2007 The Institution of Engineers (India) DE&CE Engineering Question Paper

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2007 The Institution of Engineers (India) DE&CE Engineering Question Paper

[blink]DE01 / DC01 Subject: MATHEMATICS - I[/blink]

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. The number of terms in the sequence are

(A) 8 (B) 9
(C) 10 (D) 6

b. First three terms in the expansion of are

(A) (B)
(C) (D)

c. Value of is

(A) (B)
(C) (D)

d. If , then the value of cos 2A is

(A) (B)
(C) (D)

e. The value of 'x' such that PQ = QR, where P, Q and R are (6, -1), (1, 3) and (x, respectively is given by

(A) 5, –3 (B) 3, 5
(C) 2, 5 (D) 2, 3


f. Slope of the line passing through the points & is

(A) (B)
(C) (D)
g. is equal to

(A) (B)
(C) (D)

h. If then is equal to

(A) (B)
(C) (D)

i. is equal to

(A) (B)
(C) (D)

j. Order and degree of the differential equation is given by

(A) 3, 2 (B) 2, 3
(C) 1, 3 (D) 3, 1


Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.

Q.2 a. If 5 times the 5th term of an A.P. is equal to the 10 times the 10th term, find the 15th term of the A.P. (8 )

b. If denotes the sum of n terms of a G.P., prove that . (8 )

Q.3 a. Show that . (8 )

b. If in the triangle ABC, A = , prove that . (8 )

Q.4 a. Find the equation of the straight line which passes through the intersection of the lines x + y – 3 = 0 and 2x – y = 0 and is inclined at an angle of with x-axis. (8 )

b. Show that represents an ellipse. Find its centre, vertices, foci, eccentricity, directrices, latusrectum and equations of major and minor axis. (8 )

Q.5 a. Find the equation of the circle which passes (4, 1) & (6, 5) and having centre on the line 4x+y =16. (8 )

b. Find the value of (8 )

Q.6 a. Differentiate y = tan x w.r.t. 'x' from first principle. (6)

b. Differentiate y = w.r.t 'x'. (10)

Q.7 a. Prove that straight line touches the curve at the point where the curve crosses the axis of y. (8 )

b. Find the volume generated by revolving the ellipse about x-axis. (8 )

Q.8 a. Prove that . (10)

b. Solve . (6)

Q.9 a. Solve . (8 )

b. Solve subject to the initial condition y(0) = 0. (8 )