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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
If $n \geq 2$ is a positive integer, then the sum of the series $...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $\left(1+x+2 x^2\right) 20=a_0+a_1 x+a_2 x_2+\ldots+a_{40} x^{40}$. then $\mathbf{a}_1+\mathbf{a}_3+\mathbf{a}_5+\ldots+\mathbf{a}_{37}$ is equal to
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Q JEE MAIN 2021
Let $[x]$ denote greatest integer less than or equal to $x$. If for $n \in \mathbb{N},\left(1-x+x^3\right)^n=\sum_{j=0}^{3 n} a_j x^j m$ then $...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
If $n$ is the number of irrational terms in the expansion of $\left(3^{1 / 4}+5^{1 / 8}\right)^{60}$, then $(n-1)$ is divisible by:
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $m, n \in N$ and $\operatorname{gcd}(2, n)=1$, If $$ 30\binom{30}{0}+29\binom{30}{1}+\ldots+2\binom{30}{28}+1\binom{30}{29}=n \cdot 2^m $$ then $n+m$ is equal to (Here $\binom{n}{k}={ }^n C_k$ )
JEE Main Mathematics Easy
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Q JEE MAIN 2021
The value of ${ }^{-15} C_1+2 .{ }^{15} C_2-3 .{ }^{15} C_3+\ldots \ldots$. $...
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Q JEE MAIN 2021
The maximum value of the term independent of ' t ' in the expansion of $\left(t^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{t}\right)^{10}$ where $x \in (0,1)$ is
JEE Main Mathematics Medium
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Q JEE MAIN_2022
If the coefficients of $x$ and $x^2$ in the expansion of $(1+x)^p(1-x)^q, p, q \leq 15$, are -3 and -5 respectively, then the coefficient of...
JEE Main Mathematics Medium
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Q JEE MAIN 2022
If the maximum value of the term independent of $t$ in the expansion of $\left(t^2 x^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{t}\right)^{15}, x \geq 0$ is $K$, then $8 K$ equal...
JEE Main Mathematics Medium
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Q JEE MAIN 2022
If the sum of the coefficients of all the positive powers of $x$, in the binomial expansion of $\left(x^n+\frac{2}{x^5}\right)^7$ is 939 , then the sum...
JEE Main Mathematics Medium
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