If sum of coefficients in expansion of {({α ^2}{x^2} - 2α {rm{ }}x + 1)^{51}} vanishes, then value

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7.Binomial Theorem

medium

If the sum of the coefficients in the expansion of ${({\alpha ^2}{x^2} - 2\alpha {\rm{ }}x + 1)^{51}}$ vanishes, then the value of $\alpha $ is

$2$

$-1$

$1$

$-2$

(IIT-1991)

Solution

(c) The sum of the coefficients of the polynomial ${({\alpha ^2}{x^2} – 2\alpha \,x + 1)^{51}}$is obtained by putting $x = 1$ in ${({\alpha ^2}{x^2} – 2\alpha \,x + 1)^{51}}$.

Therefore by hypothesis ${({\alpha ^2} – 2\alpha + 1)^{51}} = 0 \Rightarrow \alpha = 1$

Standard 11

Mathematics

If the sum of the coefficients in the expansion of $(x+y)^{n}$ is $4096,$ then the greatest coefficient in the expansion is …. .

medium

(JEE MAIN-2021)

The coefficient of $t^{50}$ in $(1 + t^2)^{25} (1 + t^{25}) (1 + t^{40}) (1 + t^{45}) (1 + t^{47})$ is

normal

If $a$ and $d$ are two complex numbers, then the sum to $(n + 1)$ terms of the following series $a{C_0} – (a + d){C_1} + (a + 2d){C_2} – ……..$ is

hard

The value $\sum \limits_{ r =0}^{22}{ }^{22} C _{ r }{ }^{23} C _{ r }$ is $…….$

hard

(JEE MAIN-2023)

If $C_{x} \equiv^{25} C_{x}$ and $\mathrm{C}_{0}+5 \cdot \mathrm{C}_{1}+9 \cdot \mathrm{C}_{2}+\ldots .+(101) \cdot \mathrm{C}_{25}=2^{25} \cdot \mathrm{k}$ then $\mathrm{k}$ is equal to

hard

(JEE MAIN-2020)

If the sum of the coefficients in the expansion of ${({\alpha ^2}{x^2} - 2\alpha {\rm{ }}x + 1)^{51}}$ vanishes, then the value of $\alpha $ is

Solution

Similar Questions

If the sum of the coefficients in the expansion of $(x+y)^{n}$ is $4096,$ then the greatest coefficient in the expansion is …. .

The coefficient of $t^{50}$ in $(1 + t^2)^{25} (1 + t^{25}) (1 + t^{40}) (1 + t^{45}) (1 + t^{47})$ is

If $a$ and $d$ are two complex numbers, then the sum to $(n + 1)$ terms of the following series $a{C_0} – (a + d){C_1} + (a + 2d){C_2} – ……..$ is

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