Find the coefficient of $x^{90}$ in $(x + x^{2} + x^{3} + . . . . . . . . . .)^{2} (x^{5} + x^{6} + . . . . . . . . . . .)^{9}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A

Coefficient of $x^{90}$ in $(x + x^{2} + x^{3} + . . . . . . . . . . . . . . . . .)^{2} (x^{5} + x^{6} + . . . . . . . . . . . . .)^{9}$

Coefficient of $x^{43}$ in $(1 + x + x^{2} + x^{3} + . . . . . . . . . . .)^{11}$

Coefficient of $x^{43}$ in $(1 - x)^{- 11}$

$^{53} C_{43}$

Suggest Corrections

Similar questions

Find the coefficient of $x^{15}$ in $(x^{3} + x^{6} + x^{9} + . . . . . . . . . . .) (x^{2} + x^{4} + x^{6} + . . . . . . . . . . .) (x + x^{2} + x^{3} + . . . . . . . . . .)$

You are given
$cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} . . . . . .$ ;
$sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . . .$ ;
$tan x = x + \frac{x^{3}}{3} + \frac{2 x^{5}}{15} . . . . . .$
Then the value of
$lim x \to 0 \frac{x cos x + sin x}{x^{2} + tan x}$ is

___

Q. If

{(\frac{x + 1}{x})}^{3} = 3

then find the value of

x^{206} + x^{200} + x^{90} + x^{84} + x^{18} + x^{12} + x^{6} + 1

Q. If

lim x \to - \infty (\sqrt{x^{6} + a x^{5} + b x^{3} - c x + d -} \sqrt{x^{6} - 2 x^{5} + x^{3} + x + 1}) = 2

then

Q. If

{(x + \frac{1}{x})}^{2} = 3

then find the value of

x^{206} + x^{200} + x^{90} + x^{84} + x^{18} + x^{12} + x^{6} + 1

Join BYJU'S Learning Program

Find the coefficient of x90 in (x+x2+x3+..........)2(x5+x6+...........)9

The correct option is A Coefficient of x90 in (x+x2+x3+.................)2(x5+x6+.............)9 Coefficient of x43 in (1+x+x2+x3+...........)11 Coefficient of x43 in (1−x)−11 53C43

Find the coefficient of $x^{90}$ in $(x + x^{2} + x^{3} + . . . . . . . . . .)^{2} (x^{5} + x^{6} + . . . . . . . . . . .)^{9}$