DipIETE
– ET/CS (NEW SCHEME) – Code: DE51 / DC51
Subject: ENGINEERING MATHEMATICS - I
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. 
is
(A) 
(B) 
(C) 
(D) 
b. If 
, then 
is
(A) 
(B) 
(C) 
(D) 
c. 
is
(A) 
(B) 
(C) 
(D) 
d. If 
, then value of 
is:
(A) 
(B) 
(C) 
(D)
3abc
e. If 
and 
then A+B is equal to
(A) 
(B) 
(C) 
(D) 
f. The order and degree of differential equation
is
(A) O = 1, D = 2 (B) O = 1, D = not defined
(C) O = 2, D = 1 (D) O =1, D = 1
g. The 4th
term from the end in the expansion of 
is
(A) 
(B) 
(C) 
(D) 
h. The value of 
is
(A) 
(B) 
(C) 
(D) 
i. The
slope is equal to the line 
is
(A) 
(B) 
(C) (D) 
j. The points 
and 
are the vertices of a
(A) parallelogram (B) rectangle
(C) square (D) rhombus
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. If 
, then prove that 
. (8)
b. Find the maximum
and minimum values of 
. (8)
Q.3 a. Evaluate 
. (8)
b. Evaluate
. (8)
Q.4 a. Find the matrix A satisfying the equation 
. (8)
b. Solve the following system of equations using Cramer’s rule
(8)
Q.5 a. Solve 
. (8)
b. Solve 
(8)
Q.6 a. Find the term independent of x in the
expansion of 
. (8)
b. In a set of four numbers, the first three are
in G.P. and the last three are in A.P., with common difference 6. If the first is the same as the fourth. Find the four numbers. (8)
Q.7 a. Show that 
. (8)
b. The sides of a triangle are 
and 
then prove that its
largest angle is 
. (8)
Q.8
a. If P and 
be the perpendicular
from the origin upon the straight lines 
and 
, then prove that, 
. (8)
b. Show that the perpendicular drawn from the
point (4, 1) on the line segment joining (6, 5) and (2, -1) divides it
internally in the ratio 8:5. (8)
Q.9 a. Find the equation of the
circle which passes through the points (1, -2) and (4, -3) and has its centre on line
3x+4y=7. (8)
b. Find the vertex, focus, directrix, axis and
latus-rectum of the parabola 
. (8)