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Binomial Theorem

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2019
The smallest natural number n , such that the coefficient of $x$ in the expansion of $\left(x^2+\frac{1}{x^3}\right)^n$ is ${ }^{\mathrm{n}} \mathrm{C}_{23}$, is :
JEE Main Mathematics Medium
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Q JEE MAIN 2020
If $\mathrm{C}_{\mathrm{r}} \equiv{ }^{25} \mathrm{C}_{\mathrm{r}}$ and $\mathrm{C}_0+5 . \mathrm{C}_1+9 . \mathrm{C}_2+\ldots . .+(101) . \mathrm{C}_{25}= 2^{25} \cdot \mathrm{k}$, then k is equal to $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE Main 2019
If the third term in the binomial expansion of $\left(1+x^{\log _2 x}\right)^5$ equals 2560 , then a possible value of $x$ is
JEE Main Mathematics Medium
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Q JEE MAIN 2020
$\left(2 x^2+3 x+4\right)^{10}=\sum_{r=10}^{20} a_r x^r$. Then $\frac{a_7}{a_{13}}$ is equal to $\_\_\_\_$ .
JEE Main Mathematics Hard
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Q JEE Main 2019
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is
JEE Main Mathematics Easy
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Q JEE Main 2019
If $\sum_{\mathrm{i}=1}^{20}\left(\frac{{ }^{20} \mathrm{C}_{\mathrm{i}-1}}{{ }^{20} \mathrm{C}_{\mathrm{i}}+{ }^{20} \mathrm{C}_{\mathrm{i}-1}}\right)^3=\frac{\mathrm{k}}{21}$, then k equals
JEE Main Mathematics Medium
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Q JEE MAIN 2020
The value of $\sum_{\mathrm{r}=0}^{20}{ }^{50-\mathrm{r}} \mathrm{C}_6$ is equal to:
JEE Main Mathematics Medium
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Q JEE MAIN 2020
If for some positive integer $n$, the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{n+5}$ are in the ratio $5: 10: 14$,...
JEE Main Mathematics Medium
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Q JEE MAIN 2019
Let $S_n=1+q+q^2+\ldots+q^n$ and $T_n=1+\left(\frac{q+1}{2}\right)+\left(\frac{q+1}{2}\right)^2+\ldots .+\left(\frac{q+1}{2}\right)^n$ where $q$ is a real number and $q \neq 1$. If $...
JEE Main Mathematics Hard
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Q JEE MAIN 2019
Let $(x+10)^{50}+(x-10)^{50} =a_0+a_1 x+a_2 x^2+\ldots+a_{50} x^{50}$, for all $x \in R$ : then $\frac{a_2}{a_0}$ is equal to :
JEE Main Mathematics Medium
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