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) 1 (B) -1
(C) 
(D) does not exist
b. 
is equal to
(A) 
(B) 
(C) 
(D) None of these
c. 
is equal to
(A) 
(B) 
(C) 
(D) 
d. If 
, 
, then 2A+3B is equal to
(A) 
(B) 
(C) 
(D)
e. The value of 
is
(A) 0 (B) 1
(C) -1 (D) 2
f. The order of differential equation 
is
(A) 2 (B) 1
(C) 0 (D) none of these
g. The value
of 
is
(A) 522 (B) 225
(C) 252 (D) None of these
h. The value of tan 
is equal to
(A) 
(B) 
(C) 
(D) 
i. The point (-3, 4) lie in the quadrant
(A) Ist (B) IInd
(C) IIIrd (D) IVth
j. The eccentricity of the ellipse 
is
(A) 
(B) 2
(C) 
(D) None of
these
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Find 
, when 
. (8)
b. For what value of x
does sin x (1 + cos x) become maximum?
Find the maximum values. (8)
Q.3 a. Evaluate 
(8)
b. Evaluate
(8)
Q.4 a. Solve the following equation by Cramer’s Rule
(8)
b. If 
, show that 
where I is a unit
matrix of order 3. (8)
Q.5 a. Solve the differential equation
(8)
b. Solve the differential equation
(8)
Q.6 a. Find the 5th term in the expansion
of 
(8)
b. Find three numbers in A.P. whose sum is -3
and product is 8. (8)
Q.7 a. Show that 
(8)
b. Prove that 
(8)
Q.8 a. Find the area of a triangle whose vertices are (4,4), (3,-2) and (-3, 16) (8)
b. Find the angle between two straight lines
and 
(8)
Q.9 a. Find the equation of parabola
with focus(3, -4) and equation of directrix is 6x-7y+5=0 (8)
b. Find the co-ordinate of the centre and radius of the circle
. (8)