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 the limit 
is equal to
(A) 
(B) 
(C) 0 (D) -1
b. The value of definite integral 
is equal to
(A) a (B) a2
(C) 0 (D) 2a
c. The
solution of 
is
(A) 
(B) 
(C) 
(D) None of these.
d. If z
is a complex number with 
then the value of z is
(A) 
(B) 
(C) 
(D)
e. How many seconds a clock would lose per day if the length of its pendulum were increased in the ratio 900 : 901?
(A) 48 (B) 45
(C) 40 (D) 44
f. Laplace
transform of 
is
(A) 
(B) 
(C) 
(D) 
g. 
is
(A) 
(B) 
(C) 
(D) 
h. If 
then the value of 
is
(A) 
(B) 0
(C) 
(D) 
i. The volume of the parallelopiped whose three
coterminous edges are given by 
is
(A) 282 (B) -272
(C) 262 (D) 252
j. If the admittance and current of a circuit
are given by the complex numbers 
respectively, then the voltage of the circuit is
(A) 
(B) 
(C) 
(D) 
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Evaluate
(8)
b. Find the
volume formed by
the revolution of the loop of the curve 
about x-axis. (8)
Q.3 a. Separate
into real and imaginary parts. (8)
b. Find the moment about the point
M(-2,4,-6) of the force represented in magnitude and position by
where the point A and
B have the coordinates (1,2,-3) and (3,-4,2)
respectively. (8)
Q.4 a. In a condenser discharging electricity the
Voltage V satisfies the equation 
where K is a constant
and t is the time measured in seconds. Given K=50, find the time t in which V
decreases to one tenth of its original value. (8)
b. Find the Fourier series of the function 
(8)
Q.5 a. Find
the Laplace transform of 
(10)
b. Evaluate
(6)
Q.6 a. Verify
Cauchy’s mean-value theorem for the functions 
and 
in the interval (a,
b). (8)
b. Find
the Laplace transform of the function 
(8)
Q.7 a. Solve 
(8)
b. Solve 
(8)
Q.8
a. Given that 
, find the Fourier expansion of f(x). Deduce that 
(8)
b. Two circuits of impedances 2+4j ohms and 3+4j
ohms are connected in parallel and a.c. voltage of 100 volts is applied across
the parallel combination. Calculate the magnitude of the current as well as
power factor for each circuit and the magnitude of the total current for the
parallel combination and its power factor. (8)
Q.9 a. If 
find 
(8)
b. If 
, then prove that 
. Deduce that 
(8)