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Previous year question hub

Application Of Derivatives - Calculus - Mathematics Previous Year Questions

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

145Papers
25Years
237Questions
1Topics

Application Of Derivatives question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Application Of Derivatives. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 197 83.1%
Easy 23 9.7%
Hard 17 7.2%

Question type distribution

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

Multiple Choices 200 84.4%
Numerical Answer Type (NAT) 37 15.6%

Subject weightage

Top subjects by unique question coverage.

Mathematics
237 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
237 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Derivatives
237 Qs

Paper coverage

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

JEE Main 2026 (Online) 2nd April Evening Shift
1 Qs
JEE Main 2026 (Online) 2nd April Morning Shift
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JEE Main 2026 (Online) 5th April Morning Shift
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JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT
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JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT
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JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT
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JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT
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JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT
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JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT
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JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 24TH JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT
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JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT
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JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT
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JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT
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JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT
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JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT
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JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT
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JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT
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JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT
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JEE Main 2021 (Online) 24th February Evening Shift
3 Qs
JEE Main 2021 (Online) 24th February Morning Shift
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JEE Main 2021 (Online) 25th February Morning Shift
3 Qs
JEE Main 2021 (Online) 26th February Evening Shift
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JEE Main 2021 (Online) 26th February Morning Shift
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JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
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JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT
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JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT
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JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
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JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT
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JEE Main 2021 (Online) 25th February Evening Shift
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JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
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JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT
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JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT
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JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT
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JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT
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JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
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JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
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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 8TH APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 8TH APRIL MORNING 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 9TH APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT
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JEE MAIN 2018 OFFLINE
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JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
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JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
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JEE MAIN 2017 OFFLINE
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JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
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JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT
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JEE MAIN 2016 OFFLINE
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JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
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JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
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JEE MAIN 2015 OFFLINE
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JEE MAIN 2014 OFFLINE
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JEE MAIN 2013 OFFLINE
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AIEEE 2012
3 Qs
AIEEE 2011
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AIEEE 2010
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AIEEE 2009
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AIEEE 2008
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IIT-JEE 2007
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AIEEE 2007
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AIEEE 2006
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AIEEE 2005
7 Qs
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4 Qs
AIEEE 2003
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2 Qs

Included previous year papers

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PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Evening Shift20261View paper
JEE Main 2026 (Online) 2nd April Morning Shift20261View paper
JEE Main 2026 (Online) 5th April Morning Shift20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD 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 MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT20251View 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 EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT20243View paper
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT20243View paper
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20232View 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 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 25TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING 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 MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT20225View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20221View paper
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JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT20223View 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 SHIFT20223View paper
JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JULY 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 MORNING SHIFT20222View 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 SHIFT20223View paper
JEE Main 2021 (Online) 24th February Evening Shift20213View paper
JEE Main 2021 (Online) 24th February Morning Shift20213View paper
JEE Main 2021 (Online) 25th February Evening Shift20211View paper
JEE Main 2021 (Online) 25th February Morning Shift20213View paper
JEE Main 2021 (Online) 26th February Evening Shift20213View paper
JEE Main 2021 (Online) 26th February Morning Shift20212View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 17TH MARCH EVENING 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 SHIFT20212View paper
JEE MAIN 2021 ONLINE 22TH 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 SHIFT20212View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT20212View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT20203View 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 SLOT20203View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING 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 EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT20203View paper
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20192View 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 MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT20193View paper
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2018 OFFLINE20182View paper
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT20182View paper
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT20181View paper
JEE MAIN 2017 OFFLINE20172View paper
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT20171View paper
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT20172View paper
JEE MAIN 2016 OFFLINE20162View paper
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT20162View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20162View paper
JEE MAIN 2015 OFFLINE20152View paper
JEE MAIN 2014 OFFLINE20142View paper
JEE MAIN 2013 OFFLINE20132View paper
AIEEE 201220123View paper
AIEEE 201120112View paper
AIEEE 201020103View paper
AIEEE 200920091View paper
AIEEE 200820082View paper
AIEEE 200720073View paper
IIT-JEE 200720074View paper
AIEEE 200620063View paper
AIEEE 200520057View paper
AIEEE 200420044View paper
AIEEE 200320032View paper
AIEEE 200220022View paper

All Application Of Derivatives previous year questions

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

1
2002 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2002
If \(2a+3b+6c=0,\) \(\left( {a,b,c \in R} \right)\) then the quadratic equation \(a{x^2} + bx + c = 0\) has
A
at least one root in \(\left[ {0,1} \right]\)
B
at least one root in \(\left[ {2,3} \right]\)
C
at least one root in \(\left[ {4,5} \right]\)
D
none of these
Open complete paper
2
2002 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2002
The maximum distance from origin of a point on the curve
$$x = a\sin t - b\sin \left( {{{at} \over b}} \right)$$
\(y = a\cos t - b\cos \left( {{{at} \over b}} \right),\) both \(a,b > 0\) is
A
\(a-b\)
B
\(a+b\)
C
\(\sqrt {{a^2} + {b^2}}\)
D
\(\sqrt {{a^2} - {b^2}}\)
Open complete paper
3
2003 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2003
The real number \(x\) when added to its inverse gives the minimum sum at \(x\) equal :
A
-2
B
2
C
1
D
-1
Open complete paper
4
2003 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2003
If the function \(f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,\) where \(a>0,\) attains its maximum and minimum at \(p\) and \(q\) respectively such that \({p^2} = q\) , then \(a\) equals
A
\({1 \over 2}\)
B
\(3\)
C
\(1\)
D
\(2\)
Open complete paper
5
2004 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2004
The normal to the curve x = a(1 + cos \(\theta\)), \(y = a\sin \theta\) at \('\theta '\) always passes through the fixed point
A
\((a, a)\)
B
\((0, a)\)
C
\((0, 0)\)
D
\((a, 0)\)
Open complete paper
6
2004 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2004
A function \(y=f(x)\) has a second order derivative \(f''\left( x \right) = 6\left( {x - 1} \right).\) If its graph passes through the point \((2, 1)\) and at that point the tangent to the graph is \(y = 3x - 5\), then the function is :
A
\({\left( {x + 1} \right)^2}\)
B
\({\left( {x - 1} \right)^3}\)
C
\({\left( {x + 1} \right)^3}\)
D
\({\left( {x - 1} \right)^2}\)
Open complete paper
7
2004 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2004
If \(2a+3b+6c=0\), then at least one root of the equation
\(a{x^2} + bx + c = 0\) lies in the interval
A
\((1, 3)\)
B
\((1, 2)\)
C
\((2, 3)\)
D
\((0, 1)\)
Open complete paper
8
2004 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2004
A point on the parabola \({y^2} = 18x\) at which the ordinate increases at twice the rate of the abscissa is
A
\(\left( {{9 \over 8},{9 \over 2}} \right)\)
B
\((2, -4)\)
C
\(\left( {{-9 \over 8},{9 \over 2}} \right)\)
D
\((2, 4)\)
Open complete paper
9
2005 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2005
Let f be differentiable for all x. If f(1) = -2 and f'(x) \(\ge\) 2 for
x \(\in \left[ {1,6} \right]\), then
A
f(6) \(\ge\) 8
B
f(6) < 8
C
f(6) < 5
D
f(6) = 5
Open complete paper
10
2005 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2005
The normal to the curve
\(x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)\) at any point
\(\theta\, '\) is such that
A
it passes through the origin
B
it makes an angle \({\pi \over 2} + \theta\) with the \(x\)-axis
C
it passes through \(\left( {a{\pi \over 2}, - a} \right)\)
D
it is at a constant distance from the origin
Open complete paper
11
2005 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2005
If the equation \({a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0\)
\({a_1} \ne 0,n \ge 2,\) has a positive root \(x = \alpha\), then the equation
\(n{a_n}{x^{n - 1}} + \left( {n - 1} \right){a_{n - 1}}{x^{n - 2}} + ........... + {a_1} = 0\) has a positive root, which is
A
greater than \(\alpha\)
B
smaller than \(\alpha\)
C
greater than or equal to smaller than \(\alpha\)
D
equal to smaller than \(\alpha\)
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12
2005 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2005
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
A
Interval Function
(- \(\infty\), \(\infty\)) x3 - 3x2 + 3x + 3
B
Interval Function
[2, \(\infty\)) 2x3 - 3x2 - 12x + 6
C
Interval Function
\(\left( { - \infty ,{1 \over 3}} \right]\) 3x2 - 2x + 1
D
Interval Function
(\(- \infty\), - 4 ) x3 + 6x2 + 6
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13
2005 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2005
A spherical iron ball \(10\) cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of \(50\) cm\(^3\) /min. When the thickness of ice is \(5\) cm, then the rate at which the thickness of ice decreases is
A
\({1 \over {36\pi }}\) cm/min
B
\({1 \over {18\pi }}\) cm/min
C
\({1 \over {54\pi }}\) cm/min
D
\({5 \over {6\pi }}\) cm/min
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14
2005 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2005
Area of the greatest rectangle that can be inscribed in the
ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\)
A
\(2ab\)
B
\(ab\)
C
\(\sqrt {ab}\)
D
\({a \over b}\)
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15
2005 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2005
A lizard, at an initial distance of 21 cm behind an insect moves from rest with an acceleration of $2 \mathrm{~cm} / \mathrm{s}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20 \mathrm{~cm} / \mathrm{s}$. Then the lizard will catch the insect after :
A
20 s
B
1 s
C
21 s
D
24 s
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16
2006 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2006
Angle between the tangents to the curve \(y = {x^2} - 5x + 6\) at the points \((2,0)\) and \((3,0)\) is
A
\(\pi\)
B
\({\pi \over 2}\)
C
\({\pi \over 6}\)
D
\({\pi \over 4}\)
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17
2006 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2006
The function \(f\left( x \right) = {x \over 2} + {2 \over x}\) has a local minimum at
A
\(x=2\)
B
\(x=-2\)
C
\(x=0\)
D
\(x=1\)
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18
2006 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2006
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length \(x\). The maximum area enclosed by the park is
A
\({3 \over 2}{x^2}\)
B
\(\sqrt {{{{x^3}} \over 8}}\)
C
\({1 \over 2}{x^2}\)
D
\(\pi {x^2}\)
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19
2007 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2007
A value of \(c\) for which conclusion of Mean Value Theorem holds for the function \(f\left( x \right) = {\log _e}x\) on the interval \(\left[ {1,3} \right]\) is
A
\({\log _3}e\)
B
\({\log _e}3\)
C
\(2\,\,{\log _3}e\)
D
\({1 \over 2}{\log _3}e\)
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20
2007 · Mathematics · Calculus · Application Of Derivatives
AIEEE 2007
The function \(f\left( x \right) = {\tan ^{ - 1}}\left( {\sin x + \cos x} \right)\) is an incresing function in
A
\(\left( {0,{\pi \over 2}} \right)\)
B
\(\left( { - {\pi \over 2},{\pi \over 2}} \right)\)
C
\(\left( { {\pi \over 4},{\pi \over 2}} \right)\)
D
\(\left( { - {\pi \over 2},{\pi \over 4}} \right)\)
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