JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Binomial Theorem

More JEE Main questions on Binomial Theorem

1. If the coefficient of $x$ in the expansion of $\left(a{x}^2+bx+c\right)(1-2x{)}^{26}$ is -56 and the coefficients of ${\mathrm{x}}^2$ and ${\mathrm{x}}^3$ are both zero, then $\mathrm{a}+\mathrm{b}+\mathrm{c}$ is equal to
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2. The coefficient of $x^{48}$ in $(1+x)+2(1+x{)}^2+3(1+x{)}^3+\dots +100(1+x{)}^{100}$ is equal to:
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3. Let ${\mathrm{C}}_{\mathrm{r}}$ denote the coefficient of ${\mathrm{x}}^{\mathrm{r}}$ in the binomial expansion of $(1+\mathrm{x}{)}^{\mathrm{n}},\mathrm{n}\in \mathbb{N},0\le \mathrm{r}\le \mathrm{n}$.
   
   If …
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4. The value of $\frac{{}^{100}{\mathrm{C}}_{50}}{51}+\frac{{}^{100}{\mathrm{C}}_{51}}{52}+\dots .+\frac{{}^{100}{\mathrm{C}}_{100}}{101}$ is :
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5. The sum of all possible values of $n\in N$, so that the coefficients of $x,x^2$ and $x^3$ in the expansion of $(1+x^2{)}^2(1+x{)}^n$, are in arithmetic progression is:
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6. Let $\mathrm{S}=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\dots$ up to 13 terms.
   
   If $13\mathrm{S}=\frac{2^{\mathrm{k}}}{\mathrm{n}!},\mathrm{k}\in \mathrm{N}$, then $\mathrm{n}+\mathrm{k}$ is equal to
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