A-AS Level (CIE) Mathematics Paper-1: Specimen Questions with Answers 8 - 11 of 20

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Question 8

Question

MCQ▾

If & are the roots of the equation then ________

Choices

Choice (4)

a.

b.

c.

1

d.

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

Question

MCQ▾

Let be complex numbers such that and then

Choices

Choice (4)

a.

b.

c.

d.

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

Question

MCQ▾

, is equal to ________

Choices

Choice (4)

a.

b.

c.

d.

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.

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