in 1960,which company developed the small wheeled box attached to a computer, better known as a 'mouse'?

Answer 1

The Xerox Corporation,at their Palo Alto Research Centre.

Answer 2

The SRI company- and its inventor is Dr Doug Engelbart
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Dr. Douglas C. Engelbart and his team at SRI International created many of the concepts and tools that set the global computer revolution in motion.

The first computer mouse was one of many breakthrough innovations originating at SRI. Doug Engelbart conceived of the mouse in the early 1960s while exploring the interactions between humans and computers. Bill English, then the chief engineer at SRI, built the first prototype in 1964. A replica of the original computer mouse -- a carved block of wood with a single red button -- is on display in SRI's lobby. Designs with multiple buttons followed soon. A single wheel or a pair of wheels was used to translate the motion of the mouse into cursor movement on the screen. Doug Engelbart was the inventor on the basic patent for what was then called the "X-Y Position Indicator for a Display System." For Doug, the mouse was one part of a much larger technological system whose purpose was to facilitate organizational learning and global online collaboration.

Answer 3

Douglas Engelbart of Stanford Research Institute.
(See wikipedia page in sources)