Deemed University 2011 B.C.A Computer Application University: Lingayas University Term: III Title of the : Mathematics-II - Question Paper

Roll No. ..

 

Lingayas University

BCA 1^st Year (Term II)

Examination Feb 2011

Mathematics-II (MA - 1105)

 

[Time: 3 Hours] [Max. Marks: 100]

 

Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.

 

Note: Attempt five questions in all. All questions carry equal marks. Question no. 1 is compulsory. Select two questions from Section B and two questions from Section C.

Section A

 

Q-1.

(a) (i) Prove that A∩(B-C)=(A∩B)-(A∩C)

(ii) Prove that A-(A-B)=A∩B [2x5=10]

 

(b) Consider the lattice D30={1,2,3,5,6,10,15,30} the divisor 30 ordered by divisibility

(i) Draw a hasse diagram of D30

(ii) Which element are join irreducible and atom

(iii) Find the complement of 2 and 10 if exists. [10]

 

 

 

 

Section B

 

Q-2. (a) Let U={1,2,3,4,5,6,7,8,9,10} A=(1,2,3,4,5} B={2,3,4,5,6} C={6,7,8}

Find: AUB , A-B , B-A , A-C , C∩B

(b) In a survey concerning the smoking habit of consumer, it was found that 55% smoke cigarette A, 50% smoke B, 42% smoke C ,28% smoke A and B,20% smoke A and C,12% smoke B and C and 10% smoke all three cigarette?

(i) What percentage dont smoke?

(ii) What percentage smokes exactly two brands of cigarette? [2x10=20]

 

Q-3. (a) Given A={1,2,3,4} and B ={x,y,z} let R be the relation from A to B defined as R={(1,x), (2,z), (3,x),(3,y),(3,z)}

(i) Find the Inverse relation R^-1 of R

(ii) Determine domain and range.

(b) Consider the function defined by

f : A->B such that y or f(x)=x+1

g : B->C such that z or g(y) = 2y [2x10=20]

 

Q-4. (a) Find the direction cosines of line

(b) The midpoint of the sides of a triangle are (1,5,-1), (0,4,-2), (2,3,4). Find its vertices? [2x10=20]

 

 

 

 

Section C

 

Q-5. (a) Prove that between the points P(1,2,3), Q(-1,-1,-1) and R(3,5,7) are collinear?

(b) Find the lines through (4,-3) which cut the axes so that the intercept are equal in magnitude? [2x10=20]

 

Q-6. (a) In what ratio is the line joining the point (2,1) and (5,2) divided by the line joining (3,2) and (5,0)?

(b) Find the equation and its circum circle if its center is (4,5) and its circumference passes through center of circle

x+y+4x-6y=12 [2x10=20]

 

Q-7. (a) If A={4,5,8,12} and B={1,4,6,9} C={1,2,3,4} then find

(i) A-(B-A)

(ii) A-(C-B)

(b) Find the equation of parabola whose focus is (3,-4) and directix of the line x+y-2=0. Also find the latus rectum and the equation of its axis. [2x10=20]

 

Q-8. (a) Find the equation of the line through the point of intersection of lines 5x-y=9 and x+6y=8?

(b) State and prove Demorgan laws? [2x10=20]