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Posted Date: 16 May 2009 Posted By: Ashis Dubey Member Level: Diamond
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2008 The Institution of Engineers,India Diploma Computer Engineering DPIETE : DE01 / DC01 : MATHEMATICS - I (JUN 08) University Question paper
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 best alternative in the following: (2x10)
a. Which term of the series 37+32+27+22+.............. is –103?
(A) 24th (B) 30th
(C) 15th (D) 29th
b. How many terms are there in the expansion of
(A) 4 (B) 6
(C) 16 (D) 10
c. If and , find the value of cot
(A) (B)
(C) (D)
d. Expansion of is equal to
(A) (B)
(C) (D)
e. For what value of k do the points & lie on a straight line.
(A) 3 (B) 4
(C) 0 (D) 1
f. Mid point of the line joining (3, 5) and is given by
(A) (B) (1, 2)
(C) (2, 3) (D) (2, 1)
g. is equal to
(A) (B) 2
(C) (D)
h. If y = x sin x, then is equal to
(A) cos x + sin x (B) cos x + x sin x
(C) x cos x + sin x (D) x cos x – sin x
i. is equal to
(A) tan x + c (B)
(C) (D)
j. The solution of the differential equation is
(A) (x + y) = k (1 – xy) (B) y – x = kxy
(C) (D)
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. How many terms are there in a finite AP whose first and fifth terms are respectively –14 & 2 and the sum of terms is 40. (8)
b. The sum of three numbers in G.P. is and their product is –1. Find the numbers. (8)
Q.3 a. If , prove that
(8)
b. In any triangle ABC, prove that (8)
Q.4 a. The acute angle between two lines is and slope of one of them is . Find the slope of the other line. (8)
b. Find the vertex, axis, focus, latus rectum and directrix of the parabola . (8)
Q.5 a. Find the equation of the circle which passes through the points (1, 1) & (2, 2) & whose radius is 1. (8)
b. Find the equation of the straight line perpendicular to 7x + 9y – 3 = 0 and passing through (3, 8) (8)
Q.6 a. Differentiate from the first principle the function y = sin 3x. (8)
b. Evaluate . (8)
Q.7 a. Find the points of maxima or minima values of the function . (8)
b. Evaluate. (8)
Q.8 a. Evaluate (8)
b. Find the area enclosed by the ellipse . (8)
Q.9 a. Solve . (8)
b. Solve . (8)
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