1
ASSIGNMENT No. 2
(Units 4–8) Total Marks: 100
Q.1 a) If
,
are the roots of the general quadratic equation. Then form the
equations whose roots are
i.
22,
ii.
1
,
1
iii.
22
1
,
1
iv.
33,
v.
33
1
,
1
vi.
1
,
1
vii.
22 ,
viii.
33
1
,
1
b) To do a piece of work, A takes 10 days more than B. Together they finish in
12 days. How long would B take to finish it alone?
Q.2 a) Discuss with examples the different cases of partial fraction resolution.
b) Prove by mathematical induction that
ln(1 ) ln(1 )
n
x n x
for any integer
0n
if x is a positive integer.
Q.3 a) The sum of an infinite geometric series is 9 and the sum of the squares of its
terms is 81/5. Find the series.
b) Find n A.Ms, G.Ms and H.Ms between two numbers a and b.
Q.4 a) Define the Permutation and Combinations and derive the formulae for
permutations and combinations of n different objects taken
)( nr
at a time.
b) Define the following with examples
i. Probability ii. Sample Space and Events
iii. Addition of probabilities iv. Multiplication of probabilities
Q.5 a) State and prove binomial theorem for any positive integer n.
b) Find the general term in the expansion of
4
1x
when
1.x
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