Question

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2, \sqrt{3 N}, N+2$ are in geometric progression be $\frac{k}{48}$, Then the value of $k$ is

• A. 16
• B. 2
• C. 8
• D. 4

Answer 1

Answer: (D)

4

Answer 2

The correct answer is (D) : 4
n(s)=36
Given : N−2,3N​,N+2 are in G.P.
3N=(N−2)(N+2)
3N=N2−4
⇒N2−3N−4=0
(N−4)(N+1)=0⇒N=4 or N=−1 rejected
(Sum=4)≡{(1,3),(3,1),(2,2)}
n(A)=3
P(A)=363​=121​=484​⇒k=4