Krantiguru Shyamji Krishna Verma Kachchh University 2012 B.C.A Computer Application University of maths - Question Paper

Second semester m.sc.(ca& it)

Internal examination 2010-11

Sub: advanced mathematics

Marks: 70

q1. Attempt any two :

1. Define:

I.                Square matrix.

II.            Transpose of matrix.

III.        Symmteric matrix.

2. Define;

I.                Empty graph.

II.            Degree of graph.

III.        Complete graph.

3. Define:

I.                Graph.

II.            Tree.

III.        Path in a graph.

IV.        Leaf of the tree.

(b) attempt any two:

I. If y=x^x+sinx^x, find dy/dx.

Ii. Solve the differential equation.

(1+x²) dy= xy dx.

IV.        Find the equation of the straight line which passes through the intersection of the line x+2y+3=0 and 3x+4y+7=0 and is per pendicular to the line y-x=8.

Q2. A. Attempt any two:

1.   Define:

I.                Complement of set.

II.            Cartesian product of set.

III.        Difference of two set.

2.   Let u={ 1,2,3,4,5,6,7,8}, a={ 1,2,3,4}, b={ 2,4,6} and c={1,2,5} find (aU b) Uc.

3.   If a demand function of a commodity is d=343-7p².

I.                What will be its demand when price is rs.3?

II.            At what price its demand will be zero?

(b) attempt any two.

1. Prove that

1 1 1

a b c

a² b² c² = (a-b)(b-c)(c-a)

2. If a= [1 0 2

2 1 0

3 2 1] then find a^-1.

3. Solve the following system of equation by Cramers rule:

X+2y+3z=6

2x+4y+z=7

3x+2y+9z=14

Q3. A. Attempt any two:

1. Evaluate

lim x³-8/x⁵-32

x 2

2. Function f is defined as:

f(x)= x²-1/x+1, x!=-1

=-2 , x=-1

Discuss the continuity of function f at x=-1.

3 if y=x cot x, then find dy/dx.