JEE Main 2026 · 5 Apr · Shift 2, Mathematics question 10

Mean. The value $r(r-1)$ has frequency $\binom nr$:
$$\frac{\sum r(r-1)\binom nr}{2^n}=\frac{n(n-1)2^{n-2}}{2^n}=\frac{n(n-1)}4=60,$$
so $n=16$.

Median. The frequencies $\binom{16}r$ are symmetric about $r=8$, and the values increase with r. So the median is the value at $r=8$: $8\cdot7=56$.

(A)