Agatha Christie wrote some of her best works between 1920 and 1940

IMO- E

Agatha Christie wrote some of her best works between 1920 and 1940, a period when many successful light-hearted whodunits were written.

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Note 1- As per the intended meaning of the sentence, Second portion after comma should act as a modifier modifying the duration between 1920-1940.
Note 2- "between 1920 and 1940"- Specify a period
Note 3- "During" Vs "In"
* "During" indicates a period or range of time (having duration) and is used to say that something happened. "throughout this time" or "sometime within this time".
* After a verb that focuses on an activity, "during" is used to indicate a period or range of time for the activity. The meaning of the verb expresses a durative action or state.

* "When" is used to mention about an activity which takes place ‘during a specific period of time’ i.e. to connect two events happening at the same time.
* When is used to say a longer action which was interrupted by a shorter action.

* "In" specifies when an activity occurs/occurred, the timing of the activity—part of day, month, season, year
* After a verb that focuses on an activity, "in" sounds awkward when indicating a period or range of time for the activity.
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A. a period when ----Incorrect---- With use of "when" (as stated above) the essence of continuity or "throughout the time is lost.

B. in which----Incorrect----In referring to what is ambiguous - whether 1940 or the interval between 1920 and 1940. Use of "In" to indicate a period or range of time is incorrect. "In" used when timing of activity is to be specified, but as per passage light-hearted whodunits were written throughout the passage of time between 1920 & 1940.Sense of continuity is lost in this.

C. during which ----Incorrect-------Use of during after comma no longer seems to modify duration "between 1920 and 1940". Intended meaning is lost. Also by dropping a period it become ambiguous whether the second action took place between 1920 and 1940 or throughout the year 1940 only.

D. when---Incorrect--------when referring to what is ambiguous - whether 1940 or the interval between 1920 and 1940. Also, both action , Agatha Christie wrote & light-hearted whodunits were written, are taking place at the same time. One action is not interrupted by the other. so use of when is incorrect.

E. a period during which-------Correct----------"A period" clearly refers to duration between 1920 and 1940. Use of "during" depicts the essence of continuity of both the action simultaneously.noun+noun modifier)