1
(Department of Mathematics and Statistics)
WARNING
1. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING
THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD
OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
2. SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Course: Mathematics-I (1307) Semester: Spring, 2012
Level: F.A/F/Sc Total Marks: 100
ASSIGNMENT No. 1
(Units 1–4)
Q.1 a) Define rational and irrational numbers with examples. Also show that
5
is
irrational number.
b) Define with examples the following properties of real numbers.
i. Addition Laws ii. Multiplication Laws
iii. Multiplication Addition Laws iv. Properties of Equality
v. Order Properties
Q.2 a) State and prove five different properties of the modulus of the complex
numbers.
b) A ball in dropped from height 10 m. The distance traveled by the ball each
time it hits the ground is ½ of the previous height. Find the total distance
traveled by the ball.
Q.3 a) Verify De Morgan’s Laws by using Venn Diagrams and also using suitable sets.
b) Prove that
(p
~
)~(~)()~ qppqpqp
Q.4 a) Prove that all
33
non-singular matrices over the real field form a non-
abelian group under matrix multiplication.
b) State the properties of determinants with examples.
Q.5 a) Find the value of
for which the following system does not possess a unique
solution. Also solve the system for the value of
.
16223
1122
24
321
321
321
xxx
xxx
xxx
