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MCQMediumJEE Main 2026 · 24 January, Shift 2Continuity

Mathematics Question from JEE Main 2026 · 24 January, Shift 2

Let [t][t] denote the greatest integer less than or equal to tt. If the function

f(x)={b2sin⁡ ⁣[π2[π2(cos⁡x+sin⁡x)cos⁡x]],x<0sin⁡x−12sin⁡2xx3,x>0a,x=0f(x)= \begin{cases} b^2\sin\!\left[\dfrac{\pi}{2}\left[\dfrac{\pi}{2}(\cos x+\sin x)\cos x\right]\right], & x<0\\ \dfrac{\sin x-\dfrac{1}{2}\sin 2x}{x^3}, & x>0\\ a, & x=0 \end{cases}

is continuous at x=0x=0, then a2+b2a^2+b^2 is equal to

  • A

    34\dfrac{3}{4}

  • B

    12\dfrac{1}{2}

  • C

    58\dfrac{5}{8}

  • D

    916\dfrac{9}{16}

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