Mathematical Reasoning PYQs - Last 10 Years
JEE Main / Mathematics / Algebra / 115 recent questions
MathematicsAlgebra2014-2023
Practice 115 JEE Main Mathematics questions from Mathematical Reasoning. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
115
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Mathematics / Algebra
2014-2023
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115
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115PYQs
MCQ97.4%
INTEGER1.7%
MCQM0.9%
Difficulty Mix
#1 Easy80
#2 Medium35
103 in last 5 years115 in last 10 years
Last 10 Years Mathematical Reasoning Questions
Showing 50 of 115 filtered questions.
1Mathematical Reasoning
Negation of \((p \Rightarrow q) \Rightarrow(q \Rightarrow p)\) is :
MCQ+4 / -12023
2Mathematical Reasoning
The negation of \((p \wedge(\sim q)) \vee(\sim p)\) is equivalent to :
MCQ+4 / -12023
3Mathematical Reasoning
Statement \(\mathrm{(P \Rightarrow Q) \wedge(R \Rightarrow Q)}\) is logically equivalent to :
MCQ+4 / -12023
4Mathematical Reasoning
Among the statements
(S1) : \((p \Rightarrow q) \vee((\sim p) \wedge q)\) is a tautology
(S2) : \((q \Rightarrow p) \Rightarrow((\sim p) \wedge q)\) is a contradiction
(S1) : \((p \Rightarrow q) \vee((\sim p) \wedge q)\) is a tautology
(S2) : \((q \Rightarrow p) \Rightarrow((\sim p) \wedge q)\) is a contradiction
MCQ+4 / -12023
5Mathematical Reasoning
\((\mathrm{S} 1)~(p \Rightarrow q) \vee(p \wedge(\sim q))\) is a tautology
\((\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)\) is a contradiction.
Then
\((\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)\) is a contradiction.
Then
MCQ+4 / -12023
6Mathematical Reasoning
The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \vee \mathrm{q})) \wedge((\mathrm{p} \wedge \mathrm{r}) \Rightarrow \math...
MCQ+4 / -12023
7Mathematical Reasoning
Among the statements :
\((\mathrm{S} 1)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow(\mathrm{p} \Rightarrow \mathrm{r})\)
$$(\mathrm{S} 2)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow((\math...
\((\mathrm{S} 1)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow(\mathrm{p} \Rightarrow \mathrm{r})\)
$$(\mathrm{S} 2)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow((\math...
MCQ+4 / -12023
8Mathematical Reasoning
Consider the following statements:
P : I have fever
Q: I will not take medicine
$\mathrm{R}$ : I will take rest.
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to :
P : I have fever
Q: I will not take medicine
$\mathrm{R}$ : I will take rest.
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to :
MCQ+4 / -12023
9Mathematical Reasoning
If \(p,q\) and \(r\) are three propositions, then which of the following combination of truth values of \(p,q\) and \(r\) makes the logical expression $$\left\{ {(p \vee q) \wedge \left( {( \sim p) \vee r} \right)} \right\} \to \left( {( \s...
MCQ+4 / -12023
10Mathematical Reasoning
The statement \(B \Rightarrow \left( {\left( { \sim A} \right) \vee B} \right)\) is equivalent to :
MCQM+4 / -12023
11Mathematical Reasoning
The statement \(\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)\) is
MCQ+4 / -12023
12Mathematical Reasoning
Let \(\Delta ,\nabla \in \{ \wedge , \vee \}\) be such that \(\mathrm{(p \to q)\Delta (p\nabla q)}\) is a tautology. Then
MCQ+4 / -12023
13Mathematical Reasoning
The compound statement \(\left( { \sim (P \wedge Q)} \right) \vee \left( {( \sim P) \wedge Q} \right) \Rightarrow \left( {( \sim P) \wedge ( \sim Q)} \right)\) is equivalent to
MCQ+4 / -12023
14Mathematical Reasoning
Let p and q be two statements. Then \(\sim \left( {p \wedge (p \Rightarrow \, \sim q)} \right)\) is equivalent to
MCQ+4 / -12023
15Mathematical Reasoning
The negation of the expression \(q \vee \left( {( \sim \,q) \wedge p} \right)\) is equivalent to
MCQ+4 / -12023
16Mathematical Reasoning
Which of the following statements is a tautology?
MCQ+4 / -12023
17Mathematical Reasoning
Negation of $p \wedge(q \wedge \sim(p \wedge q))$ is :
MCQ+4 / -12023
18Mathematical Reasoning
The negation of the statement \(((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A\) is
MCQ+4 / -12023
19Mathematical Reasoning
The statement \((p \wedge(\sim q)) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))\) is equivalent to _________.
MCQ+4 / -12023
20Mathematical Reasoning
Among the two statements
\((\mathrm{S} 1):(p \Rightarrow q) \wedge(p \wedge(\sim q))\) is a contradiction and
\((\mathrm{S} 2):(p \wedge q) \vee((\sim p) \wedge q) \vee(p \wedge(\sim q)) \vee((\sim p) \wedge(\sim q))\) is a tautology
\((\mathrm{S} 1):(p \Rightarrow q) \wedge(p \wedge(\sim q))\) is a contradiction and
\((\mathrm{S} 2):(p \wedge q) \vee((\sim p) \wedge q) \vee(p \wedge(\sim q)) \vee((\sim p) \wedge(\sim q))\) is a tautology
MCQ+4 / -12023
21Mathematical Reasoning
The number of ordered triplets of the truth values of \(p, q\) and \(r\) such that the truth value of the statement \((p \vee q) \wedge(p \vee r) \Rightarrow(q \vee r)\) is True, is equal to ___________.
INTEGER+4 / -12023
22Mathematical Reasoning
The converse of \(((\sim p) \wedge q) \Rightarrow r\) is
MCQ+4 / -12023
23Mathematical Reasoning
The negation of the statement \((p \vee q) \wedge (q \vee ( \sim r))\) is :
MCQ+4 / -12023
24Mathematical Reasoning
The statement \(\sim[p \vee(\sim(p \wedge q))]\) is equivalent to :
MCQ+4 / -12023
25Mathematical Reasoning
The conditional statement
\(((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q))\) is :
\(((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q))\) is :
MCQ+4 / -12022
26Mathematical Reasoning
Let \(\Delta\) \(\in\) {\(\wedge\), \(\vee\), \(\Rightarrow\), \(\Leftrightarrow\)} be such that (p \(\wedge\) q) \(\Delta\) ((p \(\vee\) q) \(\Rightarrow\) q) is a tautology. Then \(\Delta\) is equal to :
MCQ+4 / -12022
27Mathematical Reasoning
Negation of the Boolean statement (p \(\vee\) q) \(\Rightarrow\) ((\(\sim\) r) \(\vee\) p) is equivalent to :
MCQ+4 / -12022
28Mathematical Reasoning
The statement \((p \wedge q) \Rightarrow(p \wedge r)\) is equivalent to :
MCQ+4 / -12022
29Mathematical Reasoning
The statement \((p \Rightarrow q) \vee(p \Rightarrow r)\) is NOT equivalent to
MCQ+4 / -12022
30Mathematical Reasoning
Let p, q, r be three logical statements. Consider the compound statements
\({S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)\) and
\({S_2}:p \to (q \vee r)\)
Then, which of the following is NOT true?
\({S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)\) and
\({S_2}:p \to (q \vee r)\)
Then, which of the following is NOT true?
MCQ+4 / -12022
31Mathematical Reasoning
The maximum number of compound propositions, out of p\(\vee\)r\(\vee\)s, p\(\vee\)r\(\vee\)\(\sim\)s, p\(\vee\)\(\sim\)q\(\vee\)s, \(\sim\)p\(\vee\)\(\sim\)r\(\vee\)s, \(\sim\)p\(\vee\)\(\sim\)r\(\vee\)\(\sim\)s, \(\sim\)p\(\vee\)q\(\vee\)$...
INTEGER+4 / -12022
32Mathematical Reasoning
Let the operations \(*, \odot \in\{\wedge, \vee\}\). If \((\mathrm{p} * \mathrm{q}) \odot(\mathrm{p}\, \odot \sim \mathrm{q})\) is a tautology, then the ordered pair \((*, \odot)\) is :
MCQ+4 / -12022
33Mathematical Reasoning
Let
\(\mathrm{p}\) : Ramesh listens to music.
\(\mathrm{q}\) : Ramesh is out of his village.
\(\mathrm{r}\) : It is Sunday.
\(\mathrm{s}\) : It is Saturday.
Then the statement "Ramesh listens to music only if he is in his village and it is ...
\(\mathrm{p}\) : Ramesh listens to music.
\(\mathrm{q}\) : Ramesh is out of his village.
\(\mathrm{r}\) : It is Sunday.
\(\mathrm{s}\) : It is Saturday.
Then the statement "Ramesh listens to music only if he is in his village and it is ...
MCQ+4 / -12022
34Mathematical Reasoning
The boolean expression \(( \sim (p \wedge q)) \vee q\) is equivalent to :
MCQ+4 / -12022
35Mathematical Reasoning
Which of the following statement is a tautology?
MCQ+4 / -12022
36Mathematical Reasoning
\((p \wedge r) \Leftrightarrow(p \wedge(\sim q))\) is equivalent to \((\sim p)\) when \(r\) is
MCQ+4 / -12022
37Mathematical Reasoning
If the truth value of the statement \((P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)\) is F, then the truth value of which of the following is \(\mathrm{F}\) ?
MCQ+4 / -12022
38Mathematical Reasoning
Let \(\Delta\), \(\nabla\) \(\in\) {\(\wedge\), \(\vee\)} be such that p \(\nabla\) q \(\Rightarrow\) ((p \(\Delta\) q) \(\nabla\) r) is a tautology. Then (p \(\nabla\) q) \(\Delta\) r is logically equivalent to :
MCQ+4 / -12022
39Mathematical Reasoning
Let r \(\in\) {p, q, \(\sim\)p, \(\sim\)q} be such that the logical statement
r \(\vee\) (\(\sim\)p) \(\Rightarrow\) (p \(\wedge\) q) \(\vee\) r
is a tautology. Then r is equal to :
r \(\vee\) (\(\sim\)p) \(\Rightarrow\) (p \(\wedge\) q) \(\vee\) r
is a tautology. Then r is equal to :
MCQ+4 / -12022
40Mathematical Reasoning
The statement \((\sim(\mathrm{p} \Leftrightarrow \,\sim \mathrm{q})) \wedge \mathrm{q}\) is :
MCQ+4 / -12022
41Mathematical Reasoning
Negation of the Boolean expression \(p \Leftrightarrow(q \Rightarrow p)\) is
MCQ+4 / -12022
42Mathematical Reasoning
Consider the following two propositions:
\(P1: \sim (p \to \sim q)\)
\(P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)\)
If the proposition \(p \to (( \sim p) \vee q)\) is evaluated as FALSE, then :
\(P1: \sim (p \to \sim q)\)
\(P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)\)
If the proposition \(p \to (( \sim p) \vee q)\) is evaluated as FALSE, then :
MCQ+4 / -12022
43Mathematical Reasoning
The negation of the Boolean expression ((\(\sim\) q) \(\wedge\) p) \(\Rightarrow\) ((\(\sim\) p) \(\vee\) q) is logically equivalent to :
MCQ+4 / -12022
44Mathematical Reasoning
Which of the following statements is a tautology ?
MCQ+4 / -12022
45Mathematical Reasoning
Consider the following statements:
P : Ramu is intelligent.
Q : Ramu is rich.
R : Ramu is not honest.
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:
P : Ramu is intelligent.
Q : Ramu is rich.
R : Ramu is not honest.
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:
MCQ+4 / -12022
46Mathematical Reasoning
The number of choices for \(\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \}\), such that \((p\Delta q) \Rightarrow ((p\Delta \sim q) \vee (( \sim p)\Delta q))\) is a tautology, is :
MCQ+4 / -12022
47Mathematical Reasoning
Consider the following statements:
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is
MCQ+4 / -12022
48Mathematical Reasoning
Let *, ▢ \(\in\){\(\wedge\), \(\vee\)} be such that the Boolean expression (p * \(\sim\) q) \(\Rightarrow\) (p ▢ q) is a tautology. Then :
MCQ+4 / -12021
49Mathematical Reasoning
Negation of the statement (p \(\vee\) r) \(\Rightarrow\) (q \(\vee\) r) is :
MCQ+4 / -12021
50Mathematical Reasoning
The compound statement \((P \vee Q) \wedge ( \sim P) \Rightarrow Q\) is equivalent to :
MCQ+4 / -12021