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 ...

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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

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42

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41

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43

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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 $=^{10} C_{0} 2^{5} +^{10} C_{10} 3^{2} = 32 + 9 = 41$ .

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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 $=^{10} C_{0} 2^{5} +^{10} C_{10} 3^{2} = 32 + 9 = 41$ .