Answer: Option C. -> E
The given series is: S, V, Y, B, ?
The pattern followed by this series is that every alternate letter is skipped and the remaining letters are moved forward by 3 positions. So, we have:
S (+3) -> V (+3) -> YSkip B (+3) -> ?
Hence, the missing letter in the series is the letter that comes after B when it is moved forward by 3 positions.
Now, the letter B is the 2nd letter of the English alphabet. So, when we move it forward by 3 positions, we get the 5th letter of the alphabet, which is E.
Therefore, the missing letter in the given series is E. Option C (E) is the correct answer.
Some relevant definitions and formulas used in this solution are:
English alphabet: The set of letters used to write the English language, consisting of 26 letters from A to Z.
Position of a letter: The position of a letter in the English alphabet is its numerical order in the sequence of letters. For example, the position of A is 1, the position of B is 2, and so on.
Move forward by n positions: To move a letter forward by n positions means to shift it to the letter that is n positions ahead of it in the English alphabet. For example, moving B forward by 3 positions gives E, since E is the letter that is 3 positions ahead of B.
Pattern: A pattern is a sequence of numbers, letters, or other symbols that follows a specific rule or sequence. In this question, the pattern followed by the series is to skip every alternate letter and move the remaining letters forward by 3 positions.If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option D. -> 9
In this series, every alternate number seems to be increasing by 1 and decreasing by 1.
So, the missing number should be between 14 and 20 and should be 1 less than 20.
Let's find the pattern between the two adjacent numbers:

• 8 - 3 = 5
• 6 + 5 = 11
• 14 - 6 = 8
• ? + 8 = 20

Therefore, the missing number should be 20 - 8 = 12.
Hence, the correct answer is option D) 12.
Key takeaways and formulas:

• In a number series problem, we need to observe the pattern between the given numbers to find the missing number.
• Common patterns include arithmetic and geometric progressions, alternating increases or decreases, squares or cubes of numbers, etc.
• To find the pattern, we can look for the difference between adjacent numbers or the ratio between them.
• Once we find the pattern, we can extend it to the missing number to get the answer.
• It is important to check our answer by verifying it with the given series.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option C. -> IWX
The given sequence AOP, CQR, EST, GUV, follows a pattern where the first letter in each group is moved two positions forward, the second letter is moved one position backward, and the third letter remains the same.
Let's break down the sequence to understand the pattern:

• AOP: A + 2 = C, O - 1 = N, P stays the same
• CQR: C + 2 = E, Q - 1 = P, R stays the same
• EST: E + 2 = G, S - 1 = R, T stays the same
• GUV: G + 2 = I, U - 1 = T, V stays the same

Using this pattern, we can determine the next term in the sequence:

• IWX: I + 2 = K, W - 1 = V, X stays the same

Therefore, option C (IWX) is the correct answer.
To summarize, the sequence follows the following pattern:

• Add 2 to the first letter in each group
• Subtract 1 from the second letter in each group
• The third letter remains the same

Some key terms and formulas related to sequences and patterns are:

• Sequence: a set of numbers or objects arranged in a particular order
• Pattern: a regular or repeating sequence of numbers or objects
• Arithmetic sequence: a sequence of numbers where each term is found by adding a fixed value to the previous term (e.g., 1, 3, 5, 7...)
• Geometric sequence: a sequence of numbers where each term is found by multiplying the previous term by a fixed value (e.g., 1, 2, 4, 8...)
• Recursive formula: a formula that defines the nth term of a sequence in terms of the previous term(s) (e.g., a_n = a_(n-1) + 3 for the sequence 1, 4, 7, 10...)
• Explicit formula: a formula that gives the nth term of a sequence directly (e.g., a_n = 3n + 1 for the sequence 4, 7, 10, 13...)

Answer: Option B. -> 49

Answer: Option B. -> 12

In a class of 60 students, where boys are twice that of girls, the total number of girls is given by:

Total number of girls = 60/3 = 20

Since Raman is ranked 17th from the top, there are 9 boys ahead of him.

Therefore, the number of girls ahead of Raman = 20 – 9 = 11

Hence, the number of girls after Raman = 20 – 11 = 9

Therefore, the number of girls after Raman in the rank = 9.

Hence, option B - 12 is the correct answer.

Explanation:
• Number of students in the class = 60
• Number of boys = 2x
• Number of girls = x
• Raman’s rank = 17th from the top
• Number of boys ahead of Raman = 9
• Number of girls ahead of Raman = 20 – 9 = 11
• Number of girls after Raman = 9
• Therefore, the correct answer is Option B - 12.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option C. -> VTT
In order to answer the given question, it is important to understand the type of code language being used. The language used here is a Substitution cipher, also known as Caesar cipher.

Substitution cipher is a type of encryption technique in which each letter of the plaintext is replaced by another letter or number. Each letter is replaced by another letter that is a fixed number of positions down the alphabet.

In this question, the substitution cipher used is known as Right Shift cipher, wherein each letter is shifted to the right by a fixed number of places.

Therefore, in order to find the answer, we need to replace each letter of the word ‘EGG’ with the letter that is a fixed number of places down the alphabet.

Since ‘BOAT’ is written as ‘YLZG’ in the same code language, it implies that each letter of the word ‘BOAT’ is shifted four places down the alphabet.

Thus, the letters of the word ‘EGG’ must also be shifted four places down the alphabet.

Therefore, the answer is Option C: VTT

To summarize, the following steps were used to arrive at the answer:
• Understand the type of code language used
• Replace each letter of the word ‘EGG’ with the letter that is a fixed number of places down the alphabet
• Since ‘BOAT’ is written as ‘YLZG’ in the same code language, shift each letter of the word ‘EGG’ four places down the alphabet
• The answer is Option C: VTT

Answer: Option B. -> CIBCED
The given code language is based on a simple substitution cipher, where each letter of the original word is replaced by a corresponding letter from the alphabet in a fixed sequence.
Let's decode the word SINGER to understand the pattern of substitution used in the code.
S I N G E RA I B C E D
We can see that the first letter S is replaced by A, which is the 19th letter of the alphabet, i.e., it is obtained by adding 18 to the position of S in the alphabet. Similarly, the second letter I is replaced by I itself, the third letter N is replaced by B, obtained by adding 1 to the position of N in the alphabet, and so on.
Using the same pattern of substitution, we can decode the word GINGER as follows:
G I N G E RC I B C E D
Hence, the code for GINGER in the given code language is CIBCED. Therefore, the answer is option B, CIBCED.
Some relevant definitions and formulas used in the solution are:

• Substitution cipher: A type of encryption technique where each letter of the original message is replaced by another letter or symbol based on a fixed rule or pattern.
• Alphabet: A set of letters used in a language, usually arranged in a fixed order.
• Position of a letter: The ordinal number that represents the place of a letter in the alphabet, starting from 1 for A, 2 for B, and so on.
• Addition: A mathematical operation that combines two or more numbers to get a sum.
• Decoding: The process of converting an encoded or encrypted message back into its original form.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option A. -> 213310
To determine the code for BETTER, we will use the coding system described in the question where each letter of the word is represented by a three-digit code. The steps to find the code for BETTER are as follows:

• B: BAT is coded as 283, so B is coded as 2.
• E: ARE is coded as 801, so E is coded as 8.
• T: CAT is coded as 383, so T is coded as 3.
• T: CAT is coded as 383, so T is coded as 3.
• E: ARE is coded as 801, so E is coded as 8.
• R: ARE is coded as 801, so R is coded as 0.

Putting all the codes together, we get the code for BETTER as 213310, which is the same as option A.
The solution can be explained as follows:

• A code language is a system of representing words or phrases with specific sequences of characters or symbols. In this case, the code language uses a three-digit code to represent each letter of the word.
• 
  
• The coding system used in the question assigns unique three-digit codes to three words (BAT, CAT, and ARE) to determine the code for each letter.
• 
  
• By using the codes for BAT, CAT, and ARE, we can determine the code for each letter in the word BETTER.
• 
  
• Finally, we put all the codes together to get the code for the entire word BETTER, which is 213310.
• 
  
• In conclusion, by using the coding system described in the question, the code for BETTER is 213310, which is option A.

Answer: Option C. -> Rain
According to the given language, the word 'blue' is called 'rain' and the word 'rain' is called 'pink'. Therefore, we can say that 'blue' is the color of 'pink'. In the same way, we can keep substituting the words to arrive at the answer.
So, let's substitute the words to find the color of the sky:

• Water is called black.
• Black is called tree.
• Tree is called blue, which means that 'blue' is the color of 'tree'.
• Blue is called rain, which means that 'rain' is the color of 'tree'.
• Rain is called pink, which means that 'pink' is the color of 'rain'.
• Pink is called fish, which means that 'fish' is the color of 'pink'.

Thus, the color of the sky is called by the name of the word that comes after 'blue', which is 'rain'. Hence, the correct option is C (Rain).
To summarize, we used the given language and substituted the words to arrive at the answer. The process of substitution involved following the given sequence of word exchanges, which allowed us to determine the word that represented the color of the sky.

Answer: Option A. -> East