JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 66

The question does not pin down what is being counted: pairing all 15 men with distinct women gives $15!$, and choosing a single man-woman team gives 225. Neither is an option.

The keyed value, 1240, equals $\sum_{k=1}^{15}k^2=\dfrac{15\cdot16\cdot31}6$; no reading of the wording that we could find leads to it directly. The answer follows the official key.