The 30-share Sensex, which gained 606.03 points in the previous four straight sessions, added 96.71 points, or 0.33 per cent, to 28,858.30.
On Monday, the rupee had gained 9 paise to close at 66.92 per dollar in view of strong foreign capital inflows coupled with a firm equity market.
In a big revamp, Sebi had in 2014 released norms that clubbed different categories of foreign investors into a new class called FPIs.
In other Asian markets, Japan's Nikkei was up 0.46 per cent while Hong Kong's Hang Seng rose 0.04 per cent in early trade today.
It was alleged that the two entities had acted as both broker and counterparty broker of the clients while they indulged in synchronised trades on BSE and NSE.
The domestic currency gained by 15 paise, 0.21 per cent, in two days.
Major gainers were Bharti Airtel (2.23 per cent), Tata Steel (1.83 per cent), GAIL (1.74 per cent), TCS (1.53 per cent) and Sun Pharma (1.15 per cent).
The NSE Nifty was also trading lower by 8.85 points, or 0.10 per cent, at 8,812.85.
Meanwhile, the benchmark BSE Sensex fell by 40.24 points, or 0.14 per cent, to 28,428.51 in early trade.
The NSE Nifty recaptured the key 8800-level by surging 91.60 points, or 1.04 per cent, to 8,869.60.
ealers attributed the rupee's fall to increased demand for the US currency.
The 50-share NSE Nifty gained 53.30 points or 0.61 per cent to 8,778. Intra-day, it shuttled between 8,783.95 and 8,719.60.
The benchmark BSE Sensex recovered by 109.11 points, or 0.38 per cent, to 28,264.67 in the opening trade today.
The NSE Nifty fell by 17.10 points, or 0.19 per cent, to 8,775.20 and the rupee had recovered by 9 paise to end at 66.93 on fresh selling of dollars by banks.
The rupee opened higher at 66.97 per dollar as against the on Monday's closing level of 67.02 at the Interbank Foreign Exchange (FOREX) market
On similar lines, the NSE Nifty was up by 33.35 points, or 0.37 per cent, at 8,826.90 points.
Sebi's plan for action for 2017-18 also includes facilitating the objective of "ease of doing business" and opening of bank and demat accounts and issue of PAN for FPIs.
The gauge had gained 39.78 points on Thursday.
The dollar index was trading down by 0.02 per cent at 100.65 against a basket of six currencies.
The 30-share Sensex was higher by 126.48 points, or 0.44 per cent, at 28,456.18 with sectoral indices led by banking, metal, capital goods, health-care an IT trading in the positive zone.
The local currency had ended 34 paise higher at a fresh 3-month high of 66.85 against the dollar.
Despite this, oil markets remain bloated as inventories especially in the United States are brimming and rising US drilling activity is pushing up production there as well.
The NSE Nifty inched higher by 9.35 points, or 0.11 per cent, to close at 8,778.40.
Earlier this week, both indexes had hit a four-month high on rate-cut hopes.
NSE's Nifty index fared better by closing with a marginal 0.75-point gain at 8,769.05.
The BSE metal index took the biggest knock, down 1.25 per cent, followed by auto, oil and gas and healthcare.
The dollar struggled against some other currencies overseas which gave the rupee an upper hand.
Global leads aligned as most Asian shares ended higher, tracking weekend gains in the US on better-than-expected jump in US jobs and a move by President Donald Trump to cut back on financial regulations, pacing up buying by investors.
The NSE’s board approved Limaye’s name for the top position but a formal announcement would be made later as some formalities need to be completed.
After listing at Rs 1,085, up 34.61 per cent from the issue price of Rs 806 per share, the BSE shares ended the first day of trading at Rs 1,069.20, a sharp gain of 32.65 per cent.
The gauge had gained 570.65 points in the previous two sessions as the markets gave a thumbs up to the Budget.
Yesterday, the rupee had surged by 10 paise to close at a nearly two-month high of 67.37 on sustained dollar.
During the initial share sale, shareholders offered 1.54 crore shares estimated to be worth around Rs 1,243.44 crore at the higher end of the price band.
Yesterday, the local currency ended at 1-1/2 month high of 67.47 by rising 40 paise, its biggest single-day gain this year, on the back of frantic dollar offloading amid expectations of a Fed rate hike delay.
The 30-share BSE index dropped 50.61 points, or 0.18 per cent, to 28,091.03, with metal, auto, capital goods, IT and realty stocks feeling the squeeze.
The market breadth turned positive as 1,935 shares ended higher, 896 closed lower while 101 ruled steady.