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MCQMediumJEE Main 2025 · 23 January, Shift 1Basics of Vectors

Mathematics Question from JEE Main 2025 · 23 January, Shift 1

Let the arc AC of a circle subtend a right angle at the center O. If the point B on the arc AC divides the arc AC such that: length of arc ABlength of arc BC=15\frac{\text{length of arc AB}}{\text{length of arc BC}} = \frac{1}{5} and OC→=αOA→+βOB→,\overrightarrow{OC} = \alpha \overrightarrow{OA} + \beta \overrightarrow{OB}, then α+2(3−1)β\alpha + \sqrt{2} (\sqrt{3}-1) \beta is equal to:

  • A

    2−32 - \sqrt{3}

  • B

    232 \sqrt{3}

  • C

    535 \sqrt{3}

  • D

    2+32 + \sqrt{3}

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