Mathematical Reasoning and Logic Practice Questions
JEE · Mathematics · 2126 free MCQs with instant results and detailed explanations.
2126
Total
417
Easy
944
Medium
765
Hard
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Topics in Mathematical Reasoning and Logic
Tautology and Contradiction
530
Converse Contrapositive
511
Statements
567
Logical Connectives
518
Sample Questions from Mathematical Reasoning and Logic
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
Which of the following statements is always true?
A.
If it rains, then the ground is wet.
B.
The sky is green.
C.
2 + 2 = 5.
D.
All birds can fly.
Show Answer & Explanation
Correct Answer: A
The implication 'If it rains, then the ground is wet' is generally true based on our understanding of cause and effect in nature.
Q2
Easy
If the statement 'p: I will study today' is false, which of the following is true?
A.
I will not study today.
B.
I will study tomorrow.
C.
I am studying.
D.
I have studied.
Show Answer & Explanation
Correct Answer: A
If the statement 'I will study today' is false, it logically follows that I will not study today.
Q3
Easy
What is the contrapositive of the statement 'If p, then q'?
A.
If not q, then not p.
B.
If p and q, then true.
C.
If q, then p.
D.
If not p, then q.
Show Answer & Explanation
Correct Answer: A
The contrapositive of 'If p, then q' is 'If not q, then not p', which is logically equivalent to the original statement.
Q4
Medium
Consider the following statements: (1) If p implies q and q is false, then p is false. (2) If p is true, then q must also be true in the case of p implies q. Which of the following statements is correct?
A.
Both statements are true.
B.
Only statement 1 is true.
C.
Only statement 2 is true.
D.
Both statements are false.
Show Answer & Explanation
Correct Answer: B
Statement 1 is true; if p implies q is true and q is false, then p must also be false. Statement 2 is false because p being true does not guarantee that q is true without the condition of implication.
Q5
Medium
Let p: 'It is raining.' q: 'The ground is wet.' If the statement 'If it is not raining, then the ground is not wet' is true, which of the following statements must also be true?
A.
If the ground is wet, it must be raining.
B.
If it is raining, the ground may or may not be wet.
C.
If it is not raining, the ground could still be wet.
D.
The ground is always wet if it is raining.
Show Answer & Explanation
Correct Answer: A
The statement 'If it is not raining, then the ground is not wet' suggests that rain is the only cause for a wet ground. Therefore, if the ground is wet, it must be raining.
Q6
Medium
Consider the statement: 'For every integer n, if n is even, then n^2 is even.' Which of the following is a valid logical statement that is equivalent to it?
A.
If n^2 is not even, then n is not even.
B.
If n is odd, then n^2 is odd.
C.
If n is even, then n^2 is odd.
D.
For every integer n, n^2 is even if n is even.
Show Answer & Explanation
Correct Answer: A
The contrapositive of a statement is logically equivalent to the original statement. The statement 'If n^2 is not even, then n is not even' is the contrapositive of the original.
Q7
Medium
If the statement 'P implies Q' is false, which of the following must be true?
A.
P is true and Q is false
B.
P is false
C.
Q is true
D.
P and Q are both true
Show Answer & Explanation
Correct Answer: A
The statement 'P implies Q' is only false when P is true and Q is false.
Q8
Hard
Consider the statements p: 'It rains today' and q: 'The ground is wet'. Which statement logically derives q from p?
A.
If p then q
B.
If q then p
C.
p and q are independent
D.
p or q
Show Answer & Explanation
Correct Answer: A
The statement 'If p then q' indicates that the wet ground (q) logically follows from it raining (p).
Q9
Hard
Which of the following is equivalent to the statement 'p and not q'?
A.
not (p or q)
B.
p and (not q)
C.
not p or q
D.
not p and not q
Show Answer & Explanation
Correct Answer: B
'p and not q' clearly states p is true while q is false. This matches directly with option B.
Q10
Hard
If p is true and q is false, what is the truth value of the statement 'p or q'?
A.
True
B.
False
C.
Undefined
D.
Depends on context
Show Answer & Explanation
Correct Answer: A
The statement 'p or q' is true if at least one component (p) is true, which it is in this case.
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Mathematical Reasoning and Logic — JEE Mathematics Practice Questions Online
This page contains 2126 practice MCQs for the chapter Mathematical Reasoning and Logic in JEE Mathematics. The questions are organized by difficulty — 417 easy, 944 medium, 765 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 4 topics, giving you comprehensive coverage of the entire chapter.