Note: Refer to the following if you need clarifications. Reference on Numbers
Question 1: State True or False:
i) : True
ii) : False
iii)
: True
iv)
: True
Question 2: State True or False: Given that , are real numbers and
i) If , then
: True
ii) If , then
: True
iii) If , then
: False
iv) If , then
: False
v) If ; then
: True
vi) If , then
: False
Question 3: If , find the solution set of the inequations:
i)
Answer
ii)
Answer:
Question 4: If the replacement set is a set of whole numbers, solve:
i)
Answer:
ii)
Answer:
iii)
Answer:
iv)
Answer:
Question 5: Solve the inequation: given that
[1987]
Answer:
Question 6: If , find: i) the smallest value of
, when
is a real number ii) smallest value of
when
is an integer
Answer:
Therefore if is a real number the
and if
is an integer then
Question 7: If the replacement set is a set of real numbers, solve
i)
Answer:
ii)
Answer:
iii)
Answer:
iv)
Answer:
Question 8: Find the smallest value of for which
, where
.
Answer:
Therefore
Question 9: Find the largest value of for which
and
.
Answer:
Therefore
Question 10: Solve the inequation:
and
. [1999]
Answer:
Question 11: Given , find the solution set for
Answer:
Equation 1:
Equation 2:
Therefore
Question 12: , find the solution set for
Answer:
Equation 1:
Equation 2:
Therefore