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Re-appear BCA/Integrated BCA+MCA II (Second)
Semester Examination 2015-16
Course Code:BCA201/ICA201
Paper ID:X832401
Mathematics II
Time: 3 Hours
Max. Marks: 70
Note: Attempt six questions in all. Q. No. 1 is compulsory.
1.
a)
b)
Attempt any five of the following.
Evaluate:
dy
 y cot x  2 cos x.
dx
Test the convergence or divergence of the series:
(4x5=20)
1
3
5
2n  1


 ........... 
 ........
1.2.3 2.3.4 3.4.5
n(n  1)( n  2)
c) Is the series 12  2 2 x  32 x 2  4 2 x 3  .......  n 2 x n1  ....,
x>0, convergent or divergent?
lim (e x  1)
d) Find the limit
.
x0
x
lim log x
..
e) Find
x  0 cot x
f) Find the nth differential coefficient of log{(ax+b)(cx+d)}.
g)
Expand e a cos
h)
Solve cos x
1
x
by Maclaurin’s theorem.
dy
 y sin x  1.
dx
2.
Solve
y 2 dx  ( xy  x 2 ) dy  0.
3. a)
Evaluate:
(10)
(5)
b) Find complete solution of
(D2-2D+1)y=2X.
4.
5.
(5)
Test the convergence of the series
a(a  1) a(a  1)( a  2)
1 a 

 .......
1.2
1.2.3
Test the series for convergence
whose nth term is
(n4+1) -
(n4-1).
(10)
(10)
6.
Expand sin x by Maclaurin’s theorem.
(10)
7.
Differentiate n-times the equation
d2y
dy
(1  x 2 ) 2  x  a 2 y  0.
dx
dx
(10)
8.
Solve:
(10)
dy
 x sin 2 y  x 3 cos 2 y.
dx