DipIETE – ET / CS (OLD SCHEME)
Code: DE01 / DC01 Subject:
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. If
x is acute then 
(A) 
(B) cosec x + cot x
(C) sec x + cosec x (D) 
b. If 
is divisible
by 25 then it always leaves the remainder
(A) 2 (B) 1
(C) 3 (D) 7
c. The points (0,–1), (–2,3), (6,7) and (8,3) are
(A) collinear
(B) vertices of a parallelogram which is not a rectangle
(C) vertices of a rectangle, which is not a square
(D) None of these.
d. If
,
the family of straight lines 
passes through a fixed
point whose coordinates are given by
(A) 
(B) 
(C) 
(D) 
e. The
eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is
equal to half the distance between the foci, is
(A) 
(B) 
(C) 
(D) None of these.
f. If
is
(A) 
(B) 
(C) 
(D) None of these.
g. If
at any point on a curve the subtangent and subnormal are equal, then the
tangent is equal to
(A) ordinate (B) 
(C) 
ordinate (D) None of these.
h. The
value of 
(A) 2 (B) 3
(C) 4 (D) 0
i. The
value of 
(A) 0 (B) 
(C) 
(D) 
j. The
solution of 
is
(A) 
(B) 
(C) 
(D) None of these.
Answer any FIVE Questions out
of EIGHT Questions.
Each question carries 16
marks.
Q.2 a. Find
the value of 
(8)
b. If 
=
28, show that either cos x =
0 or
tan x =
–1. (8)
Q.3 a. If
denotes
the sum of n terms of a G.P., prove that 
. (8)
b. For what value of n are the coefficients of
second, third and fourth terms in the expansion of 
in A.P.? (8)
Q.4 a. Reduce the
equation x + 
y + 4 = 0 to the form x cos θ + y sin θ = p. (8)
b. Show that if the three points 
are
collinear then abc – (bc +ca +ab) +3(a + b + c) = 0.
(8)
Q.5 a. Find the equations of the circle concentric
with 
and
which touches the y-axis. (8)
b.
Find the equation of the parabola
whose focus is (5, 2) and having vertex at (3, 2). (8)
Q.6 a. Differentiate 
(8)
b. Differentiate
. (8)
Q.7 a. If
touches
the curve
=1, show that
. (8)
b. Find
the maxima and minima of the function 
for
. (8)
Q.8 a. Evaluate
. (8)
b.
If
, then prove that
. Deduce
. (8)
Q.9 a. Find the area of the smaller portion enclosed by
the curves
. (8)
b. Solve
. (8)