Binomial Theorem

JEE Main · Mathematics · 9 past questions

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1. Q1 2026 2 Apr Shift 1

   The number of elements in the set…

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2. Q2 2026 2 Apr Shift 2

   If for $3 \le r \le 30$, $\binom{30}{30-r}+3\binom{30}{31-r}+3\binom{30}{32-r}+\binom{30}{33-r}={}^{m}C_r$…

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3. Q3 2026 4 Apr Shift 1

   Let the smallest value of $k \in \mathbb{N}$, for which the coefficient of $x^3$ in…

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4. Q4 2026 4 Apr Shift 2

   In the expansion of $\left(9x - \frac{1}{3\sqrt{x}}\right)^{18}$, $x > 0$, if the term independent of $x$ is…

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5. Q5 2026 5 Apr Shift 1

   If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3}-x^4\right)^n$…

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6. Q6 2026 5 Apr Shift 2

   The coefficient of $x^2$ in the expansion of $\left(2x^2+\frac{1}{x}\right)^{10}$, $x\neq 0$, is…

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7. Q7 2026 6 Apr Shift 1

   If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and…

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8. Q8 2026 6 Apr Shift 2

   If $(1-x^3)^{10} = \sum_{r=0}^{10} a_r x^r (1-x)^{30-2r}$, then $\dfrac{9a_9}{a_{10}}$ is equal to ______.

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9. Q9 2026 8 Apr Shift 2

   If…

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