Number of rational terms in the expansion of -2-3 100 is

The correct option is B 26 The general term for the following expression is #160; T_r+1= ^100C_r2^50 r2.3^r4 .Hence we get rational terms for #160; ...

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Standard XII

Mathematics

Sum of Coefficients of All Terms

Number of rat...

Question

Number of rational terms in the expansion of ${(\sqrt{2} + \sqrt[4]{3})}^{100}$ is

25

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26

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27

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28

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Solution

The correct option is B $26$
The general term for the following expression is

$T_{r + 1} =^{100} C_{r} 2^{50 - \frac{r}{2}} {.3}^{\frac{r}{4}}$ .

Hence we get rational terms for

$r = 0, 4, 8, 12....100$

$a_{n} = a + (n - 1) . d$
$100 = 0 + (n - 1) .4$

$25 = n - 1$

$n = 26$

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Number of rational terms in the expansion of (√2+4√3)100 is

The correct option is B 26The general term for the following expression is Tr+1=100Cr250−r2.3r4.Hence we get rational terms for r=0,4,8,12....100an=a+(n−1).d100=0+(n−1).425=n−1n=26

Number of rational terms in the expansion of ${(\sqrt{2} + \sqrt[4]{3})}^{100}$ is

The correct option is B $26$
The general term for the following expression is

$T_{r + 1} =^{100} C_{r} 2^{50 - \frac{r}{2}} {.3}^{\frac{r}{4}}$ .

Hence we get rational terms for

$r = 0, 4, 8, 12....100$

$a_{n} = a + (n - 1) . d$
$100 = 0 + (n - 1) .4$

$25 = n - 1$

$n = 26$