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

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

• 3rd and 4th

• 4th and 5th

• 5th and 6th

• 6th and 7th

#### Solution

The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are 5th and 6th.

Explanation:

Let rth and (r + 1)th be two successive terms in the expansion (1 + x)24

∴ "T"_(r + 1) = ""^24"C"_r * x^r

"T"_(r + 2) = "T"_(r + 1 + 1) = ""^24"C"_(r + 1) x^(r + 1)

We have (""^24"C"_r)/(""^24"C"_(r + 1)) = 1/4

⇒ ((24!)/(r!(24 - r)!))/((24!)/((r + 1)!(24 - r - 1)!)) = 1/4

⇒ (24!)/(r!(24 - r)!) xx ((r - 1)!(24 - r - 1)!)/(24!) = 1/4

⇒ ((r + 1) * r!(24 - r - 1)!)/(r!(24 - r)(24 - r - 1)!) = 1/4

⇒ (r + 1)/(24 - r) = 1/4

⇒ 4r + 4 = 24 – r

⇒ 5r = 20

⇒ r = 4

∴ T4+1 = T5 and T4+2 = T6

Concept: Binomial Theorem for Positive Integral Indices
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 20 | Page 144
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