DipIETE – ET/CS (NEW SCHEME) – Code: DE55 /
DC55
Subject: ENGINEERING MATHEMATICS - II
Time: 3 Hours
Max. Marks: 100
NOTE: There are 9
Questions in all.
· Question 1 is compulsory and carries 20 marks. Answer to Q.1 must be
written in the space provided for it in the answer book supplied and nowhere
else.
· Out of the remaining EIGHT Questions, answer any FIVE Questions.
Each question carries 16 marks.
· Any required data not explicitly given, may be suitably assumed and
stated.
Q.1 Choose the correct or the best alternative
in the following: (2
10)
a. The
value of 
is
(A) 
(B) 1
(C) 0 (D) 2
b. If 
, then 
is equal to
(A) 
(B) 
(C) 
(D) None of these
c. If 
then 
is equal to
(A) 23+2i (B) 
(C) 20+2i (D) 
d. The Modulus of 3-4i is equal to
(A) 
(B)
5
(C) 
(D) 5i
e. The cosine of angle
between the vectors 
and j+k is
(A) 
(B) 
(C) 
(D) 
f. The value of 
is
(A) 
(B) 
(C) 
(D) 
g. If roots are real & different, then C.F. (complementary function) is equal to
(A) 
(B) 
(C) 
(D) None of these
h. The Fourier series of a function f(x) of
period 
is given by
(A) 
(B) 
(C) 
(D) 
i. 
is equal to
(A) 
(B) 
(C) 
(D) 
j. 
is equal to
(A) 
(B) 
(C) 
(D) 
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Verify Rolle’s
Theorem for 
in 
. (8)
b. Using Maclaurin’s
series, expand tan x upto the term containing
. (8)
Q.3 a. Evaluate 
. (8)
b. Find
the volume of sphere of radius ‘a’. (8)
Q.4 a. If
n is a positive integer, prove that 
where 
. (8)
b. Express 
in the form of a+ib
and find Modulus of the number. (8)
Q.5 a. Show that the points
, 
, 5i+7j+3k and 
are coplanar. (8)
b. Find the area of the parallelogram determined
by the vectors i+2j+3k and 
. (8)
Q.6 a. Solve the differential equation 
. (8)
b. In an L-C-R circuit, the charge q on a plate
of a condenser is given by 
.
The circuit
is tuned to resonance so that 
. If initially the
current i and the charge q be zero, so that value of 
, the current in the circuit at a time t is given by 
. (8)
Q.7 a. Obtain the Fourier series for f(x) = 
in the interval 
. (8)
b. Expand f(x) = 1 in a sine series in 0 < x
< 
. (8)
Q.8 a. Find Laplace transform of sin2t. (8)
b. Find 
cos5t. (8)
Q.9 a. Find L -1
. (8)
b. Solve the differential equation using 
, subject to condition y(0)=3, 
and 
(8)