Does a writ of habeas corpus contain unexhausted claims?

Generally, applications for writs of habeas corpus that contain unexhausted claims are procedurally barred. 28 U.S.C. 2254(b)(1)(A) (West 2014); see Rose v. Lundy, 455 U.S. 509, 522 (1982). In addition, federal courts have the discretion to deny a habeas application on the merits notwithstanding a petitioner's failure to fully exhaust state judicial remedies. See 28 U.S.C. 2254(b)(2).