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Mathematical Reasoning

128 Questions Start JEE Mains Test
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET BITSAT
2021 Q51 JEE Mains MCQ
14 Mar 2026
Which of the following is equivalent to the Boolean expression p $\wedge$ $\sim$ q ?
A.
$\sim$ (q $\to$ p)
B.
$\sim$ p $\to$ $\sim$ q
C.
$\sim$ (p $\to$ $\sim$ q)
D.
$\sim$ (p $\to$ q)
2021 Q52 JEE Mains MCQ
14 Mar 2026
Negation of the statement (p $\vee$ r) $\Rightarrow$ (q $\vee$ r) is :
A.
p $\wedge$ $\sim$ q $\wedge$ $\sim$ r
B.
$\sim$ p $\wedge$ q $\wedge$ $\sim$ 4
C.
$\sim$ p $\wedge$ q $\wedge$ r
D.
p $\wedge$ q $\wedge$ r
2021 Q53 JEE Mains MCQ
14 Mar 2026
Let *, â–¢ $\in${$\wedge$, $\vee$} be such that the Boolean expression (p * $\sim$ q) $\Rightarrow$ (p â–¢ q) is a tautology. Then :
A.
* = $\vee$, â–¢ = $\vee$
B.
* = $\wedge$, â–¢ = $\wedge$
C.
* = $\wedge$, â–¢ = $\vee$
D.
* = $\vee$, â–¢ = $\wedge$
2021 Q54 JEE Mains MCQ
14 Mar 2026
The Boolean expression (p $\wedge$ q) $\Rightarrow$ ((r $\wedge$ q) $\wedge$ p) is equivalent to :
A.
(p $\wedge$ q) $\Rightarrow$ (r $\wedge$ q)
B.
(q $\wedge$ r) $\Rightarrow$ (p $\wedge$ q)
C.
(p $\wedge$ q) $\Rightarrow$ (r $\vee$ q)
D.
(p $\wedge$ r) $\Rightarrow$ (p $\wedge$ q)
2021 Q55 JEE Mains MCQ
14 Mar 2026
The statement (p $ \wedge $ (p $\to$ q) $\wedge$ (q $\to$ r)) $\to$ r is :
A.
a tautology
B.
equivalent to p $\to$ $\sim$ r
C.
a fallacy
D.
equivalent to q $\to$ $\sim$ r
2021 Q56 JEE Mains MCQ
14 Mar 2026
Consider the two statements :

(S1) : (p $\to$ q) $ \vee $ ($ \sim $ q $\to$ p) is a tautology .

(S2) : (p $ \wedge $ $ \sim $ q) $ \wedge $ ($\sim$ p $\wedge$ q) is a fallacy.

Then :
A.
only (S1) is true.
B.
both (S1) and (S2) are false.
C.
both (S1) and (S2) are true.
D.
only (S2) is true.
2021 Q57 JEE Mains MCQ
14 Mar 2026
If the truth value of the Boolean expression $\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge \left( { \sim r} \right)} \right) \to \left( {p \wedge q} \right)$ is false, then the truth values of the statements p, q, r respectively can be :
A.
T F T
B.
F F T
C.
T F F
D.
F T F
2021 Q58 JEE Mains MCQ
14 Mar 2026
Which of the following is the negation of the statement "for all M > 0, there exists x$\in$S such that x $\ge$ M" ?
A.
there exists M > 0, such that x < M for all x$\in$S
B.
there exists M > 0, there exists x$\in$S such that x $\ge$ M
C.
there exists M > 0, there exists x$\in$S such that x < M
D.
there exists M > 0, such that x $\ge$ M for all x$\in$S
2021 Q59 JEE Mains MCQ
14 Mar 2026
The compound statement $(P \vee Q) \wedge ( \sim P) \Rightarrow Q$ is equivalent to :
A.
$P \vee Q$
B.
$P \wedge \sim Q$
C.
$ \sim (P \Rightarrow Q)$
D.
$ \sim (P \Rightarrow Q) \Leftrightarrow P \wedge \sim Q$
2021 Q60 JEE Mains MCQ
14 Mar 2026
Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :
A.
The match will not be played and weather is not good and ground is wet.
B.
If the match will not be played, then either weather is not good or ground is wet.
C.
The match will be played and weather is not good or ground is wet.
D.
The match will not be played or weather is good and ground is not wet.
2021 Q61 JEE Mains MCQ
14 Mar 2026
The Boolean expression $(p \Rightarrow q) \wedge (q \Rightarrow \sim p)$ is equivalent to :
A.
$ \sim $ q
B.
q
C.
p
D.
$ \sim $ p
2021 Q62 JEE Mains MCQ
14 Mar 2026
Which of the following Boolean expressions is not a tautology?
A.
(p $\Rightarrow$ q) $ \vee $ ($ \sim $ q $\Rightarrow$ p)
B.
(q $\Rightarrow$ p) $ \vee $ ($ \sim $ q $\Rightarrow$ p)
C.
(p $\Rightarrow$ $ \sim $ q) $ \vee $ ($ \sim $ q $\Rightarrow$ p)
D.
($ \sim $ p $\Rightarrow$ q) $ \vee $ ($\sim$ q $\Rightarrow$ p)
2021 Q63 JEE Mains MCQ
14 Mar 2026
Consider the following three statements :

(A) If 3 + 3 = 7 then 4 + 3 = 8

(B) If 5 + 3 = 8 then earth is flat.

(C) If both (A) and (B) are true then 5 + 6 = 17.

Then, which of the following statements is correct?
A.
(A) is false, but (B) and (C) re true
B.
(A) and (C) are true while (B) is false
C.
(A) is true while (B) and (C) are false
D.
(A) and (B) are false while (C) is true
2021 Q64 JEE Mains MCQ
14 Mar 2026
The Boolean expression $(p \wedge \sim q) \Rightarrow (q \vee \sim p)$ is equivalent to :
A.
$q \Rightarrow p$
B.
$p \Rightarrow q$
C.
$ \sim q \Rightarrow p$
D.
$p \Rightarrow \, \sim q$
2021 Q65 JEE Mains MCQ
14 Mar 2026
If P and Q are two statements, then which of the following compound statement is a tautology?
A.
((P $ \Rightarrow $ Q) $ \wedge $ $ \sim $ Q) $ \Rightarrow $ (P $ \wedge $ Q)
B.
((P $ \Rightarrow $ Q) $ \wedge $ $ \sim $ Q) $ \Rightarrow $ Q
C.
((P $ \Rightarrow $ Q) $ \wedge $ $ \sim $ Q) $ \Rightarrow $ P
D.
((P $ \Rightarrow $ Q) $ \wedge $ $ \sim $ Q) $ \Rightarrow $ $ \sim $ P
2021 Q66 JEE Mains MCQ
14 Mar 2026
If the Boolean expression $(p \wedge q) \odot (p \otimes q)$ is a tautology, then $ \odot $ and $ \otimes $ are respectively given by :
A.
$ \vee , \to $
B.
$ \to $, $ \to $
C.
$ \wedge $, $ \vee $
D.
$ \wedge $, $ \to $
2021 Q67 JEE Mains MCQ
14 Mar 2026
If the Boolean expression (p $ \Rightarrow $ q) $ \Leftrightarrow $ (q * ($ \sim $p) is a tautology, then the boolean expression (p * ($ \sim $q)) is equivalent to :
A.
q $ \Rightarrow $ p
B.
p $ \Rightarrow $ q
C.
p $ \Rightarrow $ $ \sim $ q
D.
$ \sim $q $ \Rightarrow $ p
2021 Q68 JEE Mains MCQ
14 Mar 2026
Which of the following Boolean expression is a tautology?
A.
(p $ \wedge $ q) $ \vee $ (p $ \to $ q)
B.
(p $ \wedge $ q) $ \vee $ (p $\vee$ q)
C.
(p $ \wedge $ q) $ \to $ (p $ \to $ q)
D.
(p $ \wedge $ q) $ \wedge $ (p $ \to $ q)
2021 Q69 JEE Mains MCQ
14 Mar 2026
Let F1(A, B, C) = (A $ \wedge $ $ \sim $ B) $ \vee $ [$\sim$C $\wedge$ (A $\vee$ B)] $\vee$ $\sim$ A and
F2(A, B) = (A $\vee$ B) $\vee$ (B $ \to $ $\sim$A) be two logical expressions. Then :
A.
Both F1 and F2 are not tautologies
B.
F1 and F2 both are tautologies
C.
F1 is not a tautology but F2 is a tautology
D.
F1 is a tautology but F2 is not a tautology
2021 Q70 JEE Mains MCQ
14 Mar 2026
The contrapositive of the statement "If you will work, you will earn money" is :
A.
If you will not earn money, you will not work
B.
If you will earn money, you will work
C.
You will earn money, if you will not work
D.
To earn money, you need to work
2021 Q71 JEE Mains MCQ
14 Mar 2026
The statement A $ \to $ (B $ \to $ A) is equivalent to :
A.
A $ \to $ (A $\mathrel{\mathop{\kern0pt\longleftrightarrow} \limits_{}} $ B)
B.
A $ \to $ (A $ \vee $ B)
C.
A $ \to $ (A $ \wedge $ B)
D.
A $ \to $ (A $ \to $ B)
2021 Q72 JEE Mains MCQ
14 Mar 2026
The negation of the statement

$ \sim p \wedge (p \vee q)$ is :
A.
$p \vee \sim q$
B.
$ \sim p \vee q$
C.
$ \sim p \wedge q$
D.
$p \wedge \sim q$
2021 Q73 JEE Mains MCQ
14 Mar 2026
For the statements p and q, consider the following compound statements :

(a) $( \sim q \wedge (p \to q)) \to \sim p$

(b) $((p \vee q) \wedge \sim p) \to q$

Then which of the following statements is correct?
A.
(b) is a tautology but not (a).
B.
(a) and (b) both are not tautologies.
C.
(a) and (b) both are tautologies.
D.
(a) is a tautology but not (b).
2021 Q74 JEE Mains MCQ
14 Mar 2026
The statement among the following that is a tautology is :
A.
$B \to \left[ {A \wedge \left( {A \to B} \right)} \right]$
B.
$\left[ {A \wedge \left( {A \to B} \right)} \right] \to B$
C.
$\left[ {A \wedge \left( {A \vee B} \right)} \right]$
D.
$\left[ {A \vee \left( {A \wedge B} \right)} \right]$
2021 Q75 AP-EAPCET MCQ
20 May 2026

For what natural number $n \in N$, the inequality $2^n > n+1$ is valid?

A.
$\forall n \in N$
B.
$\forall n \geq 2$
C.
$\forall 1 \leq n \leq 3$
D.
$\forall n \in N-\{2,3\}$
2021 Q76 AP-EAPCET MCQ
20 May 2026

$n \in N$ then, the statement $8 n+16 \leq 2^n$ is true for

A.
$n=2$
B.
$n=3$
C.
$n=6$
D.
$n=5$
2021 Q77 BITSAT MCQ
11 Jun 2026

Which of the following is always true?

A.
($\sim$ p $ \vee $ $\sim$ q) $\equiv$ (p $ \wedge $ q)
B.
(p $\to$ q) $\equiv$ ($\sim$ q $\to$ $\sim$ p)
C.
$\sim$ (p $\to$ $\sim$ q) $\equiv$ (p $\wedge$ $\sim$ q)
D.
$\sim$ (p $\leftrightarrow$ q) $\equiv$ (p $\to$ q) $\to$ (q $\to$ p)
2020 Q78 JEE Mains MCQ
14 Mar 2026
Consider the statement :
‘‘For an integer n, if n3 – 1 is even, then n is odd.’’
The contrapositive statement of this statement is :
A.
For an integer n, if n is even, then n3 – 1 is even.
B.
For an integer n, if n3 – 1 is not even, then n is not odd.
C.
For an integer n, if n is odd, then n3 – 1 is even.
D.
For an integer n, if n is even, then n3 – 1 is odd.
2020 Q79 JEE Mains MCQ
14 Mar 2026
The negation of the Boolean expression p $ \vee $ (~p $ \wedge $ q) is equivalent to :
A.
$p \wedge \sim q$
B.
$ \sim $$p \vee \sim q$
C.
$ \sim p \wedge q$
D.
$ \sim p \wedge \sim q$
2020 Q80 JEE Mains MCQ
14 Mar 2026
The statement
$\left( {p \to \left( {q \to p} \right)} \right) \to \left( {p \to \left( {p \vee q} \right)} \right)$ is :
A.
a tautology
B.
a contradiction
C.
equivalent to (p $ \vee $ q) $ \wedge $ ($ \sim $ p)
D.
equivalent to (p $ \wedge $ q) $ \vee $ ($ \sim $ q)
2020 Q81 JEE Mains MCQ
14 Mar 2026
The negation of the Boolean expression x $ \leftrightarrow $ ~ y is equivalent to :
A.
$\left( {x \wedge y} \right) \vee \left( { \sim x \wedge \sim y} \right)$
B.
$\left( { \sim x \wedge y} \right) \vee \left( { \sim x \wedge \sim y} \right)$
C.
$\left( {x \wedge y} \right) \wedge \left( { \sim x \vee \sim y} \right)$
D.
$\left( {x \wedge \sim y} \right) \vee \left( { \sim x \wedge y} \right)$
2020 Q82 JEE Mains MCQ
14 Mar 2026
Contrapositive of the statement :
‘If a function f is differentiable at a, then it is also continuous at a’, is:
A.
If a function f is continuous at a, then it is not differentiable at a.
B.
If a function f is not continuous at a, then it is differentiable at a.
C.
If a function f is not continuous at a, then it is not differentiable at a.
D.
If a function f is continuous at a, then it is differentiable at a.
2020 Q83 JEE Mains MCQ
14 Mar 2026
Given the following two statements:

$\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow \sim q} \right)$ is a tautology

$\left( {{S_2}} \right): \,\,\sim q \wedge \left( { \sim p \leftrightarrow q} \right)$ is a fallacy. Then:
A.
both (S1) and (S2) are not correct
B.
only (S1) is correct
C.
only (S2) is correct
D.
both (S1) and (S2) are correct
2020 Q84 JEE Mains MCQ
14 Mar 2026
Let p, q, r be three statements such that the truth value of
(p $ \wedge $ q) $ \to $ ($ \sim $q $ \vee $ r) is F. Then the truth values of p, q, r are respectively :
A.
T, F, T
B.
F, T, F
C.
T, T, T
D.
T, T, F
2020 Q85 JEE Mains MCQ
14 Mar 2026
The proposition p $ \to $ ~ (p $ \wedge $ ~q) is equivalent to :
A.
($ \sim $p) $ \vee $ q
B.
q
C.
($ \sim $p) $ \wedge $ q
D.
($ \sim $p) $ \vee $ ($ \sim $q)
2020 Q86 JEE Mains MCQ
14 Mar 2026
Which of the following is a tautology ?
A.
$\left( { \sim p} \right) \wedge \left( {p \vee q} \right) \to q$
B.
$\left( {q \to p} \right) \vee \sim \left( {p \to q} \right)$
C.
$\left( {p \to q} \right) \wedge \left( {q \to p} \right)$
D.
$\left( { \sim q} \right) \vee \left( {p \wedge q} \right) \to q$
2020 Q87 JEE Mains MCQ
14 Mar 2026
The contrapositive of the statement
"If I reach the station in time, then I will catch the train" is :
A.
If I will catch the train, then I reach the station in time.
B.
If I do not reach the station in time, then I will not catch the train.
C.
If I will not catch the train, then I do not reach the station in time.
D.
If I do not reach the station in time, then I will catch the train.
2020 Q88 JEE Mains MCQ
14 Mar 2026
If p $ \to $ (p $ \wedge $ ~q) is false, then the truth values of p and q are respectively :
A.
T, T
B.
T, F
C.
F, T
D.
F, F
2020 Q89 JEE Mains MCQ
14 Mar 2026
Negation of the statement :

$\sqrt 5 $ is an integer or 5 is an irrational is :
A.
$\sqrt 5 $ is not an integer and 5 is not irrational.
B.
$\sqrt 5 $ is irrational or 5 is an integer.
C.
$\sqrt 5 $ is an integer and 5 is irrational.
D.
$\sqrt 5 $ is not an integer or 5 is not irrational.
2020 Q90 JEE Mains MCQ
14 Mar 2026
Which of the following statements is a tautology?
A.
~(p $ \wedge $ ~q) $ \to $ p $ \vee $ q
B.
~(p $ \vee $ ~q) $ \to $ p $ \vee $ q
C.
~(p $ \vee $ ~q) $ \to $ p $ \wedge $ q
D.
p $ \vee $ (~q) $ \to $ p $ \wedge $ q
2020 Q91 JEE Mains MCQ
14 Mar 2026
Which one of the following is a tautology?
A.
P $ \wedge $ (P $ \vee $ Q)
B.
P $ \vee $ (P $ \wedge $ Q)
C.
Q $ \to $ (P $ \wedge $ (P $ \to $ Q))
D.
(P $ \wedge $ (P $ \to $ Q)) $ \to $ Q
2020 Q92 JEE Mains MCQ
14 Mar 2026
Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A $ \subseteq $ B and B $ \subseteq $ D, then A $ \subseteq $ C" is :
A.
If A ⊈ C, then A ⊈ B or B ⊈ D
B.
If A ⊈ C, then A ⊈ B and B $ \subseteq $ D
C.
If A $ \subseteq $ C, then B $ \subset $ A or D $ \subset $ B
D.
If A ⊈ C, then A $ \subseteq $ B and B $ \subseteq $ D
2020 Q93 JEE Mains MCQ
14 Mar 2026
The logical statement (p $ \Rightarrow $ q) $\Lambda $ ( q $ \Rightarrow $ ~p) is equivalent to :
A.
q
B.
$ \sim $p
C.
p
D.
$ \sim $q
2019 Q94 JEE Mains MCQ
14 Mar 2026
The Boolean expression ~(p $ \Rightarrow $ (~q)) is equivalent to :
A.
p $ \wedge $ q
B.
q $ \Rightarrow $ ~p
C.
p $ \vee $ q
D.
(~p) $ \Rightarrow $ q
2019 Q95 JEE Mains MCQ
14 Mar 2026
If the truth value of the statement p $ \to $ (~q $ \vee $ r) is false (F), then the truth values of the statements p, q, r are respectively :
A.
T, F, T
B.
F, T, T
C.
T, T, F
D.
T, F, F
2019 Q96 JEE Mains MCQ
14 Mar 2026
The negation of the Boolean expression ~ s $ \vee $ (~r $ \wedge $ s) is equivalent to :
A.
~ s $ \wedge $ ~ r
B.
r
C.
s $ \vee $ r
D.
s $ \wedge $ r
2019 Q97 JEE Mains MCQ
14 Mar 2026
Which one of the following Boolean expressions is a tautology?
A.
(p $ \vee $ q) $ \wedge $ (~ p $ \vee $ ~ q)
B.
(p $ \vee $ q) $ \vee $ ( p $ \vee $ ~ q)
C.
(p $ \wedge $ q) $ \vee $ ( p $ \wedge $ ~ q)
D.
(p $ \vee $ q) $ \wedge $ ( p $ \vee $ ~ q)
2019 Q98 JEE Mains MCQ
14 Mar 2026
If p $ \Rightarrow $ (q $ \vee $ r) is false, then the truth values of p, q, r are respectively :-
A.
F, F, F
B.
T, F, F
C.
F, T, T
D.
T, T, F
2019 Q99 JEE Mains MCQ
14 Mar 2026
For any two statements p and q, the negation of the expression
p $ \vee $ (~p $ \wedge $ q) is :
A.
p$ \leftrightarrow $q
B.
~p$ \wedge $~q
C.
p$ \wedge $q
D.
~p$ \vee $~q
2019 Q100 JEE Mains MCQ
14 Mar 2026
Which one of the following statements is not a tautology?
A.
(p $ \wedge $ q) $ \to $ (~ p) $ \vee $ q
B.
(p $ \wedge $ q) $ \to $ p
C.
( p $ \vee $ q) $ \to $ ( p $ \vee $ (~q))
D.
p $ \to $ ( p $ \vee $ q)