Class 9 Maths Ganita Manjari Chapter 9 MCQs – Propositions and their Converses – challenge you to decide whether a mathematical statement is true, form its converse and check whether the converse also holds. A statement may sound convincing, but can you justify it or find a counterexample? Practise these reasoning skills through questions on Propositions and their Converses, with answers and explanations that help you recognise the difference between a claim and a valid mathematical argument.
Class 9 Maths Ganita Manjari Chapter 9 MCQ Set 1
Q1. Which statement best describes a proposition?
[A]. A question that asks for information.
[B]. A statement that is either true or false.
[C]. An instruction to draw a figure.
[D]. A statement that must always be true.
Q2. What is the converse of “If P, then Q”?
[A]. If P, then not Q.
[B]. If not P, then Q.
[C]. If Q, then P.
[D]. Both P and Q are false.
Q3. Which sentence has the same meaning as “If a positive integer is a perfect square, then it has an odd number of positive factors”?
[A]. A positive integer has an odd number of positive factors when it is a perfect square.
[B]. Every positive integer has an odd number of positive factors.
[C]. A perfect square has an even number of positive factors.
[D]. A positive integer is a perfect square when it has an odd number of positive factors.
Q4. To disprove a statement of the form “If P, then Q”, which kind of example is needed?
[A]. An example in which both P and Q are true.
[B]. An example in which P is false and Q is true.
[C]. An example in which both P and Q are false.
[D]. An example in which P is true but Q is false.
Q5. A proposition has been proved true. What can we conclude about its converse without checking it separately?
[A]. The converse must be true.
[B]. The converse may be true or false.
[C]. The converse must be false.
[D]. The converse cannot be written.
Class 9 Maths Ganita Manjari Chapter 9 MCQ Set 2
Q6. For positive integers, consider P: “If a number is even, then it is a multiple of 3.” Its converse is Q: “If a number is a multiple of 3, then it is even.” Which option is correct?
[A]. Both P and Q are false.
[B]. Both P and Q are true.
[C]. P is true, but Q is false.
[D]. P is false, but Q is true.
Q7. Which situation is a counterexample to “If the road is wet, then it has rained”?
[A]. Rain falls and the road becomes wet.
[B]. The road stays dry on a day without rain.
[C]. A tanker spills water and wets the road on a day without rain.
[D]. It rains on an uncovered road.
Q8. In △ABC, AB = AC. Which equality follows?
[A]. ∠BAC = ∠ABC.
[B]. ∠BAC = ∠BCA.
[C]. BC = AB.
[D]. ∠ABC = ∠BCA.
Q9. In △ABC, ∠ABC = 50° and ∠BCA = 50°. Which conclusion must be true?
[A]. AB = AC.
[B]. AB = BC.
[C]. AC = BC.
[D]. All three sides are equal.
Q10. A transversal cuts two distinct coplanar lines and forms a pair of equal corresponding angles. What follows?
[A]. The two lines are perpendicular.
[B]. The two lines must intersect.
[C]. The two lines are parallel.
[D]. The transversal is parallel to both lines.
Class 9 Maths Ganita Manjari Chapter 9 MCQ Set 3
Q11. Which figure disproves “If all four angles of a quadrilateral are equal, then it is a square”?
[A]. A square of side 4 cm.
[B]. A rectangle of length 6 cm and breadth 4 cm.
[C]. A triangle with three equal angles.
[D]. A quadrilateral with angles 60°, 120°, 60° and 120°.
Q12. Two right triangles have perpendicular sides 3 cm and 4 cm, and 2 cm and 6 cm, respectively. Which statement about them is correct?
[A]. They are congruent because both are right triangles.
[B]. Their areas are 12 cm² and 8 cm².
[C]. Their areas are different.
[D]. They have equal areas but are not congruent.
Q13. A triangle has side lengths 8 cm, 15 cm and 17 cm. What follows from the converse of the Baudhāyana–Pythagoras theorem?
[A]. It is right-angled, with the right angle opposite the 17 cm side.
[B]. It is right-angled, with the right angle opposite the 8 cm side.
[C]. It is equilateral.
[D]. Its side lengths cannot form a triangle.
Q14. A triangle has sides a, b and c satisfying a² + b² = c². A second triangle is constructed with perpendicular sides a and b. After finding that its hypotenuse is c, which congruence criterion compares the two triangles?
[A]. ASA
[B]. SAS
[C]. SSS
[D]. RHS, by assuming both triangles are already right-angled.
Q15. A positive integer has an odd number of distinct positive factors. What must be true?
[A]. It is a prime number.
[B]. It is a perfect square.
[C]. It is an odd number.
[D]. It is a multiple of 3.
Class 9 Maths Ganita Manjari Chapter 9 MCQ Set 4
Q16. Which factor pair of 36 contains the same factor twice and explains why its number of distinct positive factors is odd?
[A]. (1, 36)
[B]. (2, 18)
[C]. (4, 9)
[D]. (6, 6)
Q17. For real numbers a, x and y, which statement is the true converse of “If x = y, then a + x = a + y”?
[A]. If a + x = a + y, then x = y.
[B]. If x = y, then a = 0.
[C]. If a + x = a + y, then x = a.
[D]. If x ≠ y, then a = 0.
Q18. If a = m² and b = n² for integers m and n, which equality proves that ab is a perfect square?
[A]. ab = (m + n)².
[B]. ab = m² + n².
[C]. ab = (mn)².
[D]. ab = m + n.
Q19. Which choice disproves “If ab is a perfect square, then both a and b are perfect squares”?
[A]. a = 4 and b = 9.
[B]. a = 2 and b = 8.
[C]. a = 2 and b = 3.
[D]. a = 1 and b = 16.
Q20. Which pair of real numbers is a counterexample to “If x² = y², then x = y”?
[A]. x = 5, y = 5.
[B]. x = 2, y = 3.
[C]. x = 0, y = 0.
[D]. x = 5, y = −5.
Class 9 Maths Ganita Manjari Chapter 9 MCQ Set 5
Q21. For real numbers x and y, consider P: “If x = y, then x³ = y³,” and its converse Q. Which option is correct?
[A]. Both P and Q are true.
[B]. P is true, but Q is false.
[C]. P is false, but Q is true.
[D]. Both P and Q are false.
Q22. Which positive integer disproves “If a number is divisible by both 4 and 6, then it is divisible by 24”?
[A]. 24
[B]. 48
[C]. 12
[D]. 6
Q23. A positive integer n is divisible by both 5 and 12. Which conclusion is guaranteed?
[A]. n is divisible by 120.
[B]. n is divisible by 60.
[C]. n is divisible by 24.
[D]. n is divisible by 25.
Q24. Which positive integer has exactly three distinct positive factors?
[A]. 12
[B]. 16
[C]. 27
[D]. 49
Q25. Which number disproves “If a positive integer has exactly four positive divisors, then it is a product of two unequal primes”?
[A]. 8
[B]. 6
[C]. 10
[D]. 15
Class 9 Maths Ganita Manjari Chapter 9 MCQ Set 6
Q26. If a positive integer n is not a multiple of 3, what is the only common positive factor of n and n + 3?
[A]. n
[B]. 3
[C]. 1
[D]. n + 3
Q27. Which value of n disproves the claim that 4n² + 1 is prime for every positive integer n?
[A]. 1
[B]. 4
[C]. 2
[D]. 3
Q28. Which value of n gives a counterexample to “n² + n + 11 is prime for every positive integer n”?
[A]. 1
[B]. 2
[C]. 3
[D]. 10
Q29. For positive integers, consider P: “If a number is divisible by 3, then its digit sum is a multiple of 3,” and Q: “If its digit sum is a multiple of 3, then the number is divisible by 3.” Which option is correct?
[A]. P and Q are true and are converses of each other.
[B]. Only P is true.
[C]. Only Q is true.
[D]. Both are true, but they are not converses of each other.
Q30. The only given rule about a category Q is: “If a quadrilateral is of type Q, then its diagonals are equal.” A quadrilateral has equal diagonals. What can we conclude from this rule alone?
[A]. It must be of type Q.
[B]. We cannot determine whether it is of type Q.
[C]. It cannot be of type Q.
[D]. It must be a square.
