JEE Mathematics 2023 Question with Solution

Given: $N$ is the sum obtained on rolling two fair dice. The probability that $N-2, \sqrt{3N}, N+2$ are in geometric progression is $\frac{k}{48}$.

Find: The value of $k$.

For three numbers to be in geometric progression, the square of the middle term must equal the product of the other two terms.

So,

Hence,

Since $N$ is the sum of two dice, only $N=4$ is possible.

The favorable outcomes are:

So the number of favorable outcomes is $3$.

The total number of outcomes when two fair dice are rolled is

Therefore,

Given that

we get

Therefore, the correct option is B.

Given: $N-2, \sqrt{3N}, N+2$ are in geometric progression.

Find: The value of $k$ from the probability expression $\frac{k}{48}$.

Using the GP condition,

So,

Factoring,

Thus $N=4$ or $N=-1$. Since the sum on two dice cannot be negative, reject $N=-1$.

Now count the outcomes for sum $4$:

• $1+3$
• $2+2$
• $3+1$

Hence favorable outcomes $=3$ and total outcomes $=36$.

Comparing with $\frac{k}{48}$,

So the required value is $4$, hence the correct option is B.