Across
1 Miss India, say (6,5) BEAUTY QUEEN
9 Unknown trash, a new aid for smokers (7) ASHTRAY
10 In the midst of a snag Tom got diverted (7) AMONGST
11 Giants, very big, take back work unit (5) OGRES
12 The work book to test the profession of eye care (9) OPTOMETRY
13 Food for a legendary friar? (4) TUCK
15 True air contaminated in a part of old Italy (7) ETRURIA
19 Against the rules? With one pound, legitimate (7)
20 Heredity factor in old dancing actor Kelly (4)
24 To knock the nitpicker is to start exposing (9)
25 Shadow cast by some dumb radicals (5)
27 Strange name, unity for a perennial herb (7)
28 Little frog seen in notice carried by troop leader North, say (7)
29 Place for valuables steadies fop in confusion (4,7)
Down
1 The state of a famous prison with a change of head (5) BIHAR
2 A time to relax when not working (2,4) AT REST
3 Preservative compound with some healthy molecules (6) THYMOL
4 The number one lost in antiquity somehow (8)
5 Huge? Right, one up with a tailless rodent in tow (8)
6 Entertainment for the insomniac perhaps (9)
7 Robbery through business: it got contained in 24 hours (7)
8 Curbs for vessel crossing Scottish river (5)
14 Measuring device to treat ill pacers (9)
16 Not really the game of a junior Woods! (8)
17 Welcome announcement for a shareholder (8)
18 Leader of business very happy though behind time (7) BELATED
21 A lot of water, once a novelty (5) OCEAN
22 Worn out, a sign of tachycardia? (4,2) BEAT UP
23 Money, American, for something in the eye (6) FUNDUS
26 Swell up, as might a trainee in craft (5) BLOAT