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# Hemchandracharya North Gujarat University 2004 B.Sc Computer Science 102 : Advance Mathematics - Question Paper

Tuesday, 22 January 2013 11:15Web

DC-2502
First Year M.Sc. (CA & IT) exam
March / April – 2004

Time: three hours] [TotalMarks:100

SECTION-1
1 (a) describe the subsequent terms with suitable examples: 3
(1) Union of 2 sets.
(2) Symmetric difference of 2 sets.
(3) Cartesian product of 2 sets.
(b) Express the subsequent sets in a Venn diagram. 4
P1=Ac n Bc n C, P2=AnBcnCc, P3=Ac n B n Cc, P4=Ac n Bc n Cc.
(c) If f, g:, IR->IR described as f (x)=3-v2.x and g(x)=2x+v3 then find: 4
(1) gof
(2) f¯¹.
(d) obtain the break-even point to the provided data: 3
Cost function C=1200+120x number article to be produced. Selling
price rs.200 per unit.

OR
one (a) State and prove the De Morgan’s legal regulations for 2 sets A and B. 4
(b) Let P={x?IN | three Q={x?IN | x is even and x<15}
R=={x?N | x+4 <15}, Universal set U=IN
find the subsequent sets.
(1) P×(Q?R)
(2) (P?Q) ×R.
(C) describe the subsequent terms with suitable example: 4
(1) Function
(2) Invertible function
(3) Even function
(4) Reverse function
(D) Let f: IR-.IR describe as f (x)=|x-2|. 3
Explain whether f¯¹ exists or not?

two (a) Saturation properties of a determinant. 3
(b) Show that r a a²
r b b² = r(a-b)(b-c)(c-a)
r c c²

0 A three
A= one A -3
-1 A one then show that ?³=A hence obtain A¯¹

(d) Solve the system of linear equations using matrix method. 4
2x+y+3z=6
4x –2y+5z=7
3x+y-2z=2

OR
two (a) show that one one one 3
X Y Z =(x-y)(y-z)(z-x).
X² Y² Z²
(b) Solve by Crammer’s rule: 15/x + 6/y =3; 16/x + 5/y =3. 3
(c) describe the subsequent terms with suitable example: 4
(1) Matrix of order m×n.
(2) Non-singular matrix.
(3) Skew-symmetric matrix.
(4) Null matrix.
(d) If 0 one two one two 3
A= three four two and B= two 0 one then obtain AB and BA(if possible). 2
one two 0
(e) If a b
A= c d then obtain AT and A¯¹. 2