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Mathematical Reasoning

122 Questions
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET
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 :
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 :
A.
$\left( { \vee , \wedge } \right)$
B.
$\left( { \vee , \vee } \right)$
C.
$\left( { \wedge , \vee } \right)$
D.
$\left( { \wedge , \wedge } \right)$
2018 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
If p $ \to $ ($ \sim $ p$ \vee $ $ \sim $ q) is false, then the truth values of p and q are respectively :
A.
F, F
B.
T, F
C.
F, T
D.
T, T
2018 JEE Mains MCQ
JEE Main 2018 (Offline)
The Boolean expression

$ \sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$ is equvalent to :
A.
${ \sim q}$
B.
${ \sim p}$
C.
p
D.
q
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
Consider the following two statements :

Statement p :
The value of sin 120o can be derived by taking $\theta = {240^o}$ in the equation
2sin${\theta \over 2} = \sqrt {1 + \sin \theta } - \sqrt {1 - \sin \theta } $

Statement q :
The angles A, B, C and D of any quadrilateral ABCD satisfy the equation
cos$\left( {{1 \over 2}\left( {A + C} \right)} \right) + \cos \left( {{1 \over 2}\left( {B + D} \right)} \right) = 0$

Then the truth values of p and q are respectively :
A.
F, T
B.
T, F
C.
T, T
D.
F, F
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
If (p $ \wedge $ $ \sim $ q) $ \wedge $ (p $ \wedge $ r) $ \to $ $ \sim $ p $ \vee $ q is false, then the truth values of $p, q$ and $r$ are, respectively :
A.
F, T, F
B.
T, F, T
C.
T, T, T
D.
F, F, F
2017 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning 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 equal.
B.
If the squares of two numbers are equal, then the numbers are not equal.
C.
If the squares of two numbers are not equal, then the numbers are not equal.
D.
If the squares of two numbers are not equal, then the numbers are equal.
2017 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
The proposition $\left( { \sim p} \right) \vee \left( {p \wedge \sim q} \right)$ is equivalent to :
A.
p $ \vee $ ~ q
B.
p $ \to $ ~ q
C.
p $ \wedge $ ~ q
D.
q $ \to $ p
2017 JEE Mains MCQ
JEE Main 2017 (Offline)
The following statement

$\left( {p \to q} \right) \to \left[ {\left( { \sim p \to q} \right) \to q} \right]$ is :
A.
equivalent to ${ \sim p \to q}$
B.
equivalent to ${p \to \sim q}$
C.
a fallacy
D.
a tautology
2016 JEE Mains MCQ
JEE Main 2016 (Online) 10th April Morning Slot
The contrapositive of the following statement,

“If the side of a square doubles, then its area increases four times”, is :
A.
If the side of a square is not doubled, then its area does not increase four times.
B.
If the area of a square increases four times, then its side is doubled.
C.
If the area of a square increases four times, then its side is not doubled.
D.
If the area of a square does not increase four times, then its side is not doubled.
2016 JEE Mains MCQ
JEE Main 2016 (Online) 9th April Morning Slot
Consider the following two statements :

P :     If 7 is an odd number, then 7 is divisible by 2.
Q :    If 7 is a prime number, then 7 is an odd number

If  V1 is the truth value of the contrapositive of P and V2 is the truth value of contrapositive of Q, then the ordered pair (V1 , V2) equals :
A.
(T, T)
B.
(T, F)
C.
(F, T)
D.
(F, F)
2016 JEE Mains MCQ
JEE Main 2016 (Offline)
The Boolean expression

$\left( {p \wedge \sim q} \right) \vee q \vee \left( { \sim p \wedge q} \right)$ is equivalent to :
A.
${ \sim p \wedge q}$
B.
${p \wedge q}$
C.
$p \vee q$
D.
$p \vee \sim q$
2015 JEE Mains MCQ
JEE Main 2015 (Offline)
The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to :
A.
$s \vee \left( {r \vee \sim s} \right)$
B.
$s \wedge r$
C.
$s \wedge \sim r$
D.
$s \wedge \left( {r \wedge \sim s} \right)$
2014 JEE Mains MCQ
JEE Main 2014 (Offline)
The statement $ \sim \left( {p \leftrightarrow \sim q} \right)$ is :
A.
equivalent to ${ \sim p \leftrightarrow q}$
B.
a tautology
C.
a fallacy
D.
equivalent to ${p \leftrightarrow q}$
2013 JEE Mains MCQ
JEE Main 2013 (Offline)
Consider :
Statement − I : $\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.
Statement − II :$\left( {p \to q} \right) \leftrightarrow \left( { \sim q \to \sim p} \right)$ is a tautology.
A.
Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
B.
Statement -I is True; Statement -II is False.
C.
Statement -I is False; Statement -II is True
D.
Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I
2012 JEE Mains MCQ
AIEEE 2012
The negation of the statement “If I become a teacher, then I will open a school” is :
A.
I will become a teacher and I will not open a school
B.
Either I will not become a teacher or I will not open a school
C.
Neither I will become a teacher nor I will open a school
D.
I will not become a teacher or I will open a school
2011 JEE Mains MCQ
AIEEE 2011
Consider the following statements
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement,

“Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as :
A.
$ \sim \left[ {Q \leftrightarrow \left( {P \wedge \sim R} \right)} \right]$
B.
$ \sim Q \leftrightarrow P \wedge R$
C.
$ \sim \left( {P \wedge \sim R} \right) \leftrightarrow Q$
D.
$ \sim P \wedge \left( {Q \leftrightarrow \sim R} \right)$
2010 JEE Mains MCQ
AIEEE 2010
Let S be a non-empty subset of R. Consider the following statement:
P : There is a rational number x ∈ S such that x > 0.
Which of the following statements is the negation of the statement P?
A.
There is no rational number x ∈ S such that x ≤ 0
B.
Every rational number x ∈ S satisfies x ≤ 0
C.
x ∈ S and x ≤ 0 $ \Rightarrow $ x is not rational
D.
There is a rational number x ∈ S such that x ≤ 0
2009 JEE Mains MCQ
AIEEE 2009
Statement-1 : $ \sim \left( {p \leftrightarrow \sim q} \right)$ is equivalent to ${p \leftrightarrow q}$.
Statement-2 : $ \sim \left( {p \leftrightarrow \sim q} \right)$ is a tautology.
A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
C.
Statement-1 is true, Statement-2 is false
D.
Statement-1 is false, Statement-2 is true
2008 JEE Mains MCQ
AIEEE 2008
Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.

Statement –1: r is equivalent to either q or p.

Statement –2: r is equivalent to $ \sim \left( {p \leftrightarrow \sim q} \right)$
A.
Statement − 1 is false, Statement − 2 is false
B.
Statement −1 is false, Statement −2 is true
C.
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
D.
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1
2008 JEE Mains MCQ
AIEEE 2008
The statement $p \to \left( {q \to p} \right)$ is equivalent to
A.
$p \to \left( {p \leftrightarrow q} \right)$
B.
$p \to \left( {p \to q} \right)$
C.
$p \to \left( {p \vee q} \right)$
D.
$p \to \left( {p \wedge q} \right)$