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ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Mathematics and Statistics)
WARNING
1.
2.
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.
SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Level: F.A/F/Sc
Total Marks: 100
Course: Mathematics-I (1307)
Semester: Autumn, 2016
Pass Marks: 40
ASSIGNMENT No. 1
(Units 1–4)
Note: Attempt all questions and each question carries equal marks.
Q.1 a)
b)
Q.2 a)
b)
Q.3 a)
Solve the following systems by reducing their augmented matrices to the
echelon form and reduced echelon form;
(20)
(i)
+ 4 +2 = 2
(ii) x + 2y +z = 2
+ -2 = 9
2x +y +2z = -1
+2 -2 =12
2x + 3y –z = 9
Use matrices to solve the following system;
Solve the following equation by factorization;
Show that
Define complex numbers and separate the following into real and imaginary
parts;
(20)
(i)
b)
c)
Q.4 a)
(i)
(20)
Prove that
Prove that
(ii)
if and only if Z is real.
is an irrational number.
If
are the roots of the equation
whose roots are;
,
(ii)
,
(iii)
1
, form the equation
(20)
,
b)
Q.5 a)
b)
If is a root of
prove that;
, Show that its other root is
and
=1
Show that each of the following statements is a tautology:
i)
(ii)
Show that the set
ordinary multiplication.
, when
,
(20)
is an Abelian group w.r.t
ASSIGNMENT No. 2
(Units 5–9)
Total Marks: 100
Pass Marks: 40
Note: Attempt all questions and each question carries equal marks.
Q.1 a)
b)
c)
Q.2 a)
b)
Q.3 a)
A die is rolled twice: Event E1 is the appearance of even number of dots and
Event E2 is the appearance of more than 4 dots, Prove that P(E1 E2) =
P(E1).P(E2).
(20)
How many 5-digit multiples of 5 can be formed from the digits 2,3,5,7,9
when no digit is repeated?
Prove that:
If y= +
+
+… and if 0
then prove that
If the H.M and A.M between two numbers are
(20)
respectively, find the
numbers.
Expand the following in ascending power of x;
(i)
(1 – x + x2 4
(ii) (1 – x – x2 4
b)
Use binomial theorem to show that
c)
Use mathematical induction to prove
(20)
for every positive integer n.
Q.4 a)
b)
The A.M between two numbers is 5 and their (positive) G.M is 4. Find the
numbers.
(20)
If
are in G.P. Show that the common ratio is
Q.5 Resolve the following into partial fractions:
(i)
(ii)
2
.
(20)