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Previous year question hub

Mathematical Reasoning - Algebra - Mathematics Previous Year Questions

Practice Mathematical Reasoning - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

120Papers
16Years
122Questions
1Topics

Mathematical Reasoning question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Mathematical Reasoning. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 85 69.7%
Medium 37 30.3%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 120 98.4%
Numerical Answer Type (NAT) 2 1.6%

Subject weightage

Top subjects by unique question coverage.

Mathematics
122 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
122 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Mathematical Reasoning
122 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 13TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT
1 Qs
JEE Main 2021 (Online) 24th February Evening Shift
2 Qs
JEE Main 2021 (Online) 24th February Morning Shift
1 Qs
JEE Main 2021 (Online) 25th February Evening Shift
1 Qs
JEE Main 2021 (Online) 25th February Morning Shift
1 Qs
JEE Main 2021 (Online) 26th February Evening Shift
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
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JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
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JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT
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JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT
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JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT
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JEE MAIN 2020 ONLINE 3RD SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 4TH SEPTEMBER EVENING SLOT
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JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT
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JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 6TH SEPTEMBER EVENING SLOT
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JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT
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JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT
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JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT
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JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT
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JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT
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JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT
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JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
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JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
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JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
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JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT
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JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
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JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT
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JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT
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JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2018 OFFLINE
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2017 OFFLINE
1 Qs
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2016 OFFLINE
1 Qs
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2015 OFFLINE
1 Qs
JEE MAIN 2014 OFFLINE
1 Qs
JEE MAIN 2013 OFFLINE
1 Qs
AIEEE 2012
1 Qs
AIEEE 2011
1 Qs
AIEEE 2010
1 Qs
AIEEE 2009
1 Qs
AIEEE 2008
2 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 13TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Evening Shift20212View paper
JEE Main 2021 (Online) 24th February Morning Shift20211View paper
JEE Main 2021 (Online) 25th February Evening Shift20211View paper
JEE Main 2021 (Online) 25th February Morning Shift20211View paper
JEE Main 2021 (Online) 26th February Evening Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT20211View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2018 OFFLINE20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT20181View paper
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT20181View paper
JEE MAIN 2017 OFFLINE20171View paper
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT20171View paper
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT20171View paper
JEE MAIN 2016 OFFLINE20161View paper
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT20161View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20161View paper
JEE MAIN 2015 OFFLINE20151View paper
JEE MAIN 2014 OFFLINE20141View paper
JEE MAIN 2013 OFFLINE20131View paper
AIEEE 201220121View paper
AIEEE 201120111View paper
AIEEE 201020101View paper
AIEEE 200920091View paper
AIEEE 200820082View paper

All Mathematical Reasoning previous year questions

Practice every matching question in batches of 20, with every available option.

1
2008 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
2
2008 · Mathematics · Algebra · Mathematical Reasoning
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
\(p \to \left( {p \wedge q} \right)\)
Open complete paper
3
2009 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
4
2010 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
5
2011 · Mathematics · Algebra · Mathematical Reasoning
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
\(\sim P \wedge \left( {Q \leftrightarrow \sim R} \right)\)
Open complete paper
6
2012 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
7
2013 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
8
2014 · Mathematics · Algebra · Mathematical Reasoning
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 \({p \leftrightarrow q}\)
Open complete paper
9
2015 · Mathematics · Algebra · Mathematical Reasoning
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
\(s \wedge \left( {r \wedge \sim s} \right)\)
Open complete paper
10
2016 · Mathematics · Algebra · Mathematical Reasoning
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
\(p \vee \sim q\)
Open complete paper
11
2016 · Mathematics · Algebra · Mathematical Reasoning
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.
Open complete paper
12
2016 · Mathematics · Algebra · Mathematical Reasoning
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)
Open complete paper
13
2017 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
14
2017 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
15
2017 · Mathematics · Algebra · Mathematical Reasoning
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.
Open complete paper
16
2018 · Mathematics · Algebra · Mathematical Reasoning
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
Open complete paper
17
2018 · Mathematics · Algebra · Mathematical Reasoning
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
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18
2018 · Mathematics · Algebra · Mathematical Reasoning
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
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19
2018 · Mathematics · Algebra · Mathematical Reasoning
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
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20
2019 · Mathematics · Algebra · Mathematical Reasoning
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
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