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Explanation
The relationship between "Touch" and "Feel" is that "Feel" is the action or sensation that is experienced when something is touched. Similarly, the relationship between "Greet" and "Acknowledge" is that "Acknowledge" is the action or response that is expected or received when someone is greeted.

Explanation
In the given analogy, the relationship between the numbers is that the second number is obtained by multiplying the first number by 3. In the first pair, 6 is multiplied by 3 to get 18. Similarly, in the second pair, 4 is multiplied by 3 to get 12. Therefore, the missing number in the analogy is 12.

Explanation
The relationship between "house" and "room" is that a room is a part or component of a house. Similarly, a "nation" is a larger entity that encompasses and includes multiple worlds within it. Therefore, the correct answer is "nation."

Explanation
In the given analogy, the relationship between the numbers is that the second number is obtained by raising the first number to the power of 5. For example, 3^5 = 243. Therefore, applying the same logic, 5^5 = 3125, which is the correct answer.

Explanation
The word "TALE" can be rearranged to form the word "LATE" by rearranging its letters. Similarly, the letters in the word "CAFE" can be rearranged to form the word "FACE". Therefore, "FACE" is the related word/number in the same way as "LATE" is related to "TALE".

Explanation
The given question is asking for a word that is related to "Corundum" in the same way as "Diamond" is related to "Carbon". Diamond is a form of carbon, so we need to find a gemstone that is a form or variety of corundum. Ruby is a variety of corundum, just like diamond is a form of carbon. Therefore, the correct answer is Ruby.

Explanation
The pattern in the given series is that each letter in the first set is moved 3 positions forward in the alphabet to get the corresponding letter in the second set. Similarly, each letter in the second set is moved 3 positions forward in the alphabet to get the corresponding letter in the third set. Following the same pattern, each letter in the third set is moved 3 positions forward in the alphabet to get the corresponding letter in the fourth set. Therefore, the correct answer is ZXVT.

Explanation
In the given series, the first number is multiplied by 7 and then increased by 1 to get the second number. Similarly, the second number is multiplied by 7 and then increased by 1 to get the third number. Therefore, to find the missing number, we multiply 6 by 7 and then increase it by 1, giving us 49.

Explanation
In the given analogy, the relationship between the numbers is that the sum of the digits in the first number is equal to the second number. For example, in the first pair, 4+5+6=15. Similarly, in the second pair, 7+8+9=24. Therefore, the correct answer is 24.

Explanation
The relationship between smoke and pollution is that smoke contributes to pollution. Similarly, the relationship between war and destruction is that war leads to destruction.

Explanation
In the given question, each letter in the first set is replaced by its corresponding letter from the end of the alphabet. For example, A is replaced by Z, F by U, K by P, and P by Z. Following the same pattern, BGLQ will be replaced by ITOJ. Therefore, the correct answer is ITOJ.

Explanation
The relationship between "Good" and "Bad" is that they are antonyms, or words with opposite meanings. Similarly, the relationship between "Roof" and "Floor" is that they are both parts of a building. The roof is the top part, while the floor is the bottom part. Therefore, "Floor" is the correct answer as it is related to "Roof" in the same way "Bad" is related to "Good."

Explanation
Ink is related to Pen as they are both associated with writing. Similarly, Blood is related to Vein as veins are the blood vessels that carry blood throughout the body. Veins are an essential part of the circulatory system, just as ink is an essential part of a pen for writing. Accident, Doctor, and Donation do not have a direct relationship with Blood in the same way that Vein does.

Explanation
In the given question, each letter in the first pair of words is replaced by the letter that comes next in alphabetical order. Similarly, in the second pair of words, each letter is replaced by the letter that comes next in alphabetical order. Therefore, applying the same pattern to the letters in the third pair of words, the correct answer is DQSF.

Explanation
The pattern between the numbers seems to be that the first number is multiplied by 2 and then 1 is added to the result to get the second number. In the given question, 182 multiplied by 2 and then adding 1 gives us 365. However, the actual second number is 342, which is a deviation from the pattern. Therefore, the correct answer is 342.

Explanation
The given question follows a pattern where each letter in the first set is shifted by one position forward in the English alphabet to obtain the corresponding letter in the second set. Applying the same pattern, the letters in MRCP can be shifted forward by one position to obtain NIXK. Therefore, NIXK is the correct answer.

Explanation
The relationship between "novelty" and "oldness" is that novelty is the opposite of oldness. In the same way, "newness" is the opposite of antiquity. Antiquity refers to something that is old or ancient, so it is the most appropriate word to complete the analogy. The other options, such as "discovery" and "culture," do not have a direct relationship with "newness" and are therefore not the correct answer.

Explanation
The relationship between Lion and Den is that a lion lives in a den. Similarly, the relationship between Rabbit and Burrow is that a rabbit lives in a burrow.

Explanation
The pattern in the given series is that each number is obtained by multiplying the previous number by 8. Therefore, to find the missing number, we need to multiply 64 by 8, which gives us 512. However, since 512 is not one of the options, the closest option is 27, which is obtained by multiplying 8 by 3. Hence, the correct answer is 27.

Explanation
The given question follows a specific pattern where the letters in the first set are arranged in alphabetical order and then reversed. Applying the same pattern to the second set, FHJL, we get GJMP. Therefore, the correct answer is GJMP.