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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2023
The mean of the coefficients of $x, x^2$ $\_\_\_\_$ $x^7$ in the binomial expansion of $(2+x)^9$ is $\_\_\_\_$ .
JEE Main Mathematics Easy
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Q JEE MAIN 2023
The largest natural number $n$ such that $3^n$ divides $66!$ is $\_\_\_\_$
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Q JEE MAIN 2023
Let $[t]$ denotes the greatest integer $\leq t$. If the constant term in the expansion of $\left(3 x^2-\frac{1}{2 x^5}\right)^7$ is $\alpha$, then $[\alpha]$ is equal...
JEE Main Mathematics Easy
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Q JEE MAIN 2023
If $\frac{1}{n+1}{ }^n C_n+\frac{1}{n}{ }^n C_{n-1}+\ldots . .+\frac{1}{2}{ }^n C_1+{ }^n C_0=\frac{1023}{10}$ then $n$ is equal to-
JEE Main Mathematics Easy
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Q JEE MAIN 2023
The sum, of the coefficients of the first 50 terms in the binomial expansion of $(1-x)^{100}$, is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2023
If the coefficients of the three consecutive terms in the expansion of $(1+x)^n$ are in the ratio $1: 5: 20$, then the coefficient of the...
JEE Main Mathematics Hard
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Q JEE MAIN 2023
The coefficient of $x^7$ in $\left(1-x+2 x^3\right)^{10}$ is $\_\_\_\_$
JEE Main Mathematics Hard
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Q JEE-Main 2023
The coefficient of $x^{18}$ in the expansion of $\left(x^4-\frac{1}{x^3}\right)^{15}$ is $\_\_\_\_$
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Q JEE MAIN 2023
If the coefficient of $x^7$ in $\left(a x-\frac{1}{b x^2}\right)^{13}$ and the coefficient of $x^{-5}$ in $\left(a x+\frac{1}{b x^2}\right)^{13}$ are equal, then $a^4 b^4$ is equal...
JEE Main Mathematics Easy
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Q JEE-Main 2023
If the ratio of the fifth term from the begining to the fifth term from the end in the expansion of $\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^n$ is $\sqrt{6}: 1$...
JEE Main Mathematics Easy
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