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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
If the remainder when x is divided by 4 is 3 , then the remainder when $(2020+\mathrm{x})^{2022}$ is divided by 8 is $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021
The total number of two digit numbers ' n ', such that $3^n+7^n$ is a multiple of 10 , is $\_\_\_\_$ .
JEE Main Mathematics Easy
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Q JEE MAIN_2021_
If $(2021)^{3762}$ is divided by 17 , then the remainder is $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let ${ }^n C_r$ denote the binomial coefficient of $\underline{X^r}$ in the expansion of $(1+\mathrm{x})^{\mathrm{n}}$. If $...
JEE Main Mathematics Hard
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Q JEE MAIN 2021
The term independent of x in the expansion of $\left[\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right]^{10}, x \neq 1$ is equal to $\_\_\_\_$ .
JEE Main Mathematics Hard
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Q JEE MAIN 2021
If $\sum_{r=1}^{10} r!\left(r^3+6 r^2+2 r+5\right)=\alpha(11!)$ then the value of $\alpha$ is equal to $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE-MAIN 2021
The value of $\sum_{\mathrm{r}=0}^6\left({ }^6 \mathrm{C}_{\mathrm{r}} \cdot{ }^6 \mathrm{C}_{6-\mathrm{r}}\right)$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN_2021_
If the fourth term in the expansion of $\left(x+x^{\log _2 x}\right)^7$ is 4480 , then the value of $x$ where $x \in N$ is equal...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
For the natural numbers $m, n$, if $(1-y)^m(1+y)^n=1+a_1 y+a_2 y^2+\ldots . .+a_{m+n} y^{m+n}$ and $a_1=a_2=10$, then the value of $(m+n)$ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2021
For integers $n$ and $r$, let $...
JEE Main Mathematics Easy
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