MTH202 Final Term Solved Subjective with References by Moaaz

LATEST SOLVED SUBJECTIVES FROM Final term PAPERS · July 12,2011 · Latest Subjective · Spring 2011

Q1. R

be defined by

5marks

x x

f x

Is f one-to-one?

Solution:

x x x x

x x x x

x x x x x x x x

x x x x 4x x x x

x x x x x x x x x x x x

x1 = x2 Therefore this function is one to one function

Q2. Find the gcd of 1075, 45 using dividing algorithm.

5marks

Solution:

1. Divide 1075 by 45:
2. Divide 45 by 40:
3. Divide 40 by 5:

Hence gcd (1075, 45) = 5.

Q3.  and x

 for x=-2.01

3 marks

–2.01 = –3 + 0.99 = –3 –2.01 = –3+ 0.999 = –3 + 1 = –2

Q4. Find the greatest common division for the following pair of integer: 30,105 2marks Solution:

1. Divide 105 by 30:

Hence gcd (105,30) = 30

Q5. Find the Spanning tree for the graph

1,5 ?

K

2marks

Q6. Determine which f is a function?

n

f x

Q7. What is the difference between? {a,b} and {{a,b}}? Solution:

{a,b} is a set while {{a,b}} is a subset of some set.

Q8. How many 3-digits can be formed by using each one of the digits 2,3,5,7,9 only once?

Solution:

5* 4* 3 = 60

Q9. what is the smallest integer N such that [N/9] =6?

N 

Spring 2010

Q31. “A or not B occurs” (2 marks)

Q32. Find a non-isomorphic tree with four vertices. (2 marks)

Any tree with four vertices has (4-1=3) three edges. Thus, the total degree of a tree with 4 vertices must be 6 [by using total degree=2(total number of edges)].

Also, every tree with more than one vertex has at least two vertices of degree 1, so the only possible combinations of degrees for the vertices of the trees are 1, 1, 1, 3 and 1, 1, 2, 2. The corresponding trees (clearly non-isomorphic, by definition) are

Q33. Write the following in the factorial form: (2 marks)

n(n -1)(n-2)…( n-r+1)

n n n n r n r n n n n r n r

n n r