Class 9 Maths Chapter 9 MCQs with Answers – Propositions and Their Converses

Class 9 Maths Chapter 9 MCQs

15 MCQs for Class 9 Maths Chapter 9 – Propositions and Their Converses

Question 1. Which of the following is a proposition?

A. Please sit down.

B. What is your name?

C. 7 is a prime number.

D. Close the door.

Question 2. Which of the following statements is false?

A. 2 is an even number.

B. 9 is a prime number.

C. 5 is a prime number.

D. 12 is divisible by 3.

Question 3. What is the truth value of the statement “10 is greater than 6”?

A. True

B. False

C. Neither true nor false

D. Cannot be determined

Question 4. Which of the following is not a proposition?

A. 4 + 3 = 7.

B. 11 is an odd number.

C. Every square has four sides.

D. Please solve this equation.

Question 5. Consider the statement: “If a number is divisible by 4, then it is even.” Which is its converse?

A. If a number is even, then it is divisible by 4.

B. If a number is odd, then it is divisible by 4.

C. If a number is divisible by 2, then it is odd.

D. If a number is not divisible by 4, then it is even.

Question 6. Which statement is the converse of “If a figure is a square, then it has four sides”?

A. If a figure has four sides, then it is a square.

B. If a figure is not a square, then it has four sides.

C. If a figure has three sides, then it is a square.

D. If a figure is a square, then it has equal sides.

Question 7. Consider the statement: “If a number is divisible by 10, then it ends in 0.” Is the statement true?

A. Yes, always.

B. No, never.

C. Only for odd numbers.

D. Only for prime numbers.

Question 8. Which of the following is the converse of “If a number is divisible by 6, then it is divisible by 3”?

A. If a number is divisible by 3, then it is divisible by 6.

B. If a number is not divisible by 6, then it is not divisible by 3.

C. If a number is divisible by 2, then it is divisible by 3.

D. If a number is divisible by 3, then it is odd.

Question 9. Which statement is true?

A. Every rectangle is a square.

B. Every square is a rectangle.

C. No square is a rectangle.

D. Every quadrilateral is a square.

Question 10. Which is the converse of “If a shape is an equilateral triangle, then all its sides are equal”?

A. If all sides of a triangle are equal, then it is an equilateral triangle.

B. If a triangle has unequal sides, then it is equilateral.

C. If a shape has four sides, then it is equilateral.

D. If a triangle is equilateral, then it has three sides.

Question 11. Which statement is a proposition with a false truth value?

A. 8 is an even number.

B. 15 is divisible by 5.

C. 13 is an even number.

D. 3 + 4 = 7.

Question 12. Let p be the statement “A number is divisible by 8” and q be the statement “A number is divisible by 4.” Which implication is always true for integers?

A. If p, then q.

B. If q, then p.

C. If p, then the number is odd.

D. If q, then the number is prime.

Question 13. What is the converse of “If a number is a multiple of 12, then it is a multiple of 3”?

A. If a number is a multiple of 3, then it is a multiple of 12.

B. If a number is not a multiple of 12, then it is not a multiple of 3.

C. If a number is a multiple of 12, then it is odd.

D. If a number is a multiple of 4, then it is a multiple of 3.

Question 14. Which statement is true for every integer?

A. If an integer is divisible by 2, then it is even.

B. If an integer is odd, then it is divisible by 2.

C. If an integer is negative, then it is prime.

D. If an integer is even, then it is odd.

Question 15. A statement has the form “If p, then q.” Which option gives its converse?

A. If not p, then not q.

B. If q, then p.

C. If not q, then not p.

D. If p, then not q.

Answer Key – Class 9 Maths Chapter 9 MCQs

Answer Key with Explanations – Class 9 Maths Chapter 9

Question 1 — Correct Answer: C. 7 is a prime number.

A proposition is a declarative statement that has a definite truth value. “7 is a prime number” is a true proposition.

Question 2 — Correct Answer: B. 9 is a prime number.

This statement is false because 9 = 3 × 3, so 9 is not prime.

Question 3 — Correct Answer: A. True

Since 10 is greater than 6, the statement is true.

Question 4 — Correct Answer: D. Please solve this equation.

This is a command, not a declarative statement with a truth value.

Question 5 — Correct Answer: A. If a number is even, then it is divisible by 4.

To form the converse, interchange the hypothesis and conclusion of the original statement. The converse is not always true; for example, 6 is even but is not divisible by 4.

Question 6 — Correct Answer: A. If a figure has four sides, then it is a square.

The converse swaps the original condition and conclusion. This converse is false because many four-sided figures are not squares.

Question 7 — Correct Answer: A. Yes, always.

In the base-ten number system, every integer divisible by 10 ends in 0.

Question 8 — Correct Answer: A. If a number is divisible by 3, then it is divisible by 6.

The converse reverses the condition and conclusion. It is not always true; 9 is divisible by 3 but not by 6.

Question 9 — Correct Answer: B. Every square is a rectangle.

A square satisfies the defining properties of a rectangle: it has four right angles and opposite sides parallel.

Question 10 — Correct Answer: A. If all sides of a triangle are equal, then it is an equilateral triangle.

This is the converse of the original statement. A triangle with all three equal sides is an equilateral triangle.

Question 11 — Correct Answer: C. 13 is an even number.

This is a proposition, but it is false because 13 is odd.

Question 12 — Correct Answer: A. If p, then q.

Every integer divisible by 8 is also divisible by 4. The reverse implication is not always true; for example, 12 is divisible by 4 but not by 8.

Question 13 — Correct Answer: A. If a number is a multiple of 3, then it is a multiple of 12.

This is the converse. It is not always true; for example, 6 is a multiple of 3 but not a multiple of 12.

Question 14 — Correct Answer: A. If an integer is divisible by 2, then it is even.

This is the definition of an even integer.

Question 15 — Correct Answer: B. If q, then p.

The converse of “If p, then q” is “If q, then p.”

Quick Revision

• Proposition: A declarative statement with a definite truth value.
• Truth value: Whether a proposition is true or false.
• Conditional statement: “If p, then q.”
• Converse: “If q, then p.”
• Important: A true conditional statement does not necessarily have a true converse.

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