Hi there!!!

ISI exam will be held on 13th of May 2018 for this year and CLAT 2018 is also going to held on 13th of May 2018( timings of CLAT exam are 3:00-5:00 p.m) and ISI exam timings are not mentioned  only date is mentioned  in their official website but as per last year trends ISI exam is taken from 10:00 A.M to 1:00 P.M so you can assume that this year too exam will be taken in same timing slot..

It is advisable from my side not to give both the exams as giving both the exams on same day will be very hectic and it can affect your performance .

Hope you got your answer,Best of luck for your Future!!!

Regards,
Rajdeep Sinha

ISI application form 2018 is available in online mode from February 7 to March 9, 2018. However, candidates can pay the application fee for ISI Admission Test 2018 from February 9 to March 11. The institute will conduct ISI Admission Test 2018 on May 13 in offline mode for M.Tech admissions in CS, QROR and CrS programmes.

Source- Careers360

it's very difficult to predict the exam time 

well most of the entrance exam occurs during the morning schedule 

in my view, you candidates must drop a mail citing your genuine problem to both of the concerned authorities 

I am all sure they will sort it out

ISI Kolkata

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