Out of the 1126 pairs of M/E trains, First Class accommodation is available in 34 services. Here is the list (open to corrections)
10001/10002 BALAGHAT JABALPUR SATPURA EXP
12601/12602 CHENNAI CENTRAL MANGALORE CENTRAL MAIL
12631/12632 CHENNAI EGMORE TIRUNELVELI NELLAI EXP
12637/12638 CHENNAI EGMORE MADURAI PANDYAN EXP
12695/12696 CHENNAI...
more...

CENTRAL THIRUVANATHAPURAM EXP
12919/12920 INDORE JAMMU TAWI MALWA EXP
12921/12922 MUMBAI CENTRAL SURAT FLYING RANI EXP
12929/12930 VALSAD DAHOD EXP
12935/12936 BANDRA(T) SURAT EXP
14235/14236 VARANASI BAREILLY EXP
14629/14630 LUDHIANA FIROZPUR SUTLEJ EXP
14631/14632 DEHRADUN AMRITSAR EXP
15307/15308 LUCKNOW AISHBAGH NAINITAL EXP
15311/15312 PALIA KALAN AISHBAGH SANCTUARY EXP
16041/16042 CHENNAI CENTRAL ALAPPUZHA EXP
16089/16090 CHENNAI CENTRAL TIRUPATTUR YELAGIRI EXP
16175/16176 CHENNAI EGMORE KARAIKAL EXP
16177/16178 CHENNAI EGMORE TIRUCHCHIRAPALLI/KUMBAKONAM ROCK FORT EXP
16203/16204 CHENNAI CENTRAL TIRUPATI EXP
16227/16228 BANGALORE SHIMOGA EXP
16301/16302 SHORANUR THIRUVANATHAPURAM VENAD EXPRESS
16603/16604 MANGALORE CENTRAL THIRUVANATHAPURAM MAVELI EXP
16627/16628 CHENNAI CENTRAL MANGALORE CENTRAL WEST COAST EXP
16629/16630 THIRUVANATHAPURAM MANGALORE CENTRAL MALABAR EXP
16649/16650 MANGALORE CENTRAL THIRUVANATHAPURAM PARASURAM EXP
16865/16866 KARAIKAL ERNAKULAM EXP
18235/18236 BHOPAL BILASPUR EXP
19011/19012 MUMBAI CENTRAL AHMEDABAD GUJARAT EXP
19059/19060 SURAT HAPA/JAMNAGAR/VERAVAL EXP
19109/19110 VALSAD AHMEDABAD GUJARAT QUEEN EXP
19113/19114 BHILAD VADODARA EXP
19215/19216 MUMBAI CENTRAL PORBANDAR SAURASHTRA EXP
52453/52454 KALKA SHIMLA MAIL
52457/52458 KALKA SHIMLA EXP