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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2023
The number of elements in the set $\left\{n \in N: 10 \leq n \leq 100\right.$ and $3^n-3$ is a multiple of 7$\}$ is
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Q JEE MAIN 2023
Fractional part of the number $\frac{4^{2022}}{15}$ is equal to
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Q JEE MAIN 2023
Let $\left(a+b x+c x^2\right)^{10}=\sum_{i=0}^{20} p_i x^i, a, b, c \in \mathbb{N}$. If $p_1=20$ and $p_2=210$, then $2(a+b+c)$ is equal to
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Q JEE MAIN 2023
The number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}$ is equal to
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Q JEE-Main
If the ratio of the fifth term from the begining to the fifth term from the end in the expansion of $\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^n$ is $\sqrt{6}: 1$,...
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Q JEE MAIN 2023
The mean of the coefficients of $x, x^2$ $\_\_\_\_$ $x^7$ in the binomial expansion of $(2+x)^9$ is $\_\_\_\_$ .
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Q JEE MAIN 2023
The largest natural number $n$ such that $3^n$ divides $66!$ is $\_\_\_\_$
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Q JEE MAIN 2023
Let $[t]$ denotes the greatest integer $\leq t$. If the constant term in the expansion of $\left(3 x^2-\frac{1}{2 x^5}\right)^7$ is $\alpha$, then $[\alpha]$ is equal...
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Q JEE MAIN 2023
If $\frac{1}{n+1}{ }^n C_n+\frac{1}{n}{ }^n C_{n-1}+\ldots . .+\frac{1}{2}{ }^n C_1+{ }^n C_0=\frac{1023}{10}$ then $n$ is equal to-
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Q JEE MAIN 2023
The sum, of the coefficients of the first 50 terms in the binomial expansion of $(1-x)^{100}$, is equal to
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