Sum of all the rational terms in the expansion of (3(1/4)+4(1/3))12, is

Question

Sum of all the rational terms in the expansion of (3(1/4)+4(1/3))12, is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

[Tr+1= 12 Cr(3(1/4))12-r ⋅(4)r / 3 = 12 Cr ⋅ 3(3-r / 4) ⋅(4)r / 3 For rational term r=0 or 12 ∴ sum =T1+T13= 12 C0 ⋅ 33+ 12 C12 ⋅ 44 =33+44=27+256=283

Q. Sum of all the rational terms in the expansion of $(3^{\frac{1}{4}} + 4^{\frac{1}{3}})^{12},$ is

[ $T_{r + 1} =^{12} C_{r} (3^{\frac{1}{4}})^{12 - r} \cdot (4)^{r /3}$
$=^{12} C_{r} \cdot 3^{(3 - r /4)} \cdot (4)^{r /3}$
For rational term $r = 0$ or $12$
$∴$ sum $= T_{1} + T_{13} =^{12} C_{0} \cdot 3^{3} +^{12} C_{12} \cdot 4^{4}$
$= 3^{3} + 4^{4} = 27 + 256 = 283$

Q. Sum of all the rational terms in the expansion of (341​+431​)12, is

[Tr+1​=12Cr​(341​)12−r⋅(4)r/3 =12Cr​⋅3(3−r/4)⋅(4)r/3 For rational term r=0 or 12 ∴ sum =T1​+T13​=12C0​⋅33+12C12​⋅44 =33+44=27+256=283

Q. Sum of all the rational terms in the expansion of $(3^{\frac{1}{4}} + 4^{\frac{1}{3}})^{12},$ is

[ $T_{r + 1} =^{12} C_{r} (3^{\frac{1}{4}})^{12 - r} \cdot (4)^{r /3}$
$=^{12} C_{r} \cdot 3^{(3 - r /4)} \cdot (4)^{r /3}$
For rational term $r = 0$ or $12$
$∴$ sum $= T_{1} + T_{13} =^{12} C_{0} \cdot 3^{3} +^{12} C_{12} \cdot 4^{4}$
$= 3^{3} + 4^{4} = 27 + 256 = 283$