Binomial Theorem

JEE Advanced · Mathematics · 9 past questions

1. Q1 2025 Paper 2

   Let $a_0,a_1,\ldots,a_{23}$ be real numbers such that…

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2. Q2 2023 Paper 1

   Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^5$ in the expansion of…

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3. Q3 2020 Paper 2

   For nonnegative integers $s$ and $r$, let…

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4. Q4 2019 Paper 2

   Suppose $$\det\begin{bmatrix} \sum_{k=0}^{n} k & \sum_{k=0}^{n} {}^{n}C_k\,k^2 \\ \sum_{k=0}^{n} {}^{n}C_k\,k…

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5. Q5 2018 Paper 2

   Let $X=({}^{10}C_1)^2+2({}^{10}C_2)^2+3({}^{10}C_3)^2+\cdots+10({}^{10}C_{10})^2$, where ${}^{10}C_r$…

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6. Q6 2016 Paper 1

   Let $m$ be the smallest positive integer such that the coefficient of $x^2$ in the expansion of…

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7. Q7 2014 Paper 2

   Coefficient of $x^{11}$ in the expansion of $(1+x^2)^4(1+x^3)^7(1+x^4)^{12}$ is

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8. Q8 2013 Paper 1

   The coefficients of three consecutive terms of $(1+x)^{n+5}$ are in the ratio $5:10:14$. Then $n =$

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9. Q9 2010 Paper 2

   For $r = 0, 1, \ldots, 10$, let $A_r$, $B_r$ and $C_r$ denote, respectively, the coefficient of $x^r$ in the…

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