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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
The number of integral terms in the expansion of $\left(5^{\frac{1}{2}}+7^{\frac{1}{8}}\right)^{1016}$ is
JEE Main Mathematics Easy
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Q JEE MAIN 2023
Let the number $(22)^{2022}+(2022)^{22}$ leave the remainder a when divided by 3 and $\beta$ when divided by 7 . Then $\left(\alpha^2+\beta^2\right)$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN 2023
If the coefficients of $x$ and $x^2$ in $(1+x)^p(1-x)^q$ are 4 and -5 respectively, then $2 p+3 q$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN 2023
If $(20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots \ldots . .+20(21)^{19}=\mathrm{k}(20)^{19}$, then k is equal to $\_\_\_\_$ .
JEE Main Mathematics Hard
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Q JEE-Main 2023
The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left\{2 x^2+\frac{1}{2 x}\right\}^{11}$ is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2023
If the coefficients of $x^7$ in $\left(a x^2+\frac{1}{2 b x}\right)^{11}$ and $x^{-7}$ in $\left(a x-\frac{1}{3 b x^2}\right)^{11}$ are equal, then
JEE Main Mathematics Easy
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Q JEE MAIN_2025
The sum of the series $...
JEE Main Physics Hard
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Q JEE MAIN 2023
The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $\left(1+x+x^2\right)^{10}=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}$. If $\left(a_1+a_3+a_5+\ldots+a_{19}\right)-11 a_2=121 k$, then $k$ is equal to $\_\_\_\_$
JEE Main Mathematics Medium
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Q JEE MAIN 2025
If $\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^r}\right) \cdot{ }^{11} C_{r+1}=\frac{\alpha^{11}-11^{11}}{10^{10}}$, then $\alpha$ is equal to :
JEE Main Mathematics Medium
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