Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If (5 + 
) n = I + ƒ, where I ∈ N, n ∈ N and 0 ≤ ƒ < 1, then I equals -
A
– ƒ
B
– ƒ
C
– ƒ
D
+ ƒ
Text Solution
Verified by ExpertsThe correct answer is:
C
We have I + ƒ = (5 + 
) n
Let G = (5 – 
) n
0 < 5 – 
< 1 ⇒ 0 < (5 – 
) n < 1 ⇒ 0 < G < 1
I + ƒ + G = (5 + 
) n + (5 – 
) n
= 2 [ n C 0 5 n + n C 2 5 n–2 ( 
) 2 + ….] ∈ Z
⇒ ƒ + G ∈ Z ( I ∈ Z)
Now 0 ≤ ƒ < 1, 0 < G < 1 ⇒ 0 < ƒ + G < 2
⇒ ƒ + G = 1
Now I = (I + ƒ) – ƒ = (5 + 
) n –ƒ
= 
– ƒ = 
– ƒ
= 
– ƒ ( ƒ + G = 1)
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