Code: DE-01
/ DC-01 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 best alternative in the following: (2x10)
a. If 
, then n is equal to
(A) 8 (B) 12
(C) 16 (D) 20
b. 
is
equal to
(A) 0 (B) 1
(C) 2 (D) 3
c. If the point P(x,
y) is equidistant from the points 
and 
, then
(A) bx = ay (B) ax = by
(C) x = y (D) x + y = 0
d. The area of the triangle formed by the lines y = a + x, y = a – x, y = 0, where a > 0, is
(A) 1 (B) a
(C) 
(D)
zero
e. If 
is equal to
(A) 1 (B) 2
(C) 
(D)
f. 
is equal to
(A)
sec x
+ cosec x (B) 
(C) 
(D)
g. The area bounded
by the parabola 
and
its latus rectum is
(A)
(B)
(C) 
(D)
h. The solution of differential
equation 
is
(A)
(B)
(C) 
(D) 
i. Value of 
is
(A)
(B)
(C) 
(D)
j. Value of 
is
(A) 0 (B) 1
(C) 
(D)
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. The sum of first p terms of an A.P. is the same as the sum of its first q terms. Find the sum of its first (p + q) terms. (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.3 a. Solve
for 
the equation 
, where 
. (8)
b. If a, b, c be the
sides opposite to the angles A, B, C for a triangle ABC, show that 
. (8)
Q.4 a. Derive the formula
for the angle between the straight lines 
and 
. (8)
b. Find the equation of a straight line which is perpendicular to 2x – 5y = 30 and the sum of its intercepts on the coordinate axes is 7. (8)
Q.5 a. Find the equation
of the circle concentric with the circle 
and having its area equal to 
. (8)
b. Find
the centre, eccentricity, foci and length of the latus rectum of the ellipse 
. (8)
Q.6 a. Differentiate from the first principle the function y = tan x. (8)
b. Evaluate 
. (8)
Q.7 a. Find
the local maximum and minimum values of the function y =
sin 3x – 3 sin x, 
. (8)
b. Evaluate 
. (8)
Q.8 a. Find
the area bounded by the curve 
and the coordinate axes. (8)
b. Evaluate
. (8)
Q.9 Solve any TWO of the following differential equations:-
(i) 
.
(ii)
.
(iii)
. (2
x 8 = 16)