The greatest terms of the expansion (2 x+5 y)13 when x=10, y=2 is :

Question

The greatest terms of the expansion (2 x+5 y)13 when x=10, y=2 is : (A)  13 C 5 ⋅ 208 ⋅ 105 (B)  13 C 6 ⋅ 207 ⋅ 104 (C)  13 C 4 ⋅ 209 ⋅ 104 (D) none of these

Tardigrade Admin · Accepted Answer

( T r +1/ T r )=(14- r / r ) ⋅ (5 y /2 n )=(14- r / r ) ⋅ (1/2)>1 ⇒ r <4 (2/3) ⇒ text 5th term is greatest .⇒ T 5= 13 C 4(2 x )9(5 y )4]

Q. The greatest terms of the expansion $(2 x + 5 y)^{13}$ when $x = 10, y = 2$ is :

$^{13} C_{5} \cdot 2 0^{8} \cdot 1 0^{5}$

$^{13} C_{6} \cdot 2 0^{7} \cdot 1 0^{4}$

$^{13} C_{4} \cdot 2 0^{9} \cdot 1 0^{4}$

none of these

$\frac{T _{r + 1}}{T _{r}} = \frac{14 - r}{r} \cdot \frac{5 y}{2 n} = \frac{14 - r}{r} \cdot \frac{1}{2} > 1 \Rightarrow r < 4 \frac{2}{3}$
$\Rightarrow 5th term is greatest \Rightarrow T_{5} =^{13} C_{4} (2 x)^{9} (5 y)^{4}]$

Q. The greatest terms of the expansion (2x+5y)13 when x=10,y=2 is :

13C5​⋅208⋅105

13C6​⋅207⋅104

13C4​⋅209⋅104