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Previous year question hub

Binomial Theorem - Algebra - Mathematics Previous Year Questions

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

175Papers
25Years
248Questions
1Topics

Binomial Theorem question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 187 75.4%
Hard 38 15.3%
Easy 23 9.3%

Question type distribution

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

Multiple Choices 162 65.3%
Numerical Answer Type (NAT) 86 34.7%

Subject weightage

Top subjects by unique question coverage.

Mathematics
248 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
248 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Binomial Theorem
248 Qs

Paper coverage

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

JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT
2 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT
2 Qs
JEE Main 2026 (Online) 2nd April Evening Shift
1 Qs
JEE Main 2026 (Online) 4th April Evening Shift
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JEE Main 2026 (Online) 4th April Morning Shift
1 Qs
JEE Main 2026 (Online) 5th April Evening 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
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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 EVENING SHIFT
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JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT
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JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT
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JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT
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JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT
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JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 22ND JANUARY MORNING 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 EVENING SHIFT
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JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 29TH JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 3RD APRIL EVENING 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 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 31ST JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 1ST FEBRUARY 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 29TH JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 11TH 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 EVENING SHIFT
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JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT
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JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT
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JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT
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JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT
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JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING 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 2022 ONLINE 25TH JUNE EVENING SHIFT
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JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT
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JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT
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JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT
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JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT
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JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT
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JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT
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JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT
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JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT
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JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT
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JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT
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JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT
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JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
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JEE Main 2021 (Online) 24th February Evening Shift
2 Qs
JEE Main 2021 (Online) 25th 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 MORNING SHIFT
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JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT
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JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT
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JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT
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JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT
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JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
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JEE Main 2021 (Online) 24th February Morning Shift
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JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
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JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT
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JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
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JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT
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JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT
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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
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JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT
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JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT
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JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
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JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT
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JEE MAIN 2020 ONLINE 4TH 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 EVENING SLOT
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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 4TH SEPTEMBER EVENING 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 7TH JANUARY EVENING SLOT
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JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT
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JEE MAIN 2020 ONLINE 9TH JANUARY 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 12TH APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT
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JEE MAIN 2019 ONLINE 10TH APRIL MORNING 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 12TH JANUARY MORNING SLOT
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JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
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JEE MAIN 2019 ONLINE 9TH JANUARY 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 EVENING SLOT
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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 8TH APRIL MORNING SLOT
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JEE MAIN 2017 ONLINE 9TH 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
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AIEEE 2011
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AIEEE 2010
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AIEEE 2009
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AIEEE 2008
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AIEEE 2007
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AIEEE 2006
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AIEEE 2005
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AIEEE 2004
3 Qs
AIEEE 2003
2 Qs
AIEEE 2002
4 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 Evening Shift20261View paper
JEE Main 2026 (Online) 4th April Evening Shift20261View paper
JEE Main 2026 (Online) 4th April Morning Shift20261View paper
JEE Main 2026 (Online) 5th April Evening Shift20261View 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 21ST JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT20262View paper
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT20262View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 22ND JANUARY MORNING 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 EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT20252View 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 SHIFT20252View 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 SHIFT20242View paper
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20242View 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 EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 13TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT20232View 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 29TH JANUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT20233View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20233View 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 SHIFT20222View 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 SHIFT20222View 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 SHIFT20222View paper
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT20222View 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 Shift20212View paper
JEE Main 2021 (Online) 26th February Morning Shift20212View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 18TH MARCH MORNING 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 SHIFT20212View paper
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20215View paper
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT20213View 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 4TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT20202View 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 7TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT20202View paper
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT20201View 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 SLOT20192View 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 EVENING SLOT20192View 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 SLOT20192View 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 200820081View paper
AIEEE 200720072View paper
AIEEE 200620062View paper
AIEEE 200520054View paper
AIEEE 200420043View paper
AIEEE 200320032View paper
AIEEE 200220024View paper

All Binomial Theorem previous year questions

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

1
2002 · Mathematics · Algebra · Binomial Theorem
AIEEE 2002
\(r\) and \(n\) are positive integers \(\,r > 1,\,n > 2\) and coefficient of \(\,{\left( {r + 2} \right)^{th}}\) term and \(3{r^{th}}\) term in the expansion of \({\left( {1 + x} \right)^{2n}}\) are equal, then \(n\) equals
A
\(3r\)
B
\(3r + 1\)
C
\(2r\)
D
\(2r + 1\)
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2
2002 · Mathematics · Algebra · Binomial Theorem
AIEEE 2002
If the sum of the coefficients in the expansion of \(\,{\left( {a + b} \right)^n}\) is 4096, then the greatest coefficient in the expansion is
A
1594
B
792
C
924
D
2924
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3
2002 · Mathematics · Algebra · Binomial Theorem
AIEEE 2002
The positive integer just greater than \({\left( {1 + 0.0001} \right)^{10000}}\) is
A
4
B
5
C
2
D
3
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4
2002 · Mathematics · Algebra · Binomial Theorem
AIEEE 2002
The coefficients of \({x^p}\) and \({x^q}\) in the expansion of \({\left( {1 + x} \right)^{p + q}}\) are
A
equal
B
equal with opposite signs
C
reciprocals of each other
D
none of these
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5
2003 · Mathematics · Algebra · Binomial Theorem
AIEEE 2003
If \(x\) is positive, the first negative term in the expansion of \({\left( {1 + x} \right)^{27/5}}\) is
A
6th term
B
7th term
C
5th term
D
8th term.
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6
2003 · Mathematics · Algebra · Binomial Theorem
AIEEE 2003
The number of integral terms in the expansion of \({\left( {\sqrt 3 + \root 8 \of 5 } \right)^{256}}\) is
A
35
B
32
C
33
D
34
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7
2004 · Mathematics · Algebra · Binomial Theorem
AIEEE 2004
If \({S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}},\,}\)then \({{{t_{ n}}} \over {{S_n}}}\) is equal to
A
\({{2n - 1} \over 2}\)
B
\({1 \over 2}n - 1\)
C
n - 1
D
\({1 \over 2}n\)
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8
2004 · Mathematics · Algebra · Binomial Theorem
AIEEE 2004
The coefficient of the middle term in the binomial expansion in powers of \(x\) of \({\left( {1 + \alpha x} \right)^4}\) and \({\left( {1 - \alpha x} \right)^6}\) is the same if \(\alpha\) equals
A
\({3 \over 5}\)
B
\({10 \over 3}\)
C
\({{ - 3} \over {10}}\)
D
\({{ - 5} \over {3}}\)
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9
2004 · Mathematics · Algebra · Binomial Theorem
AIEEE 2004
The coefficient of \({x^n}\) in expansion of \(\left( {1 + x} \right){\left( {1 - x} \right)^n}\) is
A
\({\left( { - 1} \right)^{n - 1}}n\)
B
\({\left( { - 1} \right)^n}\left( {1 - n} \right)\)
C
\({\left( { - 1} \right)^{n - 1}}{\left( {n - 1} \right)^2}\)
D
\(\left( {n - 1} \right)\)
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10
2005 · Mathematics · Algebra · Binomial Theorem
AIEEE 2005
The value of \(\,{}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}} {C_3}\) is
A
\({}^{55}{C_4}\)
B
\({}^{55}{C_3}\)
C
\({}^{56}{C_3}\)
D
\({}^{56}{C_4}\)
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11
2005 · Mathematics · Algebra · Binomial Theorem
AIEEE 2005
If the coefficients of rth, (r+1)th, and (r + 2)th terms in the binomial expansion of \({{\rm{(1 + y )}}^m}\) are in A.P., then m and r satisfy the equation
A
\({m^2} - m(4r - 1) + 4\,{r^2} - 2 = 0\)
B
\({m^2} - m(4r + 1) + 4\,{r^2} + 2 = 0\)
C
\({m^2} - m(4r + 1) + 4\,{r^2} - 2 = 0\)
D
\({m^2} - m(4r - 1) + 4\,{r^2} + 2 = 0\)
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12
2005 · Mathematics · Algebra · Binomial Theorem
AIEEE 2005
If \(x\) is so small that \({x^3}\) and higher powers of \(x\) may be neglected, then \({{{{\left( {1 + x} \right)}^{{3 \over 2}}} - {{\left( {1 + {1 \over 2}x} \right)}^3}} \over {{{\left( {1 - x} \right)}^{{1 \over 2}}}}}\) may be approximated as
A
\(1 - {3 \over 8}{x^2}\)
B
\(3x + {3 \over 8}{x^2}\)
C
\(- {3 \over 8}{x^2}\)
D
\({x \over 2} - {3 \over 8}{x^2}\)
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13
2005 · Mathematics · Algebra · Binomial Theorem
AIEEE 2005
If the coefficient of \({x^7}\) in \({\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}}\) equals the coefficient of \({x^{ - 7}}\) in \({\left[ {ax - \left( {{1 \over {b{x^2}}}} \right)} \right]^{11}}\), then \(a\) and \(b\) satisfy the relation
A
\(a - b = 1\)
B
\(a + b = 1\)
C
\({a \over b} = 1\)
D
\(ab = 1\)
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14
2006 · Mathematics · Algebra · Binomial Theorem
AIEEE 2006
For natural numbers \(m\) , \(n\), if \({\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n}\,\, = 1 + {a_1}y + {a_2}{y^2} + ..........\) and \({a_1} = {a_2} = 10,\) then \(\left( {m,\,n} \right)\) is
A
\(\left( {20,\,45} \right)\)
B
\(\left( {35,\,20} \right)\)
C
\(\left( {45,\,35} \right)\)
D
\(\left( {35,\,45} \right)\)
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15
2006 · Mathematics · Algebra · Binomial Theorem
AIEEE 2006
If the expansion in powers of \(x\) of the function \({1 \over {\left( {1 - ax} \right)\left( {1 - bx} \right)}}\) is \({a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}.....\) then \({a_n}\) is
A
\({{{b^n} - {a^n}} \over {b - a}}\)
B
\({{{a^n} - {b^n}} \over {b - a}}\)
C
\({{{a^{n + 1}} - {b^{n + 1}}} \over {b - a}}\)
D
\({{{b^{n + 1}} - {a^{n + 1}}} \over {b - a}}\)
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16
2007 · Mathematics · Algebra · Binomial Theorem
AIEEE 2007
The sum of the series \({}^{20}{C_0} - {}^{20}{C_1} + {}^{20}{C_2} - {}^{20}{C_3} + .....\, - \,.....\, + {}^{20}{C_{10}}\) is
A
\(0\)
B
\({}^{20}{C_{10}}\)
C
\(- {}^{20}{C_{10}}\)
D
\({1 \over 2}{}^{20}{C_{10}}\)
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17
2007 · Mathematics · Algebra · Binomial Theorem
AIEEE 2007
In the binomial expansion of \({\left( {a - b} \right)^n},\,\,\,n \ge 5,\) the sum of \({5^{th}}\) and \({6^{th}}\) terms is zero, then \(a/b\) equals
A
\({{n - 5} \over 6}\)
B
\({{n - 4} \over 5}\)
C
\({5 \over {n - 4}}\)
D
\({6 \over {n - 5}}\)
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18
2008 · Mathematics · Algebra · Binomial Theorem
AIEEE 2008
Statement - 1 : \(\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r} = \left( {n + 2} \right){2^{n - 1}}.}\)
Statement - 2 : \(\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r}{x^r} = {{\left( {1 + x} \right)}^n} + nx{{\left( {1 + x} \right)}^{n - 1}}.}\)
A
Statement - 1 is false, Statement - 2 is true
B
Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1
C
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1
D
Statement - 1 is true, Statement - 2 is false
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19
2009 · Mathematics · Algebra · Binomial Theorem
AIEEE 2009
The remainder left out when \({8^{2n}} - {\left( {62} \right)^{2n + 1}}\) is divided by 9 is :
A
2
B
7
C
8
D
0
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20
2010 · Mathematics · Algebra · Binomial Theorem
AIEEE 2010
Let \({s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}\),

\({{s_2} = \sum\limits_{j = 1}^{10} {} } j.{}^{10}{C_j}\) and

$${{s_3} = \sum\limits_{j = 1}^{10} {{j^2}.{}^{10}{C_j}.} }$$

Statement-1 : \({{S_3} = 55 \times {2^9}}\).
Statement-2 : \({{S_1} = 90 \times {2^8}}\) and \({{S_2} = 10 \times {2^8}}\).

A
Statement - 1 is true, Statement- 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B
Statement - 1 is true, Statement-2 is false.
C
Statement - 1 is false, Statement-2 is true.
D
Statement - 1 is true, Statement-2 is true: -Statement - 2 is a correct explanation for Statement - 1.
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