## JEE Main Mathematical Reasoning MCQs

Mathematical reasoning involves determining the truth values of the given statements. This topic is covered under the JEE Main only and not in JEE Advanced. It carries four marks and is one of the easiest concepts in the entire syllabus. Mathematical Logic is a subject that deals with the principles of reasoning. Mathematical reasoning is also called a science of proof.

## JEE Main Maths mcq

Here are some JEE MCQs on mathematical reasoning with answers:

1. Which of the following is not a statement?

(A) The sun is shining. (B) How far is Delhi from here? (C) History is a boring subject. (D) All prime numbers are odd.

“How far is Delhi from here?” is not a statement because it is not a complete sentence. It does not make sense without more information, such as what point in Delhi you are referring to and what point you are measuring the distance from.

2. Which of the following is the negation of the statement “The sun is shining”?

(A) The sun is not shining. (B) It is not the case that the sun is shining. (C) It is false that the sun is shining. (D) All of the above.

The negation of a statement is simply the opposite of the statement. In this case, the opposite of “The sun is shining” is “The sun is not shining.” All of the other options are also negations of the original statement.

3. Which of the following is a tautology?

(A) p ∨ ¬p (B) p ∧ ¬p (C) p ⇔ ¬p (D) None of the above.

A tautology is a statement that is always true. In this case, p ∨ ¬p is always true because it is always true that a statement is either true or false.

4. Which of the following is the contrapositive of the statement “If it is raining, then the ground is wet”?

(A) If the ground is wet, then it is raining. (B) If the ground is not wet, then it is not raining. (C) If it is not raining, then the ground is not wet. (D) None of the above.

The contrapositive of a statement is formed by negating both the hypothesis and the conclusion, and then reversing the order of the statement. In this case, the contrapositive of the statement “If it is raining, then the ground is wet” is “If the ground is not wet, then it is not raining.”

Sure! Here are five multiple-choice questions on mathematical reasoning with their answers:

5. Question:
If the statement “All rectangles are squares” is true, which of the following statements must also be true?
A) All squares are rectangles.
B) All parallelograms are rectangles.
C) All squares are parallelograms.
D) All rectangles are parallelograms.

Answer: A) All squares are rectangles.

6. Question:
If the statement “Some dogs are brown” is true, which of the following statements must also be true?
A) All dogs are brown.
B) Some animals are brown.
C) Some dogs are not brown.
D) All animals are brown.

Answer: B) Some animals are brown.

7. Question:
If the statement “All prime numbers are odd” is true, which of the following statements must also be true?
A) All odd numbers are prime.
B) All even numbers are not prime.
C) All numbers are prime.
D) All odd numbers are not prime.

Answer: D) All odd numbers are not prime.

8. Question:
If the statement “All triangles have three sides” is true, which of the following statements must also be true?
A) All polygons have three sides.
B) All quadrilaterals have four sides.
C) All triangles have four sides.
D) All polygons have four sides.

9. Question:
If the statement “Some birds can fly” is true, which of the following statements must also be true?
A) All animals can fly.
B) All birds can fly.
C) No birds can fly.
D) Some animals can fly.

Answer: D) Some animals can fly.

These are just a few examples of JEE MCQs on mathematical reasoning. There are many more questions that could be asked on this topic, so it is important to be familiar with the different concepts involved in mathematical reasoning.

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