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Previous year question hub

Functions - Calculus - Mathematics Previous Year Questions

Practice Functions - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

128Papers
19Years
172Questions
1Topics

Functions question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 142 82.6%
Easy 18 10.5%
Hard 12 7%

Question type distribution

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

Multiple Choices 138 80.2%
Numerical Answer Type (NAT) 34 19.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
172 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
172 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Functions
172 Qs

Paper coverage

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

JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT
3 Qs
JEE Main 2026 (Online) 4th April Evening Shift
2 Qs
JEE Main 2026 (Online) 4th April Morning Shift
2 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT
2 Qs
JEE Main 2026 (Online) 2nd April Morning Shift
1 Qs
JEE Main 2026 (Online) 5th April Morning Shift
1 Qs
JEE Main 2026 (Online) 6th April Evening Shift
1 Qs
JEE Main 2026 (Online) 6th April Morning Shift
1 Qs
JEE Main 2026 (Online) 8th April Evening Shift
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT
2 Qs
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT
2 Qs
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
2 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT
3 Qs
JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT
3 Qs
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 10TH 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 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING 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 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING 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 2022 ONLINE 25TH JUNE MORNING SHIFT
3 Qs
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH 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 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 JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JUNE 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 2021 (Online) 25th February Evening Shift
2 Qs
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT
2 Qs
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT
2 Qs
JEE Main 2021 (Online) 24th February Evening Shift
1 Qs
JEE Main 2021 (Online) 24th February Morning 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 MORNING 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
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 2020 ONLINE 6TH SEPTEMBER EVENING SLOT
2 Qs
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT
2 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
2 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT
2 Qs
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
2 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL EVENING 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 ONLINE 15TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2017 OFFLINE
2 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 9TH APRIL MORNING SLOT
1 Qs
AIEEE 2011
1 Qs
AIEEE 2009
2 Qs
AIEEE 2008
1 Qs
AIEEE 2007
1 Qs
AIEEE 2005
2 Qs
AIEEE 2004
4 Qs
AIEEE 2003
4 Qs
AIEEE 2002
3 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Morning Shift20261View paper
JEE Main 2026 (Online) 4th April Evening Shift20262View paper
JEE Main 2026 (Online) 4th April Morning Shift20262View paper
JEE Main 2026 (Online) 5th April Morning Shift20261View paper
JEE Main 2026 (Online) 6th April Evening Shift20261View paper
JEE Main 2026 (Online) 6th April Morning Shift20261View paper
JEE Main 2026 (Online) 8th April Evening Shift20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT20263View paper
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 28TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20242View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20232View 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 1ST FEBRUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT20233View 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 SHIFT20233View 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 SHIFT20232View paper
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 25TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT20223View 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 SHIFT20222View 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 SHIFT20222View paper
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Evening Shift20211View paper
JEE Main 2021 (Online) 24th February Morning Shift20211View paper
JEE Main 2021 (Online) 25th February Evening Shift20212View 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 MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT20212View 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 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 2020 ONLINE 2ND SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING 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 2019 ONLINE 10TH APRIL MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 12TH APRIL 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 SLOT20192View paper
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT20181View paper
JEE MAIN 2017 OFFLINE20172View 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 9TH APRIL MORNING SLOT20161View paper
AIEEE 201120111View paper
AIEEE 200920092View paper
AIEEE 200820081View paper
AIEEE 200720071View paper
AIEEE 200520052View paper
AIEEE 200420044View paper
AIEEE 200320034View paper
AIEEE 200220023View paper

All Functions previous year questions

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

1
2002 · Mathematics · Calculus · Functions
AIEEE 2002
The domain of \({\sin ^{ - 1}}\left[ {{{\log }_3}\left( {{x \over 3}} \right)} \right]\) is
A
[1, 9]
B
[-1, 9]
C
[9, 1]
D
[-9, -1]
Open complete paper
2
2002 · Mathematics · Calculus · Functions
AIEEE 2002
Which one is not periodic?
A
\(\left| {\sin 3x} \right| + {\sin ^2}x\)
B
\(\cos \sqrt x + {\cos ^2}x\)
C
\(\cos \,4x + {\tan ^2}x\)
D
\(cos\,2x + \sin x\)
Open complete paper
3
2002 · Mathematics · Calculus · Functions
AIEEE 2002
The period of \({\sin ^2}\theta\) is
A
\({\pi ^2}\)
B
\(\pi\)
C
\(2\pi\)
D
\(\pi /2\)
Open complete paper
4
2003 · Mathematics · Calculus · Functions
AIEEE 2003
The function \(f\left( x \right)\) \(= \log \left( {x + \sqrt {{x^2} + 1} } \right)\), is
A
neither an even nor an odd function
B
an even function
C
an odd function
D
a periodic function
Open complete paper
5
2003 · Mathematics · Calculus · Functions
AIEEE 2003
A function \(f\) from the set of natural numbers to integers defined by \(f\left( n \right) = \left\{ {\matrix{ \[{{{n - 1} \over 2},\,when\,n\,is\,odd} \cr\] \[{ - {n \over 2},\,when\,n\,is\,even} \cr\] } } \right.\) is
A
neither one -one nor onto
B
one-one but not onto
C
onto but not one-one
D
one-one and onto both
Open complete paper
6
2003 · Mathematics · Calculus · Functions
AIEEE 2003
If \(f:R \to R\) satisfies \(f\)(x + y) = \(f\)(x) + \(f\)(y), for all x, y \(\in\) R and \(f\)(1) = 7, then \(\sum\limits_{r = 1}^n {f\left( r \right)}\) is
A
\({{7n\left( {n + 1} \right)} \over 2}\)
B
\({{7n} \over 2}\)
C
\({{7\left( {n + 1} \right)} \over 2}\)
D
\(7n + \left( {n + 1} \right)\)
Open complete paper
7
2003 · Mathematics · Calculus · Functions
AIEEE 2003
Domain of definition of the function f(x) = \({3 \over {4 - {x^2}}}\) + \({\log _{10}}\left( {{x^3} - x} \right)\), is
A
(-1, 0)\(\cup\)(1, 2)\(\cup\)(2, \(\infty\))
B
(1, 2)
C
(-1, 0) \(\cup\) (1, 2)
D
(1, 2)\(\cup\)(2, \(\infty\))
Open complete paper
8
2004 · Mathematics · Calculus · Functions
AIEEE 2004
The domain of the function
$$f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x - 3} \right)} \over {\sqrt {9 - {x^2}} }}$$
A
[1, 2]
B
[2, 3)
C
[1, 2)
D
[2, 3]
Open complete paper
9
2004 · Mathematics · Calculus · Functions
AIEEE 2004
The graph of the function y = f(x) is symmetrical about the line x = 2, then
A
\(f\left( x \right) = - f\left( { - x} \right)\)
B
\(f\left( {2 + x} \right) = f\left( {2 - x} \right)\)
C
\(f\left( x \right) = f\left( { - x} \right)\)
D
\(f\left( {x + 2} \right) = f\left( {x - 2} \right)\)
Open complete paper
10
2004 · Mathematics · Calculus · Functions
AIEEE 2004
The range of the function f(x) = \({}^{7 - x}{P_{x - 3}}\) is
A
{1, 2, 3, 4, 5}
B
{1, 2, 3, 4, 5, 6}
C
{1, 2, 3, 4}
D
{1, 2, 3}
Open complete paper
11
2004 · Mathematics · Calculus · Functions
AIEEE 2004
If \(f:R \to S\), defined by
\(f\left( x \right) = \sin x - \sqrt 3 \cos x + 1\),
is onto, then the interval of \(S\) is
A
[-1, 3]
B
[-1, 1]
C
[0, 1]
D
[0, 3]
Open complete paper
12
2005 · Mathematics · Calculus · Functions
AIEEE 2005
A real valued function f(x) satisfies the functional equation

f(x - y) = f(x)f(y) - f(a - x)f(a + y)

where a is given constant and f(0) = 1, f(2a - x) is equal to
A
- f(x)
B
f(x)
C
f(a) + f(a - x)
D
f(- x)
Open complete paper
13
2005 · Mathematics · Calculus · Functions
AIEEE 2005
Let \(f:( - 1,1) \to B\), be a function defined by
\(f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}\),
then \(f\) is both one-one and onto when B is the interval
A
\(\left( {0,{\pi \over 2}} \right)\)
B
\(\left[ {0,{\pi \over 2}} \right)\)
C
\(\left[ { - {\pi \over 2},{\pi \over 2}} \right]\)
D
\(\left( { - {\pi \over 2},{\pi \over 2}} \right)\)
Open complete paper
14
2007 · Mathematics · Calculus · Functions
AIEEE 2007
The largest interval lying in \(\left( { - {\pi \over 2},{\pi \over 2}} \right)\) for which the function

\(f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {{x \over 2} - 1} \right)\)\(+ \log \left( {\cos x} \right)\),

is defined, is
A
\(\left[ { - {\pi \over 4},{\pi \over 2}} \right)\)
B
\(\left[ {0,{\pi \over 2}} \right)\)
C
\(\left[ {0,\pi } \right]\)
D
\(\left( { - {\pi \over 2},{\pi \over 2}} \right)\)
Open complete paper
15
2008 · Mathematics · Calculus · Functions
AIEEE 2008
Let \(f:N \to Y\) be a function defined as f(x) = 4x + 3 where
Y = { y \(\in\) N, y = 4x + 3 for some x \(\in\) N }.
Show that f is invertible and its inverse is
A
\(g\left( y \right) = {{3y + 4} \over 4}\)
B
\(g\left( y \right) = 4 + {{y + 3} \over 4}\)
C
\(g\left( y \right) = {{y + 3} \over 4}\)
D
\(g\left( y \right) = {{y - 3} \over 4}\)
Open complete paper
16
2009 · Mathematics · Calculus · Functions
AIEEE 2009
For real x, let f(x) = x3 + 5x + 1, then
A
f is one-one but not onto R
B
f is onto R but not one-one
C
f is one-one and onto R
D
f is neither one-one nor onto R
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17
2009 · Mathematics · Calculus · Functions
AIEEE 2009
Let \(f\left( x \right) = {\left( {x + 1} \right)^2} - 1,x \ge - 1\)

Statement - 1 : The set \(\left\{ {x:f\left( x \right) = {f^{ - 1}}\left( x \right)} \right\} = \left\{ {0, - 1} \right\}\).

Statement - 2 : \(f\) is a bijection.
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
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18
2011 · Mathematics · Calculus · Functions
AIEEE 2011
The domain of the function f(x) = \({1 \over {\sqrt {\left| x \right| - x} }}\) is
A
\(\left( {0,\infty } \right)\)
B
\(\left( { - \infty ,0} \right)\)
C
\(\left( { - \infty ,\infty } \right) - \left\{ 0 \right\}\)
D
\(\left( { - \infty ,\infty } \right)\)
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19
2016 · Mathematics · Calculus · Functions
JEE MAIN 2016 OFFLINE
If $f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0$, and $\mathrm{S}=\{x \in \mathbf{R}: f(x)=f(-x)\}$; then $\mathrm{S}:$
A
is an empty set.
B
contains exactly one element.
C
contains exactly two elements.
D
contains more than two elements.
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20
2016 · Mathematics · Calculus · Functions
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
For x \(\in\) R, x \(\ne\) 0, Let f0(x) = \({1 \over {1 - x}}\) and
fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . .

Then the value of f100(3) + f1\(\left( {{2 \over 3}} \right)\) + f2\(\left( {{3 \over 2}} \right)\) is equal to :
A
\({8 \over 3}\)
B
\({5 \over 3}\)
C
\({4 \over 3}\)
D
\({1 \over 3}\)
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