Mathematical Reasoning Practice Questions

Class 11 · Mathematics · 1812 free MCQs with instant results and detailed explanations.

1812

Total

643

Easy

856

Medium

313

Hard

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Topics in Mathematical Reasoning

Validating Statements 240

Statements 823

Logical Connectives 749

Sample Questions from Mathematical Reasoning

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

Which of the following is a statement?

A. 2 + 2 = 4

B. What is your name?

C. Close the door.

D. Are you coming?

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Correct Answer: A

A statement is a declarative sentence that is either true or false. '2 + 2 = 4' is a true statement.

Easy

If P: It is raining, what is the negation of P?

A. It is not raining.

B. It is raining.

C. It might rain.

D. Raining is possible.

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Correct Answer: A

The negation of a statement is the opposite of the original statement. Thus, negating 'It is raining' yields 'It is not raining.'

Easy

Which of the following statements is always true?

A. All squares are rectangles.

B. Some rectangles are squares.

C. All circles are squares.

D. No triangles are polygons.

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Correct Answer: A

By definition, all squares are indeed rectangles, making this statement always true.

Medium

Which of the following statements is logically equivalent to 'If it rains, then the ground is wet'?

A. If the ground is not wet, then it does not rain

B. If it does not rain, then the ground is dry

C. It rains

D. The ground is wet

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Correct Answer: A

The contrapositive of an implication is logically equivalent.

Medium

For the statements P: 'x > 5' and Q: 'x < 10', which of the following is true if P is true?

A. Q is also true

B. Q can be false

C. Both P and Q are true

D. None of the above

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Correct Answer: B

P being true only tells us that x is greater than 5, but it could still be 10 or more, making Q false.

Medium

Consider the statements: P: 'All birds can fly' and Q: 'Penguin is a bird'. What can we conclude?

A. Penguin can fly

B. Not all birds can fly

C. Penguin is not a bird

D. All birds are penguins

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Correct Answer: B

The statement P is false because there exists at least one bird (the penguin) that cannot fly.

Medium

Which of the following represents a disjunction?

A. P and Q

B. P or Q

C. If P then Q

D. Not P

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Correct Answer: B

A disjunction is represented by 'or' in logical terms.

Hard

If the statement 'P implies Q' is true and P is false, what can be said about Q?

A. Q must be true

B. Q must be false

C. Q can be either true or false

D. Q is independent of P

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Correct Answer: C

When P is false, 'P implies Q' is true regardless of the truth value of Q. Thus, Q can be either true or false.

Hard

Which of the following is logically equivalent to the statement 'If it rains, then the ground is wet'?

A. If the ground is not wet, then it did not rain.

B. If it does not rain, the ground is not wet.

C. Either it rains or the ground is wet.

D. It rains only if the ground is wet.

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Correct Answer: A

The contrapositive of an implication is logically equivalent to the original statement. The contrapositive here is 'If not Q, then not P'.

Q10

Hard

Consider the statements: 1. All cats are mammals. 2. Some mammals are dogs. What can be concluded?

A. All mammals are cats.

B. Some cats are dogs.

C. Some mammals are not cats.

D. All dogs are mammals.

Show Answer & Explanation

Correct Answer: C

From the given statements, we cannot conclude anything about the relationship between cats and dogs. However, since not all mammals are cats, some may not be.

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Mathematical Reasoning — Class 11 Mathematics Practice Questions Online

This page contains 1812 practice MCQs for the chapter Mathematical Reasoning in Class 11 Mathematics. The questions are organized by difficulty — 643 easy, 856 medium, 313 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.