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  • The two successive terms in the expansion of <img alt="(1+x)^{24}" src="https://entrancecorner.on

The two successive terms in the expansion of (1+x)^{24} whose coefficients are in the ratio 4 :1 are

Option: 1

3^{\text {rd }} \text { and } 4^{\text {th }}


Option: 2

4^{\text {th }} \text { and } 5^{\text {th }}


Option: 3

5^{\text {th }} \text { and } 6^{\text {th }}


Option: 4

6^{\text {th }} \text { and } 7^{\text {th }}


Answers (1)

best_answer

Let the coefficient of successive terms be { }^{24} \mathrm{C}_{\mathrm{r}} and { }^{24} C_{r+1}, then

\frac{{ }^{24} C_r}{{ }^{24} C_{r+1}}=4 \Rightarrow \frac{r+1}{(24-r)}=4 \Rightarrow r=19

{ }^{24} \mathrm{C}_{19},{ }^{24} \mathrm{C}_{20} \Rightarrow{ }^{24} \mathrm{C}_5,{ }^{24} \mathrm{C}_4 \Rightarrow 6^{\text {th }} \text { and } 5^{\text {th }} terms.

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Gunjita

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