Question: The 1960 VMI Keydets football team represented which state-supported military college in Lexington, Virginia, the oldest such institution in the United States?

Context paragraphs:
VMI Keydets football: The VMI Keydets football team represents the Virginia Military Institute in Lexington, Virginia.  The Keydets compete in the Southern Conference of the NCAA Division I FCS, and are coached by Scott Wachenheim, named head coach on December 14, 2014.  VMI plays their home contests at 10,000-seat Alumni Memorial Field, as they have since 1962.

2009 VMI Keydets football team: The 2009 VMI Keydets football team represented the Virginia Military Institute during the 2009 NCAA Division I FCS football season.  It was VMI's 119th all-time football season which started in 1891.  They competed in the Big South Conference, and they were led by 2nd year head coach Sparky Woods, who was appointed VMI's 30th head coach in 2008.  VMI played its home games at Alumni Memorial Field, as they still do ever since 1962.

2015 VMI Keydets football team: The 2015 VMI Keydets football team represented the Virginia Military Institute in the 2015 NCAA Division I FCS football season.  It was VMI's 125th football season and the Keydets were led by first year head coach Scott Wachenheim.  They played their home games at 10,000–seat Alumni Memorial Field at Foster Stadium, as they have since 1962.  This was VMI's second season as a member of the Southern Conference, following 11 seasons in the Big South Conference, which followed 78 years in the Southern Conference.  They finished the season 2–9, 1–6 in SoCon play to finish in last place.

2008 VMI Keydets football team: The 2008 VMI Keydets football team represented the Virginia Military Institute during the 2008 NCAA Division I FCS football season.  It was the Keydets 118th year of football, which began in 1891, and their 6th season in the Big South Conference.  VMI was run by first year head coach Sparky Woods, who was previously a head coach at Appalachian State and South Carolina.  Woods was a replacement for his predecessor Jim Reid, who departed from the Institute to be linebackers coach of the Miami Dolphins.

2014 VMI Keydets football team: The 2014 VMI Keydets football team represented the Virginia Military Institute in the 2014 NCAA Division I FCS football season.  It was VMI's 124th football season, as the Keydets were led by seventh year head coach Sparky Woods.  They played their home games at 10,000–seat Alumni Memorial Field, as they have since 1962.  This was VMI's first season as a member of the Southern Conference, following an eleven-year stint in the Big South.

1960 VMI Keydets football team: The 1960 VMI Keydets football team represented the Virginia Military Institute during the 1960 college football season.

2010 VMI Keydets football team: The 2010 VMI Keydets football team represented the Virginia Military Institute during the 2010 NCAA Division I FCS football season.  It was VMI's 120th football season, which dates back to 1891.  In his 3rd year at VMI, the Keydets were led by head coach Sparky Woods, who became the VMI's 30th all-time football coach in 2008.  VMI plays its home games at Alumni Memorial Field, as they have since 1962.

Virginia Military Institute: The Virginia Military Institute (VMI) is a state-supported military college in Lexington, Virginia, the oldest such institution in the United States.  Unlike any other senior military college in the United States, and in keeping with its founding principles, VMI enrolls cadets only and awards baccalaureate degrees exclusively.  VMI offers its students, all of whom are cadets, strict military discipline combined with a spartan, physically and academically demanding environment.  The Institute grants degrees in 14 disciplines in engineering, the sciences, and the liberal arts.

Military Classic of the South: The Military Classic of the South is an American college football rivalry game played by The Citadel Bulldogs football team of The Citadel, The Military College of South Carolina, and the VMI Keydets football team of the Virginia Military Institute.  The teams first played in 1920, but the trophy that is currently awarded, the Silver Shako, was introduced in 1976.  Today, the Citadel football team consists of both Cadets and civilian students while VMI's team is strictly Cadets only.  The game has been played nearly continuously since World War II, with no matchup in 1956, 2004, and 2008–2010.  The Citadel Bulldogs have won the past ten meetings and fourteen of the last sixteen; they lead the series 40–30–2.  At one point in 1967, the Keydets led the series 18–8–1. The Military Classic is the thirteenth oldest still-played rivalry in the Football Championship Subdivision (FCS) of the NCAA.  Both teams were members of the Southern Conference (SoCon) from 1936 until 2003, when VMI left for the Big South Conference and were reunited in the SoCon when VMI returned in 2014.

2016 VMI Keydets football team: The 2016 VMI Keydets football team represented the Virginia Military Institute in the 2016 NCAA Division I FCS football season.  It was VMI's 126th football season and the Keydets were led by second year head coach Scott Wachenheim.  They played their home games at 10,000–seat Alumni Memorial Field at Foster Stadium, as they have since 1962.  This was VMI's third season as a member of the Southern Conference, after playing for 11 seasons in the Big South Conference.  VMI was also a charter member of the Southern Conference, from 1921 through 2003.  They finished the season 3–8, 1–7 in SoCon play to finish in a tie for eighth place.

Supporting paragraphs: 1960 VMI Keydets football team Virginia Military Institute
Answer: Virginia Military Institute (VMI)