Anna University Chennai 2005 B.E MATHEMATICS - Question Paper

Code: D-01 / DC-01
Time: three Hours Subject: MATHEMATICS
Max. Marks: 100


NOTE: There are 11 ques. in all.
ques. one is compulsory and carries 16 marks. ans to Q. 1. must be written in the space given for it in the ans book supplied and nowhere else.
ans any 3 ques. every from Part I and Part II. every of these ques. carries 14 marks.
Any needed data not explicitly given, may be suitably presumed and said.
_____________________________________________________________________Q.1 select the accurate or best option in the following: (2x8)

a. The square root of 12 - 5i is

(A)
(C) (B)
(D)
b. b. If be the roots of then the quadratic formula whose roots are is

(A)
(C)
(B)
(D)
c.
The twelfth term in the binomial expansion of is

(A)
(C) (B)
(D)
d. The area of the triangle formed by the coordinate axes and the line 2x + 3y=6 is
(A) three sq. units.
(C) nine sq. units. (B) ) six sq. units.
(D) 12 sq. units.
e. The eccentricity of the ellipse if its latus rectum is equal to 1 half of its minor axis is
(A)

(C) ) ½ (B) )
(D)


f. In a triangle ABC, sin A - cos B = cos C, then angle B is
(A) . (B) .
(C) . (D) .
g. is equal to
(A) e-1. (B) e+1.
(C) 0. (D) 1.
h. If xy = ex-y, then is equal to
(A) (1 + logx)-1
(C) log x (1 + logx)-2 (B) (1 + logx)-2
(D) log x (1 + logx)-1
___________________________________________________
PART I
ans any 3 ques.. every ques. carries 14 marks.
_____________________________________________________
Q.2 If Show that (7)

Put the subsequent in the form r(cos + i sin), where r is a positive real number and .
(1 + seven i) / (2 - i)2 (7)
Q.3 A two-digit number is 4 times the sum and 3 times the product of the digits. obtain the number. (7)
Solve the simultaneous equations: (7)
Q.4 The diagonal of a square lies along the line 8x - 15y = 0 and 1 vertex of the square is (1, 2). obtain the equations of the sides of the square. (7)
Find the centroid and incentre of the triangle whose sides have the equations 3x-4y=0, 12y+5x=0 amd y-15=0. (7)
Q.5 (i) obtain the formula of the circle which touches both the axes and whose
radius is 5.
(ii) obtain the coordinates of the centre and radius of the circle
2x2 + 2y2 - 3x + 5y = 7. (7)
Find the formula of a circle passing through the points (1, 2) and (3, 0) and cutting an intercept four on the x-axis. (7)

Q.6 Find the formula of the parabola whose focus is (3, 0) and the directrix is 3x +4y = 1. (7)

Find the formula of an ellipse whose foci are at (± 3, 0) and which passes through (4, 1). (7)
___________________________________________________
PART II
ans any 3 ques.. every ques. carries 14 marks.
_____________________________________________________
Q.7 If , prove that (7)
(i) A man two metres high walks at a uniform speed of six metres per minute
away from a lamp post, five metres high. obtain the rate at which the
length of his shadow increases.
(ii) Use differentials to obtain the approximate value of .

(7)
Q.8 A square piece of tin of side 24 cm is to be made into a box without top by cutting a square from every corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the quantity of the box is maximum. (7)
Evaluate the subsequent integrals
(i) (ii) . (7)
Q.9 Draw the rough sketch of area enclosed by curves y2 +1 = x and x = 2. Also obtain this area. (7)
Using integration, show that the quantity of a sphere of radius a is . (7)
Q.10 Solve the subsequent differential equations
(i) (ii)
(iii)


(14)
Q.11
(i) obtain a unit vector perpendicular to both the vectors and .
(ii) If are unit vectors inclined at an angle , then prove that
(iii) obtain the moment of the couple formed by the forces and
acting at the points (9, -1, 2) and (3, -2, 1) respectively. (14)

Earning:   Approval pending.