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

Tuesday, 22 January 2013 11:25Web

1st Year m. sc. (CA & IT) exam
March/April – 2002
Advanced Mathematics : Paper - 102
Time : three Hours] [Total Marks : 55
Instruction : (1) All ques. are compulsory.
(2) figures to the right index the marks of the corresponding ques..

1 (a) state and prove de-morgan rules. 3
(b) if a={1,2,3,4,5} and b={4,5,6,7} then find n(A),n(B),n(AnB)
and n(AnB) 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(x) 0; if x=0;

(e) Solve the subsequent system of linear Equations by elimination method of variables: 2
3x – 4y = 7
2x + 5y =10

OR
1 (a) describe (with ilusration) the subsequent terms :
(1) Cartesian product of 2 sets
(2) Power set.
(b) (By Venn diagram) prove that :
A-(B U C)=(A - B)n(A – C)
(c)Evaluate lim tanx-sinx
x?0 ¯¯¯¯¯¯¯¯¯¯¯¯
x3
(d) Let a function F be described as
{x; if 0=x
f(x)= {0; if x=1/2
{x-1; if ½

(e) Solve the subsequent system of linear equations by elimination method of variables :
x+y-z=2,2x+z=3,x-y+4z=-1

2 (a) 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
his salary in 2002.

(b)Determine whether the function f(x)=x3 is even or odd. Also 3
determine whether it is increasing or decreasing.
(c) Trace the curve (Cubical parabola) : y=x3. 4
(d) Draw the graph of the linear inequalities : 2
2x + y = 4, x = 0, y = 0
OR
2 (a) A function f is described as : 3
(b) 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,
(1) construct the revenue function and the cost function
(2) Fine the break – even point.
(C) obtain the point of inflexion of the curve : 4
y = 3x4 – 4x3 + 1.
(d) Draw the graph of the linear inequalities : 2
x + y = 0, x = 0, y = -1.
3 (a) In what ratio does the X-axis divide the segment joining 3
A(1,2) and B(4,5) from A and at which point ?

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