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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
The remainder when ${\left( {{{(64)}^{(64)}}} \right)^{(64)}}$ is divided by 7 is equal to
JEE Main Mathematics Hard
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Q JEE MAIN 2025
In the expansion of ${\left( {\sqrt[3]{2} + \frac{1}{{\sqrt[3]{3}}}} \right)^n},n \in \;{\rm{N}}$ , if the ratio of ${15^{{\rm{th }}}}$ term from the beginning to the $...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
For an integer $n \ge 2$, if the arithmetic mean of all coefficients in the binomial expansion of ${(x + y)^{2n - 3}}$ is 16...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
The sum of all rational terms in the expansion of ${(2 + \sqrt 3 )^8}$ is
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Suppose $A$ and $B$ are the coefficients of $30^{\text {th }}$ and $12^{\text {th }}$ terms respectively in the binomial expansion of $(1+x)^{2 n-1}$. If...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
The term independent of x in the expansion of $...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
If in the expansion of $(1+x)^{\mathrm{p}}(1-x)^{\mathrm{q}}$, the coefficients of x and $x^{2}$ are 1 and -2 , respectively, then $p^{2}+q^{2}$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
The least value of n for which the number of integral terms in the Binomial expansion of ${(\sqrt[3]{7} + \sqrt[{12}]{{11}})^n}$ is 183, is :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $\alpha = 1 + \sum\limits_{r = 1}^6 {{{( - 3)}^{r - 1}}} {\quad ^{12}}{{\rm{C}}_{2r - 1}}$, then the distance of the point $(12,\sqrt 3)$...
JEE Main Mathematics Hard
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