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MCQMediumJEE Main 2026 · 22 January, Shift 1Simple Applications

Mathematics Question from JEE Main 2026 · 22 January, Shift 1

The coefficient of x48x^{48} in

(1+x)+2(1+x)2+3(1+x)3+⋯+100(1+x)100(1+x) + 2(1+x)^2 + 3(1+x)^3 + \cdots + 100(1+x)^{100}

is equal to

  • A

    100⋅(10149)−(10150)100\cdot {101 \choose 49} - {101 \choose 50}

  • B

    100⋅(10049)−(10048)100\cdot {100 \choose 49} - {100 \choose 48}

  • C

    100⋅(10049)−(10050)100\cdot {100 \choose 49} - {100 \choose 50}

  • D

    (10050)+(10149){100 \choose 50} + {101 \choose 49}

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