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Previous year question hub

Straight Lines And Pair Of Straight Lines - Coordinate Geometry - Mathematics Previous Year Questions

Practice Straight Lines And Pair Of Straight Lines - Coordinate Geometry - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

135Papers
25Years
181Questions
1Topics

Straight Lines And Pair Of Straight Lines question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Straight Lines And Pair Of Straight Lines. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 147 81.2%
Easy 21 11.6%
Hard 13 7.2%

Question type distribution

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

Multiple Choices 158 87.3%
Numerical Answer Type (NAT) 23 12.7%

Subject weightage

Top subjects by unique question coverage.

Mathematics
181 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
181 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Straight Lines And Pair Of Straight Lines
181 Qs

Paper coverage

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

JEE Main 2026 (Online) 4th April Morning Shift
2 Qs
JEE Main 2026 (Online) 2nd April Morning Shift
1 Qs
JEE Main 2026 (Online) 4th April Evening 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) 8th April Evening Shift
1 Qs
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 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 2026 ONLINE 28TH JANUARY MORNING SHIFT
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JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 22ND JANUARY 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 24TH JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 24TH 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
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL EVENING 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 7TH APRIL EVENING SHIFT
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JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING 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 31ST JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT
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JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
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JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT
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JEE MAIN 2024 ONLINE 29TH 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 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 EVENING SHIFT
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JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT
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JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
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JEE MAIN 2023 ONLINE 11TH APRIL EVENING 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 15TH APRIL MORNING SHIFT
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JEE MAIN 2023 ONLINE 24TH JANUARY 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 2022 ONLINE 26TH JULY MORNING SHIFT
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JEE MAIN 2022 ONLINE 29TH JULY 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 25TH JULY EVENING SHIFT
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JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT
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JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT
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JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT
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JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT
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JEE MAIN 2022 ONLINE 29TH JULY 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 2022 ONLINE 30TH JUNE MORNING SHIFT
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JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT
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JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT
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JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
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JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT
2 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 Morning Shift
1 Qs
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 18TH MARCH EVENING SHIFT
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JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT
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JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
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JEE MAIN 2021 ONLINE 27TH AUGUST 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 2ND SEPTEMBER EVENING SLOT
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JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT
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JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
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JEE MAIN 2019 ONLINE 10TH 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 APRIL EVENING SLOT
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JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT
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JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
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JEE MAIN 2019 ONLINE 12TH APRIL EVENING 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 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 ONLINE 15TH APRIL EVENING SLOT
2 Qs
JEE MAIN 2018 OFFLINE
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
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JEE MAIN 2017 OFFLINE
1 Qs
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
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JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
2 Qs
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
2 Qs
JEE MAIN 2016 OFFLINE
1 Qs
JEE MAIN 2015 OFFLINE
1 Qs
JEE MAIN 2014 OFFLINE
2 Qs
JEE MAIN 2013 OFFLINE
2 Qs
AIEEE 2012
1 Qs
AIEEE 2011
1 Qs
AIEEE 2010
1 Qs
AIEEE 2009
2 Qs
AIEEE 2008
1 Qs
AIEEE 2007
3 Qs
IIT-JEE 2007
2 Qs
AIEEE 2006
2 Qs
AIEEE 2005
3 Qs
AIEEE 2004
4 Qs
AIEEE 2003
5 Qs
AIEEE 2002
4 Qs

Included previous year papers

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PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Morning Shift20261View paper
JEE Main 2026 (Online) 4th April Evening Shift20261View paper
JEE Main 2026 (Online) 4th April Morning Shift20262View paper
JEE Main 2026 (Online) 5th April Evening Shift20261View paper
JEE Main 2026 (Online) 5th April Morning Shift20261View paper
JEE Main 2026 (Online) 8th April 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 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 2026 ONLINE 28TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 22ND JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING 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 SHIFT20252View 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 3RD APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL MORNING 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 SHIFT20252View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT20242View 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 SHIFT20241View 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 MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT20241View paper
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JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 13TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 6TH APRIL MORNING 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
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JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
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JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT20221View 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 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 Morning Shift20211View paper
JEE Main 2021 (Online) 25th February Morning Shift20211View paper
JEE Main 2021 (Online) 26th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT20213View paper
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT20212View 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 3RD SEPTEMBER EVENING 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 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 MORNING 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 SLOT20192View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20193View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING 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 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 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 SLOT20182View paper
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT20181View paper
JEE MAIN 2017 OFFLINE20171View paper
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT20171View paper
JEE MAIN 2016 OFFLINE20161View paper
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT20162View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20162View paper
JEE MAIN 2015 OFFLINE20151View paper
JEE MAIN 2014 OFFLINE20142View paper
JEE MAIN 2013 OFFLINE20132View paper
AIEEE 201220121View paper
AIEEE 201120111View paper
AIEEE 201020101View paper
AIEEE 200920092View paper
AIEEE 200820081View paper
AIEEE 200720073View paper
IIT-JEE 200720072View paper
AIEEE 200620062View paper
AIEEE 200520053View paper
AIEEE 200420044View paper
AIEEE 200320035View paper
AIEEE 200220024View paper

All Straight Lines And Pair Of Straight Lines previous year questions

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

1
2002 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2002
If the pair of lines

$$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$

intersect on the \(y\)-axis then :
A
\(2fgh = b{g^2} + c{h^2}\)
B
\(b{g^2} \ne c{h^2}\)
C
\(abc = 2fgh\)
D
none of these
Open complete paper
2
2002 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2002
The pair of lines represented by \(3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0\)

are perpendicular to each other for :
A
two values of \(a\)
B
\(\forall \,a\)
C
for one value of \(a\)
D
for no values of \(a\)
Open complete paper
3
2002 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2002
A triangle with vertices \(\left( {4,0} \right),\left( { - 1, - 1} \right),\left( {3,5} \right)\) is :
A
isosceles and right angled
B
isosceles but not right angled
C
right angled but not isosceles
D
neither right angled nor isosceles
Open complete paper
4
2002 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2002
Locus of mid point of the portion between the axes of

\(x\) \(cos\) \(\alpha + y\,\sin \alpha = p\) where \(p\) is constant is :
A
\({x^2} + {y^2} = {4 \over {{p^2}}}\)
B
\({x^2} + {y^2} = 4{p^2}\)
C
\({1 \over {{x^2}}} + {1 \over {{y^2}}} = {2 \over {{p^2}}}\)
D
\({1 \over {{x^2}}} + {1 \over {{y^2}}} = {4 \over {{p^2}}}\)
Open complete paper
5
2003 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2003
If the pair of straight lines \({x^2} - 2pxy - {y^2} = 0\) and \({x^2} - 2qxy - {y^2} = 0\) be such that each pair bisects the angle between the other pair, then :
A
\(pq = -1\)
B
\(p = q\)
C
\(p = -q\)
D
\(pq = 1\).
Open complete paper
6
2003 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2003
Locus of centroid of the triangle whose vertices are \(\left( {a\cos t,a\sin t} \right),\left( {b\sin t, - b\cos t} \right)\) and \(\left( {1,0} \right),\) where \(t\) is a parameter, is :
A
\({\left( {3x + 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} - {b^2}\)
B
\({\left( {3x - 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} - {b^2}\)
C
\({\left( {3x - 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} + {b^2}\)
D
\({\left( {3x + 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} + {b^2}\)
Open complete paper
7
2003 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2003
If the equation of the locus of a point equidistant from the point \(\left( {{a_{1,}}{b_1}} \right)\) and \(\left( {{a_{2,}}{b_2}} \right)\) is
\(\left( {{a_1} - {a_2}} \right)x + \left( {{b_1} - {b_2}} \right)y + c = 0\) , then the value of \('c'\) is :
A
\(\sqrt {{a_1}^2 + {b_1}^2 - {a_2}^2 - {b_2}^2}\)
B
\({1 \over 2}\left( {{a_2}^2 + {b_2}^2 - {a_1}^2 - {b_1}^2} \right)\)
C
\({{a_1}^2 - {a_2}^2 + {b_1}^2 - {b_2}^2}\)
D
\({1 \over 2}\left( {{a_1}^2 + {a_2}^2 + {b_1}^2 + {b_2}^2} \right)\).
Open complete paper
8
2003 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2003
If \({x_1},{x_2},{x_3}\) and \({y_1},{y_2},{y_3}\) are both in G.P. with the same common ratio, then the points \(\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)\) and \(\left( {{x_3},{y_3}} \right)\) :
A
are vertices of a triangle
B
lie on a straight line
C
lie on an ellipse
D
lie on a circle
Open complete paper
9
2003 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2003
A square of side a lies above the \(x\)-axis and has one vertex at the origin. The side passing through the origin makes an angle \(\alpha \left( {0 < \alpha < {\pi \over 4}} \right)\) with the positive direction of x-axis. The equation of its diagonal not passing through the origin is :
A
\(y\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\cos \alpha - \sin \alpha } \right) = a\)
B
\(y\left( {\cos \alpha - \sin \alpha } \right) - x\left( {\sin \alpha - \cos \alpha } \right) = a\)
C
\(y\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\sin \alpha - \cos \alpha } \right) = a\)
D
\(y\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\sin \alpha + \cos \alpha } \right) = a\)
Open complete paper
10
2004 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2004
If the sum of the slopes of the lines given by \({x^2} - 2cxy - 7{y^2} = 0\) is four times their product \(c\) has the value :
A
\(-2\)
B
\(-1\)
C
\(2\)
D
\(1\)
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11
2004 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2004
If one of the lines given by \(6{x^2} - xy + 4c{y^2} = 0\) is \(3x + 4y = 0,\) then \(c\) equals :
A
\(-3\)
B
\(-1\)
C
\(3\)
D
\(1\)
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12
2004 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2004
The equation of the straight line passing through the point \((4, 3)\) and making intercepts on the co-ordinate axes whose sum is \(-1\) is :
A
\({x \over 2} - {y \over 3} = 1\) and \({x \over -2} +{y \over 1} = 1\)
B
\({x \over 2} - {y \over 3} = -1\) and \({x \over -2} +{y \over 1} = -1\)
C
\({x \over 2} + {y \over 3} = 1\) and \({x \over 2} +{y \over 1} = 1\)
D
\({x \over 2} + {y \over 3} = -1\) and \({x \over -2} +{y \over 1} = -1\)
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13
2004 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2004
Let \(A\left( {2, - 3} \right)\) and \(B\left( {-2, 1} \right)\) be vertices of a triangle \(ABC\). If the centroid of this triangle moves on the line \(2x + 3y = 1\), then the locus of the vertex \(C\) is the line :
A
\(3x - 2y = 3\)
B
\(2x - 3y = 7\)
C
\(3x + 2y = 5\)
D
\(2x + 3y = 9\)
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14
2005 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2005
If a vertex of a triangle is \((1, 1)\) and the mid points of two sides through this vertex are \((-1, 2)\) and \((3, 2)\) then the centroid of the triangle is :
A
\(\left( { - 1,{7 \over 3}} \right)\)
B
\(\left( {{{ - 1} \over 3},{7 \over 3}} \right)\)
C
\(\left( { 1,{7 \over 3}} \right)\)
D
\(\left( {{{ 1} \over 3},{7 \over 3}} \right)\)
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15
2005 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2005
If non zero numbers \(a, b, c\) are in \(H.P.,\) then the straight line \({x \over a} + {y \over b} + {1 \over c} = 0\) always passes through a fixed point. That point is :
A
\((-1,2)\)
B
\((-1, -2)\)
C
\((1, -2)\)
D
\(\left( {1, - {1 \over 2}} \right)\)
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16
2005 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2005
The line parallel to the \(x\) - axis and passing through the intersection of the lines \(ax + 2by + 3b = 0\) and \(bx - 2ay - 3a = 0,\) where \((a, b)\) \(\ne\) \((0, 0)\) is :
A
below the \(x\) - axis at a distance of \({3 \over 2}\) from it
B
below the \(x\) - axis at a distance of \({2 \over 3}\) from it
C
above the \(x\) - axis at a distance of \({3 \over 2}\) from it
D
above the \(x\) - axis at a distance of \({2 \over 3}\) from it
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17
2006 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2006
If \(\left( {a,{a^2}} \right)\) falls inside the angle made by the lines \(y = {x \over 2},\) \(x > 0\) and \(y = 3x,\) \(x > 0,\) then a belong to :
A
\(\left( {0,{1 \over 2}} \right)\)
B
\(\left( {3,\infty } \right)\)
C
\(\left( {{1 \over 2},3} \right)\)
D
\(\left( {-3,-{1 \over 2}} \right)\)
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18
2006 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2006
A straight line through the point \(A (3, 4)\) is such that its intercept between the axes is bisected at \(A\). Its equation is :
A
\(x + y = 7\)
B
\(3x - 4y + 7 = 0\)
C
\(4x + 3y = 24\)
D
\(3x + 4y = 25\)
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19
2007 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2007
If one of the lines of \(m{y^2} + \left( {1 - {m^2}} \right)xy - m{x^2} = 0\) is a bisector of angle between the lines \(xy = 0,\) then \(m\) is :
A
\(1\)
B
\(2\)
C
\(-1/2\)
D
\(-2\)
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20
2007 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
AIEEE 2007
Let \(P = \left( { - 1,0} \right),\,Q = \left( {0,0} \right)\) and \(R = \left( {3,3\sqrt 3 } \right)\) be three point. The equation of the bisector of the angle \(PQR\) is :
A
\({{\sqrt 3 } \over 2}x + y = 0\)
B
\(x + \sqrt {3y} = 0\)
C
\(\sqrt 3 x + y = 0\)
D
\(x + {{\sqrt 3 } \over 2}y = 0\)
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