Let the {\arc} A C of a circle subtend a right angle at the centre O. If the point B on the are A C, divides the arc A C such that {\text{ length of } {\arc} A B}/{\text{ length of } {\arc} B C}=\frac{1}{5}, and \overrightarrow{O C} =\alpha \overrightarrow{O A}+\beta \overrightarrow{O B}, then \alpha+\sqrt{2}(\sqrt{3}-1) \beta is equal to [23 Jan 2025 Shift 1]

JEE Main 23 Jan 2025 Shift 1 Paper

Section: Mathematics

Question : 12 of 75

Marks: +1, -0

Let the arc‌A‌C of a circle subtend a right angle at the centre O. If the point B on the are AC, divides the arc AC such that ‌

‌ length of ‌arc‌A‌B

‌ length of ‌arc‌B‌C

=‌

, and

→

=α

→

+β

→

, then α+√2(√3−1)β is equal to

[23 Jan 2025 Shift 1]

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