The greatest whole number, by which the expression n4 + 6n3 + 11n2 + 6n + 24 is divisible for every natural number n , is -
A. 6
B. 24
C. 12
D. 48
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{According to the question,}} \cr & {{\text{n}}^4} + 6{{\text{n}}^3} + 11{{\text{n}}^2} + 6{\text{n + 24}} \cr & {\text{put n = 1}} \cr & = 1 + 6 + 11 + 6 + 24 \cr & = 48 \cr & {\text{put n = 2}} \cr & {\text{ = 16 + 48 + 44 + 12 + 24}} \cr & {\text{ = 144}} \cr & {\text{Clearly it is divisible by 48}} \cr} $$Join The Discussion
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Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
But for n = 48,
The given equation is not divisible by 48.