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Best answer
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Frequency : Number of times an event occurs. It is a related term of frequent which means to occur commonly or regularly.

  1. periodicity: It comes from periodic which means the tendency to repeat at regular intervals.
  2. rarity: Anything which has almost no chance of occurrence.i.e. not occurring commonly.
  3. gradualness: It comes from gradual which means occurring or developing slowly or by small increments.
  4. persistency: It comes from the word persistent which means to keep doing a course of action in spite of difficulty or opposition.

So, rarity is most nearly opposite in meaning to the given word frequency.

$\therefore$ Option B is the correct answer.

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3 votes

Ans -> (B) rarity

is opposite of "the fact or state of being frequent or happening often." Meaning of frequency is "frequentness" here, which is one of synonyms. 

http://www.merriam-webster.com/dictionary/infrequency -> Another Antonym of Frequency

the rate at which something occurs over a particular period of time or in a given sample.
"an increase in the frequency of accidents due to increased overtime"
the fact or state of being frequent or happening often.
synonyms: rate of occurrence, commonness, frequentness, prevalence, incidence, amount;
rate of repetition, recurrence, repetition, persistence, regularity;
"the frequency of errors"
   
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Ans is (c)

frequency : the fact or state of being frequent or happening often. frequency is constant over the time interval.

periodicity : tendency to occur at interval. its somewhat similar to frequency the only difference is periodicity

 means happening once over the time but frequency means happening more number of times within an interval. In other word frequency is one over the time interval.

rarity : the state or quality of being rare. somewhat frequency is 0.

gradualness : Occurring slowly or by small increments. It means frequency of occurrence will be decreasing over the time.

persistence : the ability to stick with something.

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Frequency meaning happens periodically.

Rarity means happen or don’t happen.

Gradual means decreasing with time. Hence option C

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