# 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.