JEE 2023 — Mathematics PYQ

1. $\alpha$ ki value nikalna:

   Mean ka formula $\frac{\sum f_i{x}_i}{\sum f_i}=5$ use karke, equation banti hai $\frac{288+7\alpha }{64+\alpha }=5$. Ise solve karne par $\alpha =16$ aata hai.

2. Mean Deviation ($m$) nikalna:

   Mean deviation about mean ka formula lagakar value $\frac{128}{80}$ aati hai, jo simplify hokar $m=\frac{8}{5}$ banti hai.

3. Variance (${\sigma }^2$) nikalna:

   Squares ka sum $\sum f_i(x_i-\bar{x}{)}^2$ lekar use total frequency se divide karne par ${\sigma }^2=\frac{22}{5}$ milta hai.

4. Final Answer:

   In sabhi values ko $\frac{3\alpha }{m+{\sigma }^2}$ mein rakhne par:

   $$\frac{3\times 16}{\frac{8+22}{5}}=\frac{48}{6}=8$$

Final Answer: 8