Fall 2016 Business Mathematics
This is the question set along with answers of Fall 2016 Business Mathematics, which was taken by Pokhara University.
POKHARA UNIVERSITY
Fall 2016 Business Mathematics
Level: Bachelor  Semester – Fall  Year: 2016 
Program: BCIS  Full Marks: 100  
Course: Mathematics II  Pass Marks: 45  
Time:3hrs  
Candidates are required to give their answers in their own words as far as practicable.  
The figures in the margin indicate full marks. 
Section “A”
Very Short Answer Questions
Attempt all the questions.  10×2  
1  Evaluate  2 
2  Show that  2 
3  Test whether the series is convergent.  2 
4  Prove that u = x^{2} – y^{2} is harmonic  2 
5  Solve the differential equation:
y dx – x dy = x^{2}y dx 
2 
6  Express in the polar form √ 3 + i  2 
7  Integrate  2 
8  Define a periodic function with an example.  2 
9  Find the period of the function f(x)=cosnx  2 
10  _{Solve }  2 
Section “B”
Descriptive Answer Questions
Attempt any six questions  6×10  
11  Integrate any two of the following.  
12  a) Find the volume of solid generated by revolving about the x – axis, the areas bounded by the curve y=5x – x^{2} and the lines; x = 0, x = 5.
Find the arc length of the curve, y=2/3 (x+1)^{2/3},0≤x ≤2 

13  Solve the following differential equations:
a) b) 

14  a) Solve:
Prove that the necessary condition for the convergence of an infinite series ∑un is but it is not sufficient. 

15  a) Test for the convergence series of the
b) Find Fourier sine and cosine integral of the function 

16  a) Find the Fourier series of the function
Find the Fourier series of the function . 

17  Find the harmonic conjugate and corresponding analytic function of
What are the necessary conditions for a function of complex variables to be analytic? Show that the function f(z)= is analytic. 
Section “C”
Case Analysis  
18  a) Let be defined and continuous in some neighborhoods of a point Z=x+iy and differentiable at Z itself. Then at that point , the first order Partial derivatives of u and v exist and satisfy the Cauchy Riemann equation prove.
State and prove Pseries test. 
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