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. If 
, then 
is equal to
(A) 
(B) 
(C) 
(D) 
b. 
is equal to
(A) 
(B) 
(C) 
(D)
c. 
is equal to:
(A) 
(B)
(C) 
(D)
d. If 
and 
are two vectors such that 
=2, 
=3 and 
then the angle
between the vectors is equal to
(A) 
(B)
(C) 
(D)
e. If roots are in complex number then C.F. complementary function is equal to:
(A) 
(B) 
(C) 
(D) 
f. In Fourier series 
is equal to
(A) 
(B)
(C) 
(D)
g. 
is equal to:
(A) 
(B)
(C) 
(D)
h. 
is equal to:
(A) 
(B)
(C) cos t (D) sin t
i. If P be the point represented by the complex
number z such that z = x+iy, then the locus of P is equal to :__________ when 
(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. Expand 
in the power of x by Maclaur’s
theorem upto the term of 
and deduce the expansion of 
. (8)
b. Apply Taylor’s Theorem to calculate the value of 
, where 
. (8)
Q.3 a. Find the volume of the right circular cone formed by the revolution of a right angled triangle about a side which contained the right angle. (8)
b. Find the length of curve 
from origin to the point (1, 1). (8)
Q.4 a. Use De-Movire’s Theorem to
solve the equation 
. (8)
b. A resistance of 20 ohms and
inductance of 0.2 Henry and capacitance of 100 
are connected in series
across 220 volt 50 cycle / sec main. Determine,
(i) Impedance (ii) Current
(iii) Voltage across L, R and C (iv) Power in watt
(v) Power factor. (8)
Q.5 a. A rigid body is spinning with an angular velocity of 27 radian/sec about an axis parallel to 2i + j – 2k passing through the point i + 3j – k. Find the velocity of the point whose position vector is 4i + 8j + k. (8)
b. Find the moment about a line through the origin having the direction of 2i – 2j + 2k due to a 30 Kg force acting at a point (-4, 2, 5) in the direction of 12i – 4j – 3 k. (8)
Q.6 a. An L-C-R circuit has R = 180
ohms, 
L
= 20H and applied voltage E(t) = 10 sin t. Assuming that no charge is present
but an initial current of 0 (zero) amp is flowing at t = 0 when the voltage is
first applied, find Q and 
at any time t. Q is given by the
differential equation 
.
(8)
b. Solve the differential equation 
where 
. (8)
Q.7 a. An alternating current after passing through a rectifier has the form
Where 
is the maximum
current and period . Express I in a Fourier series. (8)
b. Find half range cosine series for
the function
in the range 
. (8)
Q.8 a. Find
the Laplace Transform of 
. (8)
b. Find the Laplace Transform of 
. (8)
Q.9 a. Show that, 
. (8)
b. Solve 
if y=0, Dy=1 at t = 0 and
y = 1 at t = 
. (8)