Let A=
∈ [100 ,700 ] ∩N :n is neither a multiple of 3 nor a multiple of 4 \. Then the number of elements in A is

Question

Let A= 
 ∈ [100 ,700 ] ∩N :n is neither a multiple of 3 nor a multiple of 4 \. Then the number of elements in A is

Accepted Answer

Correct answer: C. (c) n (3 ) ⇒ multiple of3 athongel102 ,105 ,108 , … … ,699 T_n=699=102+ (n-1 ) (3 )n=200n (3 )=200 ∵n (4 ) ⇒ multiple of4100 ,104 ,108 , … ,700T_n=700=100+ (n-1 ) (4 )n=151n (4 )=151n (3 ∩4 ) ⇒ multiple of3 \&4 both108 ,120 ,132 , … ,696T_n=696=108+ (n-1 ) (12 )n=50n (3 ∩4 )=50n (3 ∪4 )=n (3 )+n (4 )-n (3 ∩4 ) =200+151-50 =301 n (3 ∪4 )= Total -n (3 ∪4 )= neither a multiple of 3 nor a multiple of 4 =601-301=300

$Let A = {n \in [100, 700] \cap N : n is neither a multiple of 3 nor a multiple of 4} . Then the number of elements in A is$

Solution

More Sequence & Series PYQs