He looked at names with heavy weight in the index that helped propel it above the psychological barrier. Najarian believes giants Apple, Microsoft and Intel will move higher.
Buyers may fall into a trap at these levels, said trader Dan Nathan. He contended that "everyone is full up on Apple" as it continues its steady climb to around $130 per share.
Nathan added that Microsoft and Intel have "lost momentum." Microsoft and Intel closed Monday near $44 and $34 per share, respectively.
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He and Najarian agreed that another stalwart, Cisco, could pop higher from roughly $30 per share if the index moves higher. Nathan believes its last few earnings reports have shown promise.
Najarian added that eBay has some room to the upside, while trader Karen Finerman liked Google because shares in the giant trade at a "reasonable multiple" for the company despite their price around $571.
Trader Guy Adami shied away from big tech, and instead touted the biotech sector.
"Biotech is a big component of that Nasdaq now that it wasn't 15 years ago," Adami said.
Pete Najarian is long AAPL, AMAT, BABA, BAC, BMY, BP, CSX, DISC, GE, JPM, KKR, KO, LLY, LOCO, MRK, PEP and PFE. He is long calls APPL, CAM, COP, DAL, FB, GE, GM, GRPN, GS, GT, HPQ, IAG, ISIL, JNJ, JPM, KNDI, MCD, NEE, RF, SPY, SYY, UAL, UFS, WFC, WMB, XOM and ZIOP. He is long puts BHP. Today, he bought AAPL calls, GM calls and GS calls.
Dan Nathan is long BBRY June call spread, KO March put spread, M March 65/67.50 call spread, MU March 31/26 put spread, QQQ May put spread, SHAK, TWTR, XLF March put spread and XRT March 90/85 put spread. Today, he bought TWTR.
Karen Finerman is long BABA, BAC, C, FL, GOOG, GOOGL, JPM, M and KORS. She is short DIA. Her firm is long AAPL, BAC, C, CMLS, DIS, FINL, FBT, FL, GOOG, GOOGL, IBB, JPM, M, KORS, SUNE and XBI. Her firm is short IWM, SPY and USO. Karen Finerman is on the board of GrafTech International.
Guy Adami is long CELG, EXAS and INTC. Guy Adami's wife, Linda Snow, works at Merck.