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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
Let $\binom{n}{k}$ denotes ${ }^n C_k$ and $...
JEE Main Mathematics Hard
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Q JEE MAIN_2021_
$3 \times 7^{22}+2 \times 10^{22}-44$ when divided by 18 leaves the remainder $\_\_\_\_$
JEE Main Mathematics Medium
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Q JEE MAIN 2019
The sum of the series $2 .{ }^{20} \mathrm{C}_0+5 .{ }^{20} \mathrm{C}_1+8 .{ }^{20} \mathrm{C}_2+ 11 .{ }^{20} \mathrm{C}_3+\ldots+62 .{ }^{20} \mathrm{C}_{20}$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN 2019
The sum of the co-efficients of all even degree terms in x in the expansion of $\left(x+\sqrt{x^3-1}\right)^6+\left(x-\sqrt{x^3-1}\right)^6,(x>1)$ is equal to :
JEE Main Mathematics Medium
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Q JEE Main 2019
If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then $k$ is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2021
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096 , then the greatest coefficient in the expansion is $\_\_\_\_$ .
JEE Main Mathematics Easy
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Q JEE MAIN_2021
The term independent of ' $x$ ' in the expansion of $\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$, where $x \neq 0,1$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN_2021
The ratio of the coefficient of the middle term in the expansion of $(1+x)^{20}$ and the sum of the coefficients of two middle terms in...
JEE Main Mathematics Medium
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Q JEE MAIN_2021
If $b$ is very small as compared to the value of $a$, so that the cube and other higher powers of $\frac{b}{a}$ can be neglected...
JEE Main Mathematics Medium
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Q JEE MAIN 2021 S2
A possible value of ' $x$ ', for which the ninth term in the expansion of $\left\{3^{\log _3 \sqrt{25^{x-1}+7}}+3^{\left(-\frac{1}{8}\right) \log _3\left(5^{x-1}+1\right)}\right\}^{10}$ in the increasing powers...
JEE Main Mathematics Medium
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