The number of rational terms in the binomial expansion of (√2+√[3]3)18 is

Question

The number of rational terms in the binomial expansion of (√2+√[3]3)18 is (A) 6 (B) 5 (C) 4 (D) 8

Tardigrade Admin · Accepted Answer

Tr+1= 18 Cr ⋅ 2((18-r)/2) ⋅ 3(r/3) For rational term r=0,3,6,9,12,15,18 ( r should be a multiple of 3 ) Also, r should be even because (18-r/2) ∈ I Θ r =0,6,12,18

Q. The number of rational terms in the binomial expansion of $(2 + 33)^{18}$ is

6

5

4

8

$T_{r + 1} =^{18} C_{r} \cdot 2^{\frac{( 18 - r )}{2}} \cdot 3^{\frac{r}{3}}$
For rational term $r = 0, 3, 6, 9, 12, 15, 18$ ( $r$ should be a multiple of 3 )
Also, $r$ should be even because $\frac{18 - r}{2} \in I$
$Θ r = 0, 6, 12, 18$

Q. The number of rational terms in the binomial expansion of (2​+33​)18 is

6

5

4

8

Tr+1​=18Cr​⋅22(18−r)​⋅33r​ For rational term r=0,3,6,9,12,15,18 ( r should be a multiple of 3 ) Also, r should be even because 218−r​∈I Θr=0,6,12,18

Q. The number of rational terms in the binomial expansion of $(2 + 33)^{18}$ is

$T_{r + 1} =^{18} C_{r} \cdot 2^{\frac{( 18 - r )}{2}} \cdot 3^{\frac{r}{3}}$
For rational term $r = 0, 3, 6, 9, 12, 15, 18$ ( $r$ should be a multiple of 3 )
Also, $r$ should be even because $\frac{18 - r}{2} \in I$
$Θ r = 0, 6, 12, 18$