JEE Advanced Model Paper 20 with solutions for online practice

AM is

21+k

2

; GM = √21k⇒k=21 λ2 here λ is an integer and also given 100 ≤ k ≤ 999.
Since

21+k

2

is in the given series, k should be odd.
⇒

100

21

≤ λ2 ≤

999

21

⇒ 4.6 ≤ λ2 ≤ 47357
⇒ λ = 3 , 4 , 5 , 6
∴ λ = 3 or 5 , hence 2 values