If in the expansion of $(1 + x)^{15}$ , the coefficient of $(2 r + 3)^{t h}$ and $(r - 1)^{t h}$ terms are equal, then the value of r is

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
5

coefficient of $(2 r + 3)^{t h}$ and $(r - 1)^{t h}$ terms in the given expansion are $^{15} C_{2 r + 2}$ and $^{15} C_{r - 2}$ Thus, we have

$^{15} C_{2 r + 2} =^{15} C_{r - 2}$

$\Rightarrow 2 r + 2 = r - 2 o r 2 r + 2 + r - 2 = 15$

$[I f^{n} C_{x} =^{n} C_{y} \Rightarrow x = y$ or x+y =n]

$\Rightarrow r = - 4$ or r =5

Neglecting the negative value, we have r =5

Suggest Corrections

Similar questions

If in the expansion of (1+x)¹⁵, the coefficients of (2r +3)^thand (r-1)^th terms are equal, then the value of r is:

{(2 r + 3)}^{t h}

{(r - 1)}^{t h}

{(1 + x)}^{15}

r

{(1 + x)}^{15}

{(2 r + 3)}^{th} and {(r - 1)}^{th}

(2 r + 3)^{t h}

(r - 1)^{t h}

(1 + x)^{18}

r

(2 r + 3)^{t h}

(r - 1)^{t h}

{(1 + x)}^{18}

r

Join BYJU'S Learning Program