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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN
If $\frac{{ }^{11} \mathrm{C}_1}{2}+\frac{{ }^{11} \mathrm{C}_2}{3}+\cdots \cdot+\frac{{ }^{11} \mathrm{C}_9}{10}=\frac{\mathrm{n}}{\mathrm{m}}$ with $\operatorname{gcd}(\mathrm{n}, \mathrm{m})=1$, then n+m is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If A denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^2\right)^n$ and B denotes the sum of all the coefficients...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
${ }^{n-1} C_r=\left(k^2-8\right)^n C_{r+1}$ if and only if :
JEE Main Mathematics Hard
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Q JEE MAIN 2025
The remainder, when $7^{103}$ is divided by 23 , is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let the coefficients of three consecutive terms $T_{r}, T_{r+1}$ and $T_{r+2}$ in the binomial expansion of $(a+b)^{12}$ be in a G.P. and let $p$ be...
JEE Main Mathematics Easy
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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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