# 20 - Binomial Theorem Questions Answers

sum of the coefficients of even powers of x in the expansion of (1-3x+2x^2)^11 is

**Asked By: PRADEEP RAO**3 year ago

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If (1+x+x^{2})^{3p} =a_{0}+a_{1}x+a_{2}x^{2}+........... and (x-1)^{3p}= x^{3p}-k_{1} x^{3p-1} +k_{2}x ^{3p-2} ........then the value of a_{0}-a_{1 }k_{1}+a_{2}k_{2}-a_{3}k_{3}=?

**Asked By: MALVIKA SINGH**5 year ago

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f(x)=x^5+ax^4+bx^3+cx^2+d;f(1)=1,f(2)=2,f(3)=3,f(4)=4,f(5)=5,then value of d is

**Asked By: R.VAGESHA VARDAN**5 year ago

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Find coefficient.of x^{n }in the expansion of [ 1 + (x/1!) + (x^{2}/2!)+...(x^{2}/n!)]

**Asked By: RESHU SINGH**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

SUBMIT THE CORRECT QUESTION

Find sum of series..1*(n)^{2 }+ 2*(n-1)^{2 }+3*(n-2)^{2} +...+n .

**Asked By: RESHU SINGH**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

general term of the series = r(n+1-r)^{2 }= r(n+1)^{2} + r^{3} - 2(n+1)r^{2}

now put sigma then solve

Let n=3^{100} ,then for n the value of tens digit is what??

**Asked By: RESHU SINGH**5 year ago

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If x+y = 1 ,then ∑ r ^{n}C_{r}x^{r}y^{n-r}equals nx....How??

**Asked By: RESHU SINGH**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

∑ r ^{n}C_{r}x^{r}y^{n-r}

= ∑ r ^{n}C_{r}x^{r}(1-x)^{n-r}

= ∑ r n!/r!(n-r)! x^{r}(1-x)^{n-r}

= n (n-1)!/(r-1)!(n-r)! x^{r}(1-x)^{n-r }

= n ^{(}^{n-1)}C_{(}_{r-1) }x^{r}(1-x)^{n-r}

= n ^{(}^{n-1)}C_{r }x^{r+1}(1-x)^{n-r-1 }let r = r+1

= nx ^{(}^{n-1)}C_{r }x^{r}(1-x)^{n-r-1 }

^{now solve}

What is the value of 0⁄0? if its otherthan 1, then how this can be true: lim (e^{x}-1)/x = 1

^{ x −−>0}

**Asked By: BONEY HAVELIWALA**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

exact 0 and lim tends to 0 are different

The probablity that out of 10 person, all born in june, at least two have the same birthday is?

**Asked By: MANISH GUPTA**6 year ago

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What is the coefficient of x^{49} in (x-1)(x^{2}-2)(x^{3}-3)................(x^{10}-10) ?

**Asked By: RUHANI SETH**6 year ago

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