Bhrigu Express: बलिया की आन बान और शान , भृगु एक्सप्रेस है तुम्हारा नाम। हर रविवार तुमसे मिलना है मेरा काम। - Shanzil Kabir

This train was inaugurated in the latter half of 1993. The inaugural service ran as an unnamed tri-weekly train and the exact date of introduction is not clear. However, a tentative date is being updated here so that the year of introduction is accurate (It was NOT introduced in 1978). [Source: Self, and inputs from senior IRFCA members]
By 1993, there were 2 trains operating between Secunderabad/Hyderabad and Bombay, the 7031/32 HYB-BBVT express and the 2101/02 Minar Superfast express. The Minar express had an RSA with the Konark express (Which used to run as SC-BBS express at that time). The incoming Minar express at SC was cleaned, boards changed and used to depart as Konark after...
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a halt of 25 minutes. (Minar arrival 12:15PM, Konark departure:12:40PM).
However, the Konark was usually delayed from BBS itself, because of which the Minar express used to be consistently delayed. The Hussain Sagar express was started in 1993 as a tri-weekly train, initially operating between HYB and Dadar to because of Minar's delays and used to depart from HYB at night.
In 1994, the Minar and Konark expresses were merged into a single train and the new train retained the name 'Konark expres' and operated between BBS-BBVT. At the same time, the Hussain Sagar was made daily. Along with this increase in frequency, the timings were altered so that Hussain Sagar followed the old schedule of the Minar express and Konark was rescheduled to follow the old timings of the Hussain Sagar express.