’s function ?
5. What do you mean by Legendre function of order n ?
Mathematical Programming - III
1.
2.
3.
4.
5.
What do you mean by operational exercise?
Define variations in the right hand side values.
What is mathematical economics. Explain briefly.
Define mathematical formulation of the strategic planning model.
Define General network flow problem.
Fluid Mechanics - IV
1. Define property of Stokes Stream function.
2. Explain Schwarz – Christoffel Transformation.
3. Air obeying Boyle’s Law, is in motion in a uniform tube of small section. Prove that if ρ be the
density and v the velocity at a distance x from a fixed point at time t.
x2
y2
∂2 ρ
∂2
= 2
2
∂t
∂x
[(v2+ k) ρ
4. Show that a2 tan2 t + b2 cot2t =1 is a possible form of the boundary surface of a liquid and find an
expression for the normal velocity.
5. Explain Group Velocity.
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