# Hemchandracharya North Gujarat University 2002 B.Sc Computer Science 102 : Advance Mathematics - Question Paper

Tuesday, 22 January 2013 11:25Web

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1st Year m. s

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

March/April – 2002

Advanced Mathematics : Paper - 102

Time : three Hours] [Total

**Marks :**55

Instruction :

**(**All ques. are compulsory.

**1)****(**figures to the right index the marks of the corresponding ques..

**2)**1

**(**state and prove de-morgan rules. 3

**a)****(**if a={1,2,3,4,5} and b={4,5,6,7} then find n(A),n(B),n(An

**b)****B)**

and n(An

**B)**3

(c)Evaluate lim v3 - x -1 . 2

x?2 ¯¯ ¯¯¯¯¯¯¯¯¯¯

x-2

(d) Examine of continuity of the function 2

{ |x|

----; if x !=0

{ x at x=0

f

**(**0; if x=0;

**x)**(e) Solve the subsequent system of linear Equations by elimination method of variables: 2

3x – 4y = 7

2x + 5y =10

OR

1

**(**describe (with ilusration) the subsequent terms :

**a)****(**Cartesian product of 2 sets

**1)****(**Power set.

**2)****(**(By Venn diagram) prove that :

**b)**A-(B U C)=(A - B)n(A – C)

(c)Evaluate lim tanx-sinx

x?0 ¯¯¯¯¯¯¯¯¯¯¯¯

x3

**(**Let a function F be described as

**d)**{x; if 0=x

f(x)= {0; if x=1/2

{x-1; if ½

**(**Solve the subsequent system of linear equations by elimination method of variables :

**e)**x+y-z=2,2x+z=3,x-y+4z=-1

2

**(**The salary of an employee in In1995 was Rs.8000. In 1997 it will be 3 10500.Express salary S, as a linear function of time t and estimate

**a)**his salary in 2002.

(b)Determine whether the function f(x)=x3 is even or od

**d.**Also 3

determine whether it is increasing or decreasing.

**(**Trace the curve (Cubical parabol

**c)****a)**: y=x3. 4

**(**Draw the graph of the linear inequalities : 2

**d)**2x + y = 4, x = 0, y = 0

OR

2

**(**A function f is described as : 3

**a)****(**For the 1st year the fixed cost for setting up new electronic pocket 3 calculators company is Rs.3,00,000. The variable cost for producing a calculator is Rs.70.The company expects the revenue from the sales of the calculators to be Rs.270 per calculator. Then,

**b)****(**construct the revenue function and the cost function

**1)****(**Fine the break – even point.

**2)****(**obtain the point of inflexion of the curve : 4

**C)**y = 3x4 – 4x3 + 1.

**(**Draw the graph of the linear inequalities : 2

**d)**x + y = 0, x = 0, y = -1.

3

**(**In what ratio does the X-axis divide the segment joining 3

**a)**A(1,

**2)**and B(4,

**5)**from A and at which point ?

Earning: Approval pending. |