A-AS Level (CIE) Mathematics Paper-1: Specimen Questions with Answers 8 - 11 of 20
Question 8
Answer
c.Explanation
For a quadratic equation , the sum of its roots and the product of its roots .
If and are roots then
Now,
Hence,
Question 9
Answer
a.Explanation
Polar form of a complex number
Let be a point representing a non-zero complex number in the Argand plane. If makes an angle with the positive direction of x-axis, then is called the polar form of the complex number, where and . Here is called argument or amplitude of and we write it as .
Given that,
Question 10
Answer
c.Explanation
Consider
For , we get
Question 11
Question MCQ▾
The relation on numbers has the following properties.
(i) (Reflexivity)
(ii) If and then (Antisymmetry)
(iii) If and then (Transitivity)
Which of the above properties the relation on has?
Choices
Choice (4) | |
---|---|
a. | (i) , (ii) and (iii) |
b. | (i) and (iii) |
c. | (i) and (ii) |
d. | (ii) and (iii) |
Answer
a.Explanation
Reflexive Relation
In a reflexive relation, every element map to itself. For example, consider a set Now an example of reflexive relation will be . The reflexive relation is given by
Transitive Relation
For transitive relation, if , then . For a transitive relation, and
(i) ( Every set is a subset of itself. Reflexivity is true)
(ii) if and then
Antisymmetric property hold
(iii) hence . Transitivity hold.
All of the above properties the relation on hold true.