2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th August Morning Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Evening Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Morning Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 25th July Evening Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 25th July Morning Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 22th July Evening Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 20th July Evening Shift
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) 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
JEE Mains
MCQ
JEE Main 2021 (Online) 20th July Morning Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 18th March Evening Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 17th March Evening Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 17th March Morning Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 16th March Morning Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 26th February Evening Shift
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 :
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
JEE Mains
MCQ
JEE Main 2021 (Online) 25th February Evening Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 25th February Morning Shift
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
JEE Mains
MCQ
JEE Main 2021 (Online) 24th February Evening Shift
The negation of the statement
$ \sim p \wedge (p \vee q)$ is :
$ \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
JEE Mains
MCQ
JEE Main 2021 (Online) 24th February Evening Shift
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) $( \sim q \wedge (p \to q)) \to \sim p$
(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
JEE Mains
MCQ
JEE Main 2021 (Online) 24th February Morning Shift
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.
$\left[ {A \vee \left( {A \wedge B} \right)} \right]$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Evening Slot
Consider the statement :
‘‘For an integer n, if n3 – 1 is even, then n is odd.’’
The contrapositive statement of this statement is :
‘‘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
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Morning Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Evening Slot
The statement
$\left( {p \to \left( {q \to p} \right)} \right) \to \left( {p \to \left( {p \vee q} \right)} \right)$ is :
$\left( {p \to \left( {q \to p} \right)} \right) \to \left( {p \to \left( {p \vee q} \right)} \right)$ 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
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Morning Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Evening Slot
Contrapositive of the statement :
‘If a function f is differentiable at a, then it is also continuous at a’, is:
‘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
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Morning Slot
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:
$\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow \sim q} \right)$ 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
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Evening Slot
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 :
(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
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Morning Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Evening Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Morning Slot
The contrapositive of the statement
"If I reach the station in time, then I will catch the train" is :
"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
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Evening Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Morning Slot
Negation of the statement :
$\sqrt 5 $ is an integer or 5 is an irrational is :
$\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
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Evening Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Morning Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Evening Slot
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
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Morning Slot
The logical statement (p $ \Rightarrow $ q) $\Lambda $ ( q $ \Rightarrow $ ~p) is equivalent to :
A.
q
B.
$ \sim $p
C.
p
D.
$ \sim $q
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
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
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
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
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
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
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
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
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
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
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
For any two statements p and q, the negation of
the expression
p $ \vee $ (~p $ \wedge $ q) is :
p $ \vee $ (~p $ \wedge $ q) is :
A.
p$ \leftrightarrow $q
B.
~p$ \wedge $~q
C.
p$ \wedge $q
D.
~p$ \vee $~q
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
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)
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
The contrapositive of the statement "If you are
born in India, then you are a citizen of India", is :
A.
If you are not a citizen of India, then you are
not born in India.
B.
If you are born in India, then you are not a
citizen of India.
C.
If you are a citizen of India, then you are born
in India.
D.
If you are not born in India, then you are not
a citizen of India
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Evening Slot
The expression $ \sim $ ($ \sim $ p $ \to $ q) is logically equivalent to :
A.
p $ \wedge $ q
B.
$ \sim $ p $ \wedge $ $ \sim $ q
C.
p $ \wedge $ $ \sim $ q
D.
$ \sim $ p $ \wedge $ q
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
The Boolean expression ((p $ \wedge $ q) $ \vee $ (p $ \vee $ $ \sim $ q)) $ \wedge $ ($ \sim $ p $ \wedge $ $ \sim $ q) is equivalent to :
A.
p $ \wedge $ q
B.
p $ \wedge $ ($ \sim $ q)
C.
p $ \vee $ ($ \sim $ q)
D.
($ \sim $ p) $ \wedge $ ($ \sim $ q)
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :
A.
If the squares of two numbers are equal, then the numbers are not equal
B.
If the squares of two numbers are equal, then the numbers are equal
C.
If the squares of two numbers are not equal, then the numbers are equal
D.
If the squares of two numbers are not equal, then the numbers are not equal
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Morning Slot
If q is false and p $ \wedge $ q $ \leftrightarrow $ r is true, then which one of the following statements is a tautology ?
A.
P $ \wedge $ r
B.
(p $ \vee $ r) $ \to $ (p $ \wedge $ r)
C.
p $ \vee $ r
D.
(p $ \wedge $ r) $ \to $ (p $ \vee $ r)
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
Consider the following three statements :
P : 5 is a prime number
Q : 7 is a factor of 192
R : L.C.M. of 5 and 7 is 35
Then the truth value of which one of the following statements is true ?
P : 5 is a prime number
Q : 7 is a factor of 192
R : L.C.M. of 5 and 7 is 35
Then the truth value of which one of the following statements is true ?
A.
(P $ \wedge $ Q) $ \vee $ ($ \sim $ R)
B.
P $ \vee $ ($ \sim $ Q $ \wedge $ R)
C.
(~ P) $ \wedge $ ($ \sim $ Q $ \wedge $ R)
D.
($ \sim $ P) $ \vee $ (Q $ \wedge $ R)
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Morning Slot
Consider the statement : "P(n) : n2 – n + 41 is prime". Then which one of the following is true ?
A.
P(5) is false but P(3) is true
B.
Both P(3) and P(5) are true
C.
P(3) is false but P(5) is true
D.
Both P(3) and P(5) are false
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
The logical statement
[ $ \sim $ ( $ \sim $ p $ \vee $ q) $ \vee $ (p $ \wedge $ r)] $ \wedge $ ($ \sim $ q $ \wedge $ r) is equivalent to :
[ $ \sim $ ( $ \sim $ p $ \vee $ q) $ \vee $ (p $ \wedge $ r)] $ \wedge $ ($ \sim $ q $ \wedge $ r) is equivalent to :
A.
( $ \sim $ p $ \wedge $ $ \sim $ q) $ \wedge $ r
B.
$ \sim $ p $ \vee $ r
C.
(p $ \wedge $ r) $ \wedge $ $ \sim $ q
D.
(p $ \wedge $ $ \sim $ q) $ \vee $ r
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Morning Slot
If the Boolean expression
(p $ \oplus $ q) $\wedge$ (~ p $ \odot $ q) is equivalent
to p $\wedge$ q, where $ \oplus , \odot \in \left\{ { \wedge , \vee } \right\}$, then the
ordered pair $\left( { \oplus , \odot } \right)$ is :
(p $ \oplus $ q) $\wedge$ (~ p $ \odot $ q) is equivalent
to p $\wedge$ q, where $ \oplus , \odot \in \left\{ { \wedge , \vee } \right\}$, then the
ordered pair $\left( { \oplus , \odot } \right)$ is :
A.
$\left( { \vee , \wedge } \right)$
B.
$\left( { \vee , \vee } \right)$
C.
$\left( { \wedge , \vee } \right)$
D.
$\left( { \wedge , \wedge } \right)$
