The coefficient of x 20 in the expansion of 1- x 230 is 30 C 10-A- TrueB- False

The correct option is A True The general term in the expansion of (1 x^2)^30 is T_r + 1 = ^30C_r × ( x^2)^r = ^30C_r × ( 1)^r x^2r to find the coefficient of ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Combination

The coefficie...

Question

The coefficient of $x^{20}$ in the expansion of $(1 - x^{2})^{30}$ is $^{30} C_{10}$ .

True

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

False

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

Open in App

Solution

The correct option is A
True

The general term in the expansion of $(1 - x^{2})^{30}$ is
$T_{r + 1} =^{30} C_{r} \times (- x^{2})^{r} =^{30} C_{r} \times (- 1)^{r} x^{2 r}$ to find the coefficient of $x^{20}$ ,
2r = 20
$\Rightarrow$ r = 10 $\Rightarrow$ The coefficient $^{30} C_{r} (- 1)^{r} =^{30} C_{10}$

Suggest Corrections

Similar questions

Q. Coefficient of

x^{5}

in the expansion of

(1 + x)^{10} . (1 + \frac{1}{x})^{20}

Q. The coefficient of

x^{10}

in the expansion of

1 + (1 + x) + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + (1 + x)^{20}

Q. The coefficient of

x^{20}

in the expansion of

{(1 + x^{2})}^{40} (x^{2} + 2 + \frac{1}{x^{2}})

Q. The coefficient of

x^{20}

in the expansion of

(1 + 3 x + 3 x^{2} + x^{3})^{20}

is :

Q. The coefficient of

x^{20}

in the expansion of

(1 + x^{2})^{40} . {(x^{2} + 2 + \frac{1}{x^{2}})}^{- 5}

Join BYJU'S Learning Program

The coefficient of x20 in the expansion of (1−x2)30 is 30C10.

The correct option is A True The general term in the expansion of (1−x2)30 is Tr+1=30Cr×(−x2)r=30Cr×(−1)rx2r to find the coefficient of x20, 2r = 20 ⇒ r = 10 ⇒ The coefficient 30Cr(−1)r=30C10

The coefficient of $x^{20}$ in the expansion of $(1 - x^{2})^{30}$ is $^{30} C_{10}$ .