Number of rational terms in the expansion of (2(1/7)+3(1/4))198 is equal to

Question

Number of rational terms in the expansion of (2(1/7)+3(1/4))198 is equal to (A) 7 (B) 8 (C) 9 (D) 10

Tardigrade Admin · Accepted Answer

Tr+1= 198 Cr(2)(198- r /7)(3)(r/4) r =0,1,2 ldots ldots ldots . .198 ∴ text For r =16,44,72,100,128,156,184 text the terms in the expansion are rational.

Q. Number of rational terms in the expansion of $(2^{\frac{1}{7}} + 3^{\frac{1}{4}})^{198}$ is equal to

7

8

9

10

$T_{r + 1} =^{198} C_{r} (2)^{\frac{198 - r}{7}} (3)^{\frac{r}{4}}$
$r = 0, 1, 2 \dots\dots\dots ..198$
$∴ For r = 16, 44, 72, 100, 128, 156, 184 the terms in the expansion are rational.$

Q. Number of rational terms in the expansion of (271​+341​)198 is equal to

7

8

9

10

Tr+1​=198Cr​(2)7198−r​(3)4r​ r=0,1,2………..198 ∴ For r=16,44,72,100,128,156,184 the terms in the expansion are rational.

Q. Number of rational terms in the expansion of $(2^{\frac{1}{7}} + 3^{\frac{1}{4}})^{198}$ is equal to

$T_{r + 1} =^{198} C_{r} (2)^{\frac{198 - r}{7}} (3)^{\frac{r}{4}}$
$r = 0, 1, 2 \dots\dots\dots ..198$
$∴ For r = 16, 44, 72, 100, 128, 156, 184 the terms in the expansion are rational.$