To scrutinize something is to examine it carefully especially in a critical way.

// I closely scrutinized my opponent's moves before making my own.

As an interjection, eureka is used to express excitement when a discovery has been made. When used as an adjective, eureka describes something (typically a moment) that is characterized by a usually sudden triumphant discovery. 

// After years of trying to piece together a concrete business idea, I had a eureka moment and everything made sense.  

Jejune is a formal word that means "uninteresting" or "boring." It is also used as a synonym of juvenile to describe things (such as behaviors, attitudes, etc.) that are immature, childish, or simplistic.

// The movie adaptation employed surreal visual effects to tell the story, making the plot, jejune in the novel, archetypal rather than artless.

// The professor made rude and jejune remarks about the students' artwork.

Tranche refers to a division or portion of a whole.

// A tranche of leaked documents was delivered to the newspaper anonymously, with more promised to come.

Rash describes something done or made quickly and without thought about what will happen as a result. It can also describe someone who is doing something rash.

// I later regretted having made such a rash promise in a moment of chaos.

// Don't be rash about this decision. Take your time.

To immure something is to enclose it within or as if within walls. Immure is also sometimes used synonymously with imprison.

// Scientists at the research station in Antarctica are immured by the frozen wild that surrounds them.

A gambit is something done or said in order to gain an advantage or to produce a desired effect.

// The workers’ opening gambit in the negotiations was to demand a wage hike.