Question: When did the majority party in the body which approves members of the American Cabinet gain control of the House?

Knowledge 1: Cabinet of the United States
The heads of the executive departments and all other federal agency heads are nominated by the President and then presented to the Senate for confirmation or rejection by a simple majority (although before the use of the ``nuclear option ''during the 113th US Congress, they could have been blocked by filibuster, requiring cloture to be invoked by ​ ⁄ supermajority to further consideration). If approved, they receive their commission scroll, are sworn in and then begin their duties. [SEP] Knowledge 2: 110th United States Congress
The Democratic Party controlled a majority in both chambers for the first time since the end of the 103rd Congress in 1995. Although the Democrats held fewer than 50 Senate seats, they had an operational majority because the two independent senators caucused with the Democrats for organizational purposes. No Democratic - held seats had fallen to the Republican Party in the 2006 elections. Democrat Nancy Pelosi became the first woman Speaker of the House. The House also received the first Muslim (Keith Ellison) and Buddhist (Hank Johnson and Mazie Hirono) members of Congress. [SEP] Knowledge 3: Party leaders of the United States House of Representatives
The current Minority Leader Nancy Pelosi, of the United States House of Representatives serves as floor leader of the opposition party, and is the counterpart to the Majority Leader. Unlike the Majority Leader, the Minority Leader is on the ballot for Speaker of the House during the convening of the Congress. If the Minority Leader's party takes control of the House, and the party officers are all re-elected to their seats, the Minority Leader is usually the party's top choice for Speaker for the next Congress, while the Minority Whip is typically in line to become Majority Leader. The Minority Leader usually meets with the Majority Leader and the Speaker to discuss agreements on controversial issues.
Knowledge 1: Cabinet of the United States
The heads of the executive departments and all other federal agency heads are nominated by the President and then presented to the Senate for confirmation or rejection by a simple majority (although before the use of the ``nuclear option ''during the 113th US Congress, they could have been blocked by filibuster, requiring cloture to be invoked by ​ ⁄ supermajority to further consideration). If approved, they receive their commission scroll, are sworn in and then begin their duties. [SEP] Knowledge 2: 110th United States Congress
The Democratic Party controlled a majority in both chambers for the first time since the end of the 103rd Congress in 1995. Although the Democrats held fewer than 50 Senate seats, they had an operational majority because the two independent senators caucused with the Democrats for organizational purposes. No Democratic - held seats had fallen to the Republican Party in the 2006 elections. Democrat Nancy Pelosi became the first woman Speaker of the House. The House also received the first Muslim (Keith Ellison) and Buddhist (Hank Johnson and Mazie Hirono) members of Congress. [SEP] Knowledge 3: United States House of Representatives
The presiding officer is the Speaker of the House, who is elected by the members thereof and is therefore traditionally the leader of the controlling party. He or she and other floor leaders are chosen by the Democratic Caucus or the Republican Conference, depending on whichever party has more voting members. The House meets in the south wing of the United States Capitol.
Knowledge 1: Cabinet of the United States
The heads of the executive departments and all other federal agency heads are nominated by the President and then presented to the Senate for confirmation or rejection by a simple majority (although before the use of the ``nuclear option ''during the 113th US Congress, they could have been blocked by filibuster, requiring cloture to be invoked by ​ ⁄ supermajority to further consideration). If approved, they receive their commission scroll, are sworn in and then begin their duties. [SEP] Knowledge 2: 2010 United States House of Representatives elections
Republicans regained control of the chamber they had lost in the 2006 midterm elections, picking up a net total of 63 seats and erasing the gains Democrats made in 2006 and 2008. Although the sitting U.S. President's party usually loses seats in a midterm election, the 2010 election resulted in the highest loss of a party in a House midterm election since 1938, and the largest House swing since 1948. This also happened to be the Republicans' largest gain in House seats since 1938. Republicans gained the most in New York state where they picked up six seats, defeating five incumbents and winning an open Democratic district. The heavy Democratic Party losses were attributed to anger with President Obama, opposition to the Affordable Care Act, large budget deficits and the weak economy. This was also the third consecutive midterm election in a president's first term where the Republican Party has made gains in the House of Representatives, as well as the second consecutive midterm election where party control of the said chamber changed hands. Notable freshmen included future Senators Cory Gardner, Todd Young, James Lankford, and Tim Scott, future Governor of Delaware John Carney, future Director of the Office of Management and Budget Mick Mulvaney, future Secretary of State Mike Pompeo, future Lieutenant Governor of Arkansas Tim Griffin, and future Louisiana Attorney General Jeff Landry. [SEP] Knowledge 3: United States House of Representatives
The presiding officer is the Speaker of the House, who is elected by the members thereof and is therefore traditionally the leader of the controlling party. He or she and other floor leaders are chosen by the Democratic Caucus or the Republican Conference, depending on whichever party has more voting members. The House meets in the south wing of the United States Capitol.

Answer: the 2010 election