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The coefficient \(x^{48}\) in \(\left(1+x\right)+2{(1+x)}^{2}+3{(1+x)}^{3}+\ldots +100{(1+x)}^{100}\) is equal to [JEE M…

Q1

The coefficient \(x^{48}\) in \(\left(1+x\right)+2{(1+x)}^{2}+3{(1+x)}^{3}+\ldots +100{(1+x)}^{100}\) is equal to

[JEE Main 2026, 22 Jan (Shift 1)]

a

\(100⋅{}^{100}{\text{C}}_{49}−{}^{100}{\text{C}}_{50}\)

b

\(100⋅{}^{100}{\text{C}}_{49}−{}^{100}{\text{C}}_{48}\)

c

\(100⋅{}^{101}{\text{C}}_{49}−{}^{101}{\text{C}}_{50}\)

d

\({}^{100}{\text{C}}_{50}+{}^{101}{\text{C}}_{49}\)

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