AP 9th Class Maths Important Questions Chapter 15 Proofs in Mathematics

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

Question 1.
The statement “the sum of two odd numbers is odd” is
A) always true
B) always false
C) ambiguous
D) none
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
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
C) Hypothesis Question 4.
The Mathematics is mainly based on ………………. reasoning.
A) Inductive
B) Deductive
C) Both
D) None
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
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
D) Rama is immortal

Question 7.
A mathematical statement whose truth has been established is called
A) Axiom
B) Conjecture
C) Theorem
D) Postulate
C) Theorem

Question 8.
The mathematical statement which we believe to be true is called
A) postulate
B) conjecture
C) axiom
D) theorem
B) conjecture

Question 9.
A) Inductive reasoning
B) Deductive reasoning
C) Proofs
D) None
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
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)
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
A) Axiom

Question 13.
A false axiom results into a ………………..
A) theorem
B) true statement
D) none

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
B) inconsistent

Question 15.
If a statement and its negation both are true, then it is a
A) Tautology
C) Conjecture
D) Postulate

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
A) Mathematical proof Question 17.
The product of two consecutive even numbers is always divisible by
A) 3
B) 5
C) 4
D) 8
C) 4

Question 18.
Counter example to”2n2 + 11 is a prime” is
A) 3
B) 4
C) 5
D) 11
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
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
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
A) axioms

Question 22.
If x is odd, then x2 is
A) even
B) prime
C) odd
D) none of these
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
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 ?
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
A) Hypothesis

Question 26.
A great Indian Mathematician is
A) Euclid
B) Pythagoras
C) Srinivasa Ramanujan
D) Gold Bach
C) Srinivasa Ramanujan

Question 27.
Which of the following subjects is based on inductive reasoning?
A) Mathematics
B) Social Studies
C) Science
D) English
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, x2 ≥ 0
B) Dogs fly Question 29.
The very helpful technique for making conjecture is
A) Inductive reasoning
B) Deductive reasoning
C) Experimental evidence
D) Observation
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.
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