The sum of the rational terms in the expansion of -2-31 - 510 is

The correct option is D 41The given expansion (√(2)+3^1/5)^10 = ∑_r=0^10 ^10C_r 2^10 r/2·3^r/5 The rational terms correspond for r=0, r=10 Hence the sum of ra ...

242

You visited us 242 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Greatest Binomial Coefficients

The sum of th...

Question

The sum of the rational terms in the expansion of $(\sqrt{2} + 3^{1 / 5})^{10}$ is

46

No worries! We‘ve got your back. Try BYJU‘S free classes today!

42

No worries! We‘ve got your back. Try BYJU‘S free classes today!

41

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

43

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $41$
The given expansion $(\sqrt{2} + 3^{1 / 5})^{10}$ = $10 \sum r = 0$ $^{10} C_{r} 2^{\frac{10 - r}{2}} \cdot 3^{\frac{r}{5}}$

The rational terms correspond for $r = 0, r = 10$

Hence the sum of rational terms $=^{10} C_{0} 2^{5} +^{10} C_{10} 3^{2} = 32 + 9 = 41$ .

Suggest Corrections

Similar questions

Q. The sum of rational terms in the expansion of

{(\sqrt{2} + 3^{1 / 5})}^{10}

Q. The sum of the rational terms in the expansion of

{(\sqrt{2} + 3^{1 / 5})}^{10}

is ......

Q. The rational term(s) in the expansion of

{(\sqrt{2} + (3)^{\frac{1}{5}})}^{10}

is/are

Q. Sum of all the rational terms in the expansion of

{(2^{1 / 3} + 3^{1 / 2})}^{6}

Q. The sum of all those terms which are rational numbers in the expansion of

{(2^{1 / 3} + 3^{1 / 4})}^{12}

Join BYJU'S Learning Program

The sum of the rational terms in the expansion of (√2+31/5)10 is

The correct option is C 41The given expansion (√2+31/5)10 = 10∑r=0 10Cr 210−r2⋅3r5 The rational terms correspond for r=0,r=10 Hence the sum of rational terms =10C025+10C1032=32+9=41.

The sum of the rational terms in the expansion of $(\sqrt{2} + 3^{1 / 5})^{10}$ is

The correct option is C $41$
The given expansion $(\sqrt{2} + 3^{1 / 5})^{10}$ = $10 \sum r = 0$ $^{10} C_{r} 2^{\frac{10 - r}{2}} \cdot 3^{\frac{r}{5}}$

The rational terms correspond for $r = 0, r = 10$

Hence the sum of rational terms $=^{10} C_{0} 2^{5} +^{10} C_{10} 3^{2} = 32 + 9 = 41$ .