These AP 9th Class Maths Important Questions 15th Lesson Proofs in Mathematics will help students prepare well for the exams.

## AP State Syllabus 9th Class Maths 15th Lesson Important Questions and Answers Proofs in Mathematics

Question 1.

If two coins are tossed, then write all possible outcomes.

Solution:

Head = H, Tail = T

All possible outcomes = HH, HT, TH, TT

Choose the correct answer:

Question 1.

The statement “the sum of two odd numbers is odd” is

A) always true

B) always false

C) ambiguous

D) none

Answer:

B) always false

Question 2.

The statement “every number can be expressed as product of primes” is

A) always true

B) always false .

C) sometimes true

D) ambiguous

Answer:

A) always true

Question 3.

A statement or an idea which gives an explanation to a series of observations is called

A) Conclusion

B) Open sentence

C) Hypothesis

D) Result

Answer:

C) Hypothesis

Question 4.

The Mathematics is mainly based on ………………. reasoning.

A) Inductive

B) Deductive

C) Both

D) None

Answer:

B) Deductive

Question 5.

Counter example to “product of two odd integers is even” is

A) 7 × 5 = 35

B) 3 × 4 = 12

C) 2 × 6 = 12

D) Not possible

Answer:

D) Not possible

Question 6.

God is immortal. Rama is a God; the conclusion based on these two statements

A) Rama is mortal

B) Rama is a God

C) God is Rama

D) Rama is immortal

Answer:

D) Rama is immortal

Question 7.

A mathematical statement whose truth has been established is called

A) Axiom

B) Conjecture

C) Theorem

D) Postulate

Answer:

C) Theorem

Question 8.

The mathematical statement which we believe to be true is called

A) postulate

B) conjecture

C) axiom

D) theorem

Answer:

B) conjecture

Question 9.

Conjecture are made based on

A) Inductive reasoning

B) Deductive reasoning

C) Proofs

D) None

Answer:

A) Inductive reasoning

Question 10.

The conjecture “If the perimeter of a rectangle increases then its area also increases” is

A) True

B) False

C) Neither true nor false

D) None

Answer:

B) False

Question 11.

A counter example to the statement “In any right triangle the square of the smallest side equals to sum of the other sides” is

A) (3, 4, 5)

B) (5, 12, 13)

C) (6, 8, 10)

D) (7, 24, 25)

Answer:

C) (6, 8, 10)

Question 12.

“A circle may be drawn with any centre and radius” is ……………….

A) Axiom

B) Conjecture

C) Theorem

D) Open sentence

Answer:

A) Axiom

Question 13.

A false axiom results into a ………………..

A) theorem

B) true statement

C) contradiction

D) none

Answer:

C) contradiction

Question 14.

If in a collection of axioms, one axiom can be used to prove other axiom, then they are said to be

A) consistent

B) inconsistent

C) false

D) true

Answer:

B) inconsistent

Question 15.

If a statement and its negation both are true, then it is a

A) Tautology

B) Contradiction

C) Conjecture

D) Postulate

Answer:

B) Contradiction

Question 16.

A process which can establish the truth of a mathematical statement based on logic is called

A) Mathematical proof

B) Disproof

C) Counter example

D) None

Answer:

A) Mathematical proof

Question 17.

The product of two consecutive even numbers is always divisible by

A) 3

B) 5

C) 4

D) 8

Answer:

C) 4

Question 18.

Counter example to”2n^{2} + 11 is a prime” is

A) 3

B) 4

C) 5

D) 11

Answer:

D) 11

Question 19.

Counter example to the statement “a quadrilateral with all sides equal is a square” is

A) Rectangle

B) Rhombus

C) Trapezium

D) Parallelogram

Answer:

B) Rhombus

Question 20.

We prove the statement “sum of interior angles of a triangle is 180°” by

A) Counter example

B) Inductive reasoning

C) Deductive reasoning

D) None

Answer:

B) Inductive reasoning

Question 21.

Statements which are assumed to be true without proof are

A) axioms

B) counter examples

C) conjectures

D) open sentences

Answer:

A) axioms

Question 22.

If x is odd, then x^{2} is

A) even

B) prime

C) odd

D) none of these

Answer:

C) odd

Question 23.

A sentence which is clearly true or false but not both is called a

A) Axiom

B) Theorem m

C) Conjecture

D) Statement

Answer:

D) Statement

Question 24.

Which of the following is a mathemati¬cal statement ?

A) She has blue eyes.

B) x + 7 = 18

C) Today is not Sunday.

D) What time is it ?

Answer:

B) x + 7 = 18

Question 25.

A statement of idea which gives an explanation to a sense of observation is

A) Hypothesis

B) Proof

C) Analysis

D) Conclusion

Answer:

A) Hypothesis

Question 26.

A great Indian Mathematician is

A) Euclid

B) Pythagoras

C) Srinivasa Ramanujan

D) Gold Bach

Answer:

C) Srinivasa Ramanujan

Question 27.

Which of the following subjects is based on inductive reasoning?

A) Mathematics

B) Social Studies

C) Science

D) English

Answer:

C) Science

Question 28.

Which of the following statement is always false?

A) February has only 28 days

B) Dogs fly

C) A rhombus is a parallelogram

D) For any real number x, x^{2} ≥ 0

Answer:

B) Dogs fly

Question 29.

The very helpful technique for making conjecture is

A) Inductive reasoning

B) Deductive reasoning

C) Experimental evidence

D) Observation

Answer:

A) Inductive reasoning

Question 30.

Which of the following is a theorem?

A) A rhombus is a parallelogram.

B) Humans are meant to rule the earth.

C) The product of two odd natural numbers is odd.

D) A straight line may be drawn from any point to any other point.

Answer:

C) The product of two odd natural numbers is odd.

Question 31.

“A quadrilateral can be a rectangle” if the following condition is satisfied.

A) When diagonals are equal

B) When one angle is right angle

C) Anyone of A or B

D) Both A and B

Answer:

A) When diagonals are equal

Question 32.

Which one of the following is an example for a primary data

A) Temperatures of a place during last 10 years

B) Mid day meals records of a school in a month

C) Literacy rate of various states in the year 2001

D) List of absentee students of a day in 9th class.

Answer:

D) List of absentee students of a day in 9th class.