Let n is selected from the set {1,2,3,...,10} and the number 2n+3n+5n is formed. Total number of ways of selecting n so that the formed number is divisible by 4 is equal to
A
4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
4.0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
4.00
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
3n=4λ1−1,5n=4λ2+1
If n is odd, ⇒2n+3n+5n is divisible by 4 if n≥2
Thus, n=3,5,7,9, i.e., n can take 4 different values.
If n is even, 3n=4λ1−1,5n=4λ2+1 ⇒2n+3n+5n is not divisible by 4
as 2n+3n+5n will be in the form of 4λ+2.
Thus, the total number of ways of selecting 'n' is equal to 4.