Right option is (c) 566.25 r.p.m.
Easy explanation: Given α = 20° ; NA = 500 r.p.m.
Let A, B and C are the driving shaft, intermediate shaft and driven shaft respectively. We know that for the driving shaft (A) and intermediate shaft (B),
Maximum speed of the driven shaft,
NC(max) = NB(max)/cosα = NA/cos^2α = 566.25 r.p.m.