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  • The two successive terms in the expansion of (1 + x)^24 whose coefficients are in the ratio 1: 4 are (A) 3rd and 4th (B) 4th and 5th (C) 5th and 6th (D) 6th and 7th

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

(A) 3rd and 4th (B) 4th and 5th (C) 5th and 6th (D) 6th and 7th

Answers (1)

(c) 5th & 6th

Let us consider (r+1)th& (r+2)th as the 2 successive terms in the expansion of (1+x)24

Now, Tr+1 = 24Crxr&    Tr+2 = 24Cr+1xr+1

Now, 24Cr/24Cr+1 = ¼     ……. (given)

Thus,

\frac{\frac{\left ( 24 \right )!}{r!\left ( 24-r \right )!}}{\frac{\left ( 24 \right )!}{\left ( r+1 \right )\left ( 24-r-1 \right )!}}=\frac{1}{4}

Thus,  (r+1)r! (23 – r)! / r!(24 – r)(23 – r)! = ¼

r + 1/24 – r = ¼

4r + 4 = 24 – r

t = 4

Thus, T4+1 = T5

& T4+2 = T6

Thus, opt (c).
 

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infoexpert22

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