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8/3/2019 Mid Term 2009
1/3
1
UNIVERSITY OF MORATUWA Name
Department of Mathematics
MA(1012) Mathematics Group .........................................
Mid Semester Examination
Level 1 Semester 1 2009 Registration No:......................................................
Time allowed: 1 hour
Answer all questions in the given spaces
Q(1). If , and are the roots of the equation 03 cbxax then the determinant of
is .
Q(2). Find the value of for which the system of linear equations has unique solution:
2)1(
)1(
1)1(
zyx
zyx
zyx
then =..
Q(3)Find the rank of matrix
835
753
132
A , then rank of A ...
Q(4) Let
123
012
001
A and 321 ,, XXX be three columns of matrix X such that
1
3
2
,
9
3
2
,
0
0
1
321 AXXAAX then matrix X is
Q(5) Find the value of the following determinant
25250222324
1
.....
.......
.
21
.....
22
.....
23
.....22.....01223.......101
24......210
x
..
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Q(6) a) Number of primes between 40 and 100 =
b) Number of twin primes between 40and 100 =
Q(7) Let )x(f = 12 x
Given ,0 find the value so that 3x Min 10},2{ xf
Q(8) Find the solution to .652 xx
Q(9) Let 21
21 xxf
xxg sin
174 35 xxxxh
Find the formula for xhgf
Q(10) fxxx 111 4
Where f is a polynomial in . Find that f .
Q(11). p: x is a Mathematician
q: x is clever.
r: x is rich.
Write )()]([ prrqqp in words.
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Q(12). Define a sequence of sets ,.......,, 210 XXX by 0X and for 0n
}.{1 nnn XXX . Write down 321 ,, XXX .
1X =
2X =
3X =
Q(13). Let )},(),,(),,(),,(),,{( cbbbcabaaaR be a relation on the set }.,,,{ dcba What is
the minimum number of elements which need to be added to R in order that r is
becomes
(i) reflexive (ii) symmetric (iii) transitive
Q(14). Let family of set defined as
}4,|),{( myxandRyxyxAm for .Rm
Find (i) AU Rm .
Q(15). Give examples to disprove the followings
(i) )()( BABA (ii) )()()( CABACBA