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JEE • MATHEMATICS • MATHEMATICAL REASONING

Mathematical reasoning practice · Mixed difficulty

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 232 questions
1 Easy
1 of 232
Understanding +4 | -1
If p:Ap:A man is happy
q:Aq:A man is rich
Then, the statement, "If a man is not happy, then he is not rich" is written as
View answer and explanation
Correct option: A
∼p→∼q\sim p \to \sim q
Option A (∼p→∼q\sim p \to \sim q) is correct because it directly translates the given statement \"If a man is not happy, then he is not rich\" into symbolic form.
2 Medium
2 of 232
Understanding +4 | -1
Consider the following compound statements.
(i) Mumbai is the capital of Rajasthan or Maharashtra.
(ii) 3\sqrt{3} is a rational or an irrational number.
(iii) 125 is a multiple of 7 or 8 .
(iv) A rectangle is a quadrilateral or a regular hexagon.
Which of the above statements is not true?
View answer and explanation
Correct option: C
(iii)
The correct answer is (iii) because 125 is neither a multiple of 7 nor 8.
3 Easy
3 of 232
Understanding +4 | -1
Let pp and qq be two Statements. Amongst the following, the Statement that is equivalent to p→qp \rightarrow q is
View answer and explanation
Correct option: B
∼p∨q\sim p \vee q
Option B (∼p∨q\sim p \vee q) is correct because it is the logically equivalent form of the implication p→qp \rightarrow q.
4 Easy
4 of 232
Analyzing +4 | -1
Let F1(A, B, C)=(A∧∼B)∨[∼C∧(A∨B)]∨∼A{F_1}(A,\,B,\,C) = \left( {A \wedge \sim B} \right) \vee \left[ { \sim C \wedge \left( {A \vee B} \right)} \right] \vee \sim A and F2(A, B)=(A∨B)∨(B→ ∼ A){F_2}(A,\,B) = \left( {A \vee B} \right) \vee (B \to \, \sim \,A) be two logical expressions. Then,
View answer and explanation
Correct option: C
F1{F_1} is not tautology but F2{F_2} is a tautology
Option C (F1{F_1} is not tautology but F2{F_2} is a tautology) is correct because F1 can be false for some truth values of A, B, and C, while F2 is always true.
5 Easy
5 of 232
Understanding +4 | -1
The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is :
View answer and explanation
Correct option: C
If the area of a square does not increases four times, then its side is not doubled.
Option C (If the area of a square does not increases four times, then its side is not doubled) is correct because it is the contrapositive of the given statement.
6 Medium
6 of 232
Understanding +4 | -1
Suppose pp : A natural number nn is odd and q:q: Natural number nn is not divisible by 2 , then the biconditional statement p⇔qp \Leftrightarrow q is
View answer and explanation
Correct option: B
a natural number nn is odd, if and only if it is not divisible by 2
Option B (a natural number nn is odd, if and only if it is not divisible by 2) correctly represents the biconditional statement p⇔qp \Leftrightarrow q based on the given definitions of pp and qq.
7 Easy
7 of 232
Understanding +4 | -1
The negation of the proposition "If 2 is prime, then 3 is odd" is
View answer and explanation
Correct option: B
2 is prime and 3 is not odd
Option B (2 is prime and 3 is not odd) is correct because it represents the negation of the conditional statement using the rule ∼(p→q)≡p∧∼q\sim (p \to q) \equiv p \wedge \sim q.
8 Easy
8 of 232
Understanding +4 | -1
Statement - 1: Contrapositive of "If the weather is cold, then it will snow" is "If it will not snow, then the weather is not cold".

Statement - 2: Negation of "If it snows then they do not drive the car" is "it snows and they drive the car".

Which of the following is true, regarding the above statements?
View answer and explanation
Correct option: B
Both S1,S2S_1, S_2
Option B (Both S1,S2S_1, S_2) is correct because Statement 1 correctly states the contrapositive, and Statement 2 correctly states the negation of the given conditional statements.
9 Easy
9 of 232
Analyzing +4 | -1
Statement (P⇒Q)∧(R⇒Q)(P \Rightarrow Q) \wedge(R \Rightarrow Q) is logically equivalent to
View answer and explanation
Correct option: D
(P∧R)⇒Q(P \wedge R) \Rightarrow Q
Option D ((P∧R)⇒Q(P \wedge R) \Rightarrow Q) is correct because it is the logical equivalent derived by converting implications to disjunctions and applying De Morgan's law.
10 Easy
10 of 232
Analyzing +4 | -1
p\mathrm{p} and q\mathrm{q} be two statements then ∼(∼p∧q)∧(p∨q)\sim(\sim p \wedge q) \wedge(p \vee q) is logically equivalent to
View answer and explanation
Correct option: C
pp
The correct answer is C. By simplifying the given logical expression using De Morgan's laws and other logical equivalences, it is shown to be logically equivalent to p.
11 Easy
11 of 232
Understanding +4 | -1
The expression ∼(∼p→q)\sim \left( { \sim p \to q} \right) is logically equivalent to
View answer and explanation
Correct option: D
∼p∧∼q\sim p \wedge \sim q
Option A (p∧∼qp \wedge \sim q) is correct because the expression simplifies to p∧∼qp \wedge \sim q using logical equivalences.
12 Medium
12 of 232
Application +4 | -1
If p,qp, q are true statements and r,sr, s are false statements, then the truth value of ∼[(p∧∼r)∨(∼q∨s)]\sim[(p \wedge \sim r) \vee(\sim q \vee s)] is
View answer and explanation
Correct option: B
0
Option B (0) is correct because by substituting the truth values of p,q,r,p, q, r, and ss into the expression and simplifying, we find the truth value to be false (0).
13 Easy
13 of 232
Understanding +4 | -1
The statement A→(B→A)A \to \left( {B \to A} \right) is equivalent to
View answer and explanation
Correct option: D
A→(A∨B)A \to \left( {A \vee B} \right)
Option D (A→(A∨B)A \to (A \vee B)) is correct because the given statement is a tautology and is equivalent to A→(A∨B)A \to (A \vee B).
14 Easy
14 of 232
Understanding +4 | -1
Consider the proposition : “ If the pressure increases, the volume decreases:. The negation of this proposition is
View answer and explanation
Correct option: C
If the volume does not decreases, the pressure does not increase
The correct answer is D because it represents the contrapositive of the original implication, which is logically equivalent to the negation.
15 Medium
15 of 232
Understanding +4 | -1
The negation of the statement, " if a quadrilateral is a square then it is a rhombus" is
View answer and explanation
Correct option: C
a quadrilateral is a square and it is not a rhombus
The correct answer is 'a quadrilateral is a square and it is not a rhombus' because it correctly represents the negation of a conditional statement (p -> q) as (p and not q).

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16 Easy
16 of 232
Understanding +4 | -1
If pp is any statement, tt is tautology & cc is a contradiction, then which of following is not correct-
View answer and explanation
Correct option: A
p∨(∼p)≡cp \vee(\sim p) \equiv c
Option A is correct because p OR (NOT p) is always true (tautology), not a contradiction.
17 Hard
17 of 232
Understanding +4 | -1
The contrapositive statement and the converse statement of "If the points P,QP, Q and R\mathrm{R} are collinear, then △PQR\triangle P Q R is not possible' are respectively ...... and ...... .
View answer and explanation
Correct option: D
Contrapositive statement : If △PQR\triangle \mathrm{PQR} is possible, then the points P,Q\mathrm{P}, \mathrm{Q} and R\mathrm{R} are not collinear, Converse : If △PQR\triangle \mathrm{PQR} is not possible, then the points P,Q\mathrm{P}, \mathrm{Q} and \mathrm\mathrm
Option C is correct because it correctly identifies the converse of the given implication.
18 Easy
18 of 232
Understanding +4 | -1
Negation of the statement (p∨q)⇒(q∨r)(p \vee q) \Rightarrow (q \vee r) is
View answer and explanation
Correct option: A
p∧∼q∧∼rp \wedge \sim q \wedge \sim r
The correct answer is A (p∧∼q∧∼rp \wedge \sim q \wedge \sim r) because it represents the negation of the given implication using logical equivalences.
19 Easy
19 of 232
Understanding +4 | -1
Which of the following not a statement in logic?
1. Earth is planet.
2. Plants are living objects.
3. −3\sqrt { - 3} is a rational number.
4. x2−5x+6<0{x^2} - 5x + 6 < 0 , when x∈−Rx \in - R.
View answer and explanation
Correct option: C
2
Option D (4) is correct because x2−5x+6<0{x^2} - 5x + 6 < 0 is a statement for a specific x value, but not a statement in logic for all x in R.
20 Medium
20 of 232
Understanding +4 | -1
Consider the following statements.

I. A sentence is called a statement, if it is either true or false.

II. The sentence, "Today is a windy day", is not a statement.

Choose the correct option.
View answer and explanation
Correct option: A
Both I and II are true
Option A (Both I and II are true) is correct because both statements accurately describe statements and non-statements in mathematical logic.
21 Medium
21 of 232
Understanding +4 | -1
If pp : It rains today, qq : I go to school, r:r: I shall meet any friends and ss : I shall go for a movie, then which of the following is the proposition: If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
View answer and explanation
Correct option: A
∼(p∧q)⇒(r∧s)\sim(p \wedge q) \Rightarrow(r \wedge s)
The correct answer is ∼(p∧q)⇒(r∧s)\sim(p \wedge q) \Rightarrow(r \wedge s) because it correctly translates the given English sentence into a logical proposition.
22 Easy
22 of 232
Understanding +4 | -1
Assertion: The compound statement with 'And' is true if all its component statements are true.

Reason: The compound statement with 'And' is false if any of its component statements is false.
View answer and explanation
Correct option: B
Assertion is correct, reason is correct; reason is not a correct explanation for assertion
Option B (Assertion is correct, reason is correct; reason is not a correct explanation for assertion) is correct because both statements about compound statements with 'And' are true, but the reason doesn't explain the assertion.
23 Easy
23 of 232
Understanding +4 | -1
Let p,q,rp, q, r be the following three statements:

p:np: n is prime

q:nq: n is odd

r:nr: n is 2

Then p→q∨rp \rightarrow q \vee r means
View answer and explanation
Correct option: A
If nn is prime then nn is odd or 2
Option A (If nn is prime then nn is odd or 2) is correct because p→q∨rp \rightarrow q \vee r means "If nn is prime, then nn is odd or nn is 2".
24 Easy
24 of 232
Analyzing +4 | -1
(p∧∼q)∧(∼p∧q)(p \wedge \sim q) \wedge(\sim p \wedge q) is
View answer and explanation
Correct option: B
A contradiction
Option B (A contradiction) is correct because the given expression simplifies to a contradiction using associative and commutative laws.
25 Easy
25 of 232
Understanding +4 | -1
p∧q→pp \wedge q \to p is
View answer and explanation
Correct option: A
A tautology
Option A is correct because p∧q→pp \wedge q \to p is always true, making it a tautology.
26 Medium
26 of 232
Understanding +4 | -1
For two statements pp and qq pp : A quadrilateral is a parallelogram. qq : The opposite sides are parallel.
Then, the compound proposition, 'A quadrilateral is a parallelogram if and only if the opposite sides are parallel', is represented by
View answer and explanation
Correct option: D
p↔qp \leftrightarrow q
Option D (p↔qp \leftrightarrow q) is correct because the \"if and only if\" statement represents a biconditional, which is denoted by the double arrow.
27 Medium
27 of 232
Analyzing +4 | -1
Statement - I - The Boolean expression (p∧∼q)∨q∨(∼p∧q)(p \wedge \sim q) \vee q \vee(\sim p \wedge q) is equivalent to p∨qp \vee q

Statement- II - The Boolean expression (p∧q)∨(p∨∼q)∧(∼p∧∼q)(p \wedge q) \vee(p \vee \sim q) \wedge(\sim p \wedge \sim q) is equivalent to (∼p)∧(∼q)(\sim p) \wedge(\sim q)
View answer and explanation
Correct option: C
Both statements are true
Option C (Both statements are true) is correct because both Boolean expressions simplify to the stated equivalences using Boolean algebra rules.
28 Medium
28 of 232
Analyzing +4 | -1
Which of the following statements is a tautology?
View answer and explanation
Correct option: C
(p∧q)→(∼(p)→q)(p \wedge q) \rightarrow(\sim(p) \rightarrow q)
Option C is correct because the truth table or logical simplification shows that the statement is always true, regardless of the truth values of p and q.
29 Easy
29 of 232
Understanding +4 | -1
The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is
View answer and explanation
Correct option: C
If I will not go to the doctor, then I am feeling well
Option C (If I will not go to the doctor, then I am feeling well) is correct because it is the contrapositive of the given statement.
30 Easy
30 of 232
Understanding +4 | -1
If pp is any logical statement, then:
View answer and explanation
Correct option: C
p∧p≡pp \wedge p \equiv p
Option C (p∧p≡pp \wedge p \equiv p) is correct because it represents the idempotent law, which states that the conjunction of a statement with itself is equivalent to the statement itself.
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Key Takeaways

  • ✓ This set contains 232 single-correct-answer MCQs on MATHEMATICAL REASONING.
  • ✓ Try each question before opening its answer. Read the explanation where one is available.
  • ✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.
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