8-Binomial Theorem

Binomial Theorem

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How to prepare for Binomial Theorem for JEE Mains
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Moderator2
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Ques no. 13,14 in detail
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kruti s.das
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Abhay Raj
Binomial
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LiveDoubtClearing
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Abhay Raj
Binomial
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LiveDoubtClearing
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L
Explain binomial theorem ?
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Amodini
Amodini
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Let 75 .............57 denote the (r+2) digit number where the first and the last digits are 7 and the remaining r digits .......?
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Abhineet
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Define $S_j=\sum_{n=j}^{\infty} \frac{1}{\binom{n}{j}}$ for $j \geqslant 2$.
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Amodini
Amodini
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The coefficient of $x^{324}$ in the expansion of $(x+1)(x-2)^2(x+3)^3(x-4)^4 \ldots$
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258
Anurag07
Anurag07
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If $\mathrm{a}=\sum_{r=0}^{33}{ }^{33} \mathrm{C}_{\mathrm{r}}, \mathrm{b}=\sum_{r=0}^{33}{ }^{66} \mathrm{C}_{2 \mathrm{r}},$
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274
Anurag07
Anurag07
AGRIMA M
The number of rational terms in the expansion of $\left(\sqrt[3]{\underline{4}}+\frac{1}{\sqrt[4]{6}}\right)^{20}$ is
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1
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297
solution.livedoubt
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AGRIMA M
Number of Rational Terms in Expansion of \((\sqrt[3]{4}+\frac{1}{\sqrt[4]{6}})^{20}\)
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268
solution.livedoubt
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Angel
Finding the Value of \( m-n \) from a Combinatorial Sum with GCD Constraint
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2
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solution.livedoubt
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Angel
If $\sum_{r=1}^{30} \frac{r^2\left({ }^{30} C_r\right)^2}{{ }^{30} C_{r-1}}=\alpha \times 2^{29}$, then $\alpha$ is equal to_____?
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1
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497
solution.livedoubt
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Angel
If $\alpha=1+\sum_{r=1}^6(-3)^{r-1} \quad{ }^{12} \mathrm{C}_{2 r-1}$, then the distance of the point $(12, \sqrt{3})$
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391
solution.livedoubt
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Angel
Find the Largest Coefficient in the Expansion of $(1+x)^{n+4}$ Given A.P. Condition on Terms
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382
solution.livedoubt
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A
Find the fifth term in the expansion of $(2+ \frac{3}{2} x)^8$?
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solution.livedoubt
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janes arya
The term independent of $x$ in the expansion of $\left(1-x^2+3 x^3\right)\left(\frac{5}{2} x^3-\frac{1}{5 x^2}\right)^{11}, x \neq 0$ is:
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2
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LiveDoubtClearing
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M
$P( n ): 2^{3 n+3}-7 n-8$, where $n$ is a natural number. What the value of the biggest positive whole number by which the term is divisible ?
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219
Math.LiveDoubtClearing
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M
$\begin{gathered}\left({ }^{10} C_1\right)^2+2\left({ }^{10} C_2\right)^2+\cdots+{ }^{10}({ }^{10} C_{10})^2=m\left({ }^n C_m\right)\end{gathered}$
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1
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225
Math.LiveDoubtClearing
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M
The coefficient of $x^9$ in the expansion of $(1+x)\left(1+x^2\right)\left(1+x^3\right) \ldots \ldots\left(1+x^{100}\right)$ is
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1
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207
Math.LiveDoubtClearing
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Prove that: : ${ }^n C_0 \cdot{ }^{2 n} C_n-{ }^n C_1 \cdot{ }^{2 n-2} C_{n-2}+{ }^n C_2 \cdot{ }^{2 n-4} C_{n-4}+\ldots .=2^n$
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1
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203
Math.LiveDoubtClearing
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