Sticky delta

The 30-day Nifty smile is $\sigma(K)=0.14-0.25\ln(K/S)$ near the money (at $K=S$ the vol is 14%). For the 30-day ATM call ($S=K=25{,}000$, $r=6\%$), $\Delta_{BS}=0.5568$ and vega $=2{,}830.3$ (per 1.00 of vol). (a) Under sticky strike, what delta should you hedge with? (b) Under sticky moneyness (smile a fixed function of $K/S$), derive $\partial\sigma/\partial S$ and the hedge delta. (c) For a desk long 100 lots of this call, how many units of futures does the choice change? Which regime is closer to what Nifty implied vols usually do in a sell-off?