Correct option is B

Final Arrangement:

Clues: J was born on an odd numbered date in the month having odd number of days. Three persons were born between J and the one who likes Grape. E was born on an odd number date but doesn’t like Grape.
Inference: Here we get two possible cases

Clues: The one who likes Cherry was born three persons after E. The number of persons born after the one who likes Cherry is one less than the number of persons born before M. M was born immediately before the one who likes Orange.
Inference: Above clues are placed in both cases:

Clues: One person was born between the one who likes Orange and N. H likes Mango. The one who likes Pear was born after the one who likes Apple. The one who likes Apple was not born on an even number date.
Inference: Case 2 gets cancelled here:
Inference: Only place for K is left. Now, the final Arrangement is:

N was born on 9 May.

Correct option is A

Final Arrangement:

Clues: J was born on an odd numbered date in the month having odd number of days. Three persons were born between J and the one who likes Grape. E was born on an odd number date but doesn’t like Grape.
Inference: Here we get two possible cases

Clues: The one who likes Cherry was born three persons after E. The number of persons born after the one who likes Cherry is one less than the number of persons born before M. M was born immediately before the one who likes Orange.
Inference: Above clues are placed in both cases:

Clues: One person was born between the one who likes Orange and N. H likes Mango. The one who likes Pear was born after the one who likes Apple. The one who likes Apple was not born on an even number date.
Inference: Case 2 gets cancelled here:
Inference: Only place for K is left. Now, the final Arrangement is:

Correct option is B

Final Arrangement:

Clues: J was born on an odd numbered date in the month having odd number of days. Three persons were born between J and the one who likes Grape. E was born on an odd number date but doesn’t like Grape.
Inference: Here we get two possible cases

Clues: The one who likes Cherry was born three persons after E. The number of persons born after the one who likes Cherry is one less than the number of persons born before M. M was born immediately before the one who likes Orange.
Inference: Above clues are placed in both cases:

Clues: One person was born between the one who likes Orange and N. H likes Mango. The one who likes Pear was born after the one who likes Apple. The one who likes Apple was not born on an even number date.
Inference: Case 2 gets cancelled here:

Inference: Only place for K is left. Now, the final Arrangement is:

The number of persons born after the one who likes Pear  is same as the number of persons born between K and J

Correct option is C

Final Arrangement:

Clues: J was born on an odd numbered date in the month having odd number of days. Three persons were born between J and the one who likes Grape. E was born on an odd number date but doesn’t like Grape.
Inference: Here we get two possible cases

Clues: The one who likes Cherry was born three persons after E. The number of persons born after the one who likes Cherry is one less than the number of persons born before M. M was born immediately before the one who likes Orange.
Inference: Above clues are placed in both cases:

Clues: One person was born between the one who likes Orange and N. H likes Mango. The one who likes Pear was born after the one who likes Apple. The one who likes Apple was not born on an even number date.
Inference: Case 2 gets cancelled here:
Inference: Only place for K is left. Now, the final Arrangement is:

N- Cherry’ is incorrect

Correct option is E

Final Arrangement:

Clues: J was born on an odd numbered date in the month having odd number of days. Three persons were born between J and the one who likes Grape. E was born on an odd number date but doesn’t like Grape.
Inference: Here we get two possible cases

Clues: The one who likes Cherry was born three persons after E. The number of persons born after the one who likes Cherry is one less than the number of persons born before M. M was born immediately before the one who likes Orange.
Inference: Above clues are placed in both cases:

Clues: One person was born between the one who likes Orange and N. H likes Mango. The one who likes Pear was born after the one who likes Apple. The one who likes Apple was not born on an even number date.
Inference: Case 2 gets cancelled here:
Inference: Only place for K is left. Now, the final Arrangement is:

Only III is correct