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

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DC-2502

First Year M.S

**c.**(CA & IT) exam

March / April – 2004

Advance Mathematics: Paper – 102

**Time:**three hours] [Total

**Marks:**100

**SECTION-1**

1

**(**describe the subsequent terms with suitable examples: 3

**a)**(1) Union of 2 sets.

(2) Symmetric difference of 2 sets.

(3) Cartesian product of 2 sets.

**(**Express the subsequent sets in a Venn diagram. 4

**b)**P1=Ac n Bc n C, P2=AnBcnCc, P3=Ac n B n Cc, P4=Ac n Bc n Cc.

**(**If f, g:, IR->IR described as f (x)=3-v2.x and g(x)=2x+v3 then find: 4

**c)**(1) gof

(2) f¯¹.

**(**obtain the break-even point to the provided data: 3

**d)**Cost function C=1200+120x number article to be produce

**d.**Selling

price rs.200 per unit.

OR

one

**(**State and prove the De Morgan’s legal regulations for 2 sets A and B. 4

**a)****(**Let P={x?IN | three

**b)**R=={x?N | x+4 <15}, Universal set U=IN

find the subsequent sets.

(1) P×(Q?R)

(2) (P?Q) ×R.

**(**describe the subsequent terms with suitable example: 4

**C)**(1) Function

(2) Invertible function

(3) Even function

(4) Reverse function

**(**Let f: IR-.IR describe as f (x)=|x-2|. 3

**D)**Explain whether f¯¹ exists or not?

two

**(**Saturation properties of a determinant. 3

**a)****(**Show that r a a²

**b)**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

**(**Solve the system of linear equations using matrix method. 4

**d)**2x+y+3z=6

4x –2y+5z=7

3x+y-2z=2

OR

two

**(**show that one one one 3

**a)**X Y Z =(x-y)(y-z)(z-x).

X² Y² Z²

**(**Solve by Crammer’s rule: 15/x + 6/y =3; 16/x + 5/y =3. 3

**b)****(**describe the subsequent terms with suitable example: 4

**c)**(1) Matrix of order m×n.

(2) Non-singular matrix.

(3) Skew-symmetric matrix.

(4) Null matrix.

**(**If 0 one two one two 3

**d)**A= three four two and B= two 0 one then obtain AB and BA(if possible). 2

one two 0

**(**If a b

**e)**A= c d then obtain AT and A¯¹. 2

Earning: Approval pending. |