The sum of middle terms in the expansion of 2 a - a 2-49A- 63-32 a148-aB- 63-32 a138-aC- 63-32 a148-aD- 63-32 a138-a

The correct option is D Middle terms are T_9+1/2=T_5 and T_9+3/2=T_6 ∴ S=^9C_4(2a)^9 4( a^2/4 )^4+^9C_5(2a)^9 5( a^2/4 )^5 =126× 32a^5×a^3/256 126×16a^4×a^10/ ...

You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Middle Terms

The sum of mi...

Question

The sum of middle terms in the expansion of ${(2 a - \frac{a^{2}}{4})}^{9}$ is

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

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

Open in App

Solution

The correct option is D
$M i d d l e t e r m s a r e T_{\frac{9 + 1}{2}} = T_{5} a n d T_{\frac{9 + 3}{2}} = T_{6} ∴ S =^{9} C_{4} (2 a)^{9 - 4} {(- \frac{a^{2}}{4})}^{4} +^{9} C_{5} (2 a)^{9 - 5} {(- \frac{a^{2}}{4})}^{5} = 126 \times 32 a^{5} \times \frac{a^{3}}{256} - 126 \times 16 a^{4} \times \frac{a^{10}}{1024} = \frac{63}{4} a^{13} - \frac{63}{32} a^{14} = \frac{63}{32} (8 - a) a^{13}$

Suggest Corrections

Similar questions

Q. If the middle term in the binomial expansion of

(\frac{1}{x} + x sin x)^{10}

is equal to

\frac{63}{8}

, find the value of

x

Q. An AP consists of 21 terms. The sum of the three terms in the middle is 63 and sum of least three terms is 90. Find the AP.

Q. 1 g of hydrogen is converted into 0.993 g of helium in a thermonuclear reaction. The energy released

Q. If the middle term in the expansion of

{(\frac{1}{x} + x sin x)}^{10}

\frac{63}{8},

then the value of

6 {sin}^{2} x + sin x - 2

If $A = [\begin{matrix} 1 & 3 8 & 9 \end{matrix}]$ , find the sum of the principal diagonal elements of $A^{2} - A . 2$

Join BYJU'S Learning Program

The sum of middle terms in the expansion of (2a−a24)9 is

The correct option is D Middle terms are T9+12=T5 and T9+32=T6∴ S=9C4(2a)9−4(−a24)4+9C5(2a)9−5(−a24)5=126×32a5×a3256−126×16a4×a101024=634a13−6332a14=6332(8−a)a13

The sum of middle terms in the expansion of ${(2 a - \frac{a^{2}}{4})}^{9}$ is