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The logic followed in this pattern is a series of alphabetical shifts based on the positional values of the letters.

For 'LK' related to 'GE':

For 'FG' related to 'AA':

Applying the same logic to find the cluster related to 'YD':

Thus, DJ is the letter cluster that is related to YD.

Hence, the correct answer is 'Option 3'.

Given that the 2^nd of the current month is Monday.

The total number of days in the current month is 31 days.

Days remaining in the current month after the 2^nd = 31 − 2 = 29 days.

Days in the next month to reach the target date = 10 days.

Total days from the 2^nd of the current month to the 10^th of the next month = 29 + 10 = 39 days.

Number of odd days = 39 ÷ 7 ⇒ Remainder = 4 odd days

Now, add 4 days to the starting day (Monday):

Monday + 4 days = Friday

Hence, the 10^th of the next month will be Friday.

Hence, the correct answer is “Option 3”.

To find the first day of the year 1666, we need the day of the week on January 1, 1666.

Number of completed years = 1665 years

Breakdown of 1665 years = 1600 years + 65 years

Odd days in 1600 years = 0 (as 1600 is a multiple of 400)

In the remaining 65 years, number of leap years = 65 ÷ 4 = 16 (quotient)

Number of ordinary years = 65 − 16 = 49

Odd days in 65 years = (16 × 2) + (49 × 1) = 32 + 49 = 81 odd days

Converting 81 days into weeks: 81 ÷ 7 = 11 weeks and 4 odd days.

Total odd days until December 31, 1665 = 0 (from 1600 years) + 4 (from 65 years) = 4 odd days.

Number of odd days for January 1, 1666 = 4 (completed years) + 1 (current day) = 5 odd days.

According to the mapping, 5 odd days corresponds to Friday.

Hence, the first day of the year 1666 was Friday.

Key Points 

​Number of odd days in 100 years = 5

Number of odd days in 200 years = 3

Number of odd days in 300 years = 1

Number of odd days in 400 years = 0

An ordinary year has 1 odd day, and a leap year has 2 odd days.

Day code mapping: 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday.

Alternate Method

Using the formula: Day = (Date + Month Code + Century Code + Year + Leap Year Code) ÷ 7

For January 1, 1666:

Date = 1

Month Code (January) = 0

Century Code (1600s) = 6

Year = 66

Leap Year Code (66 ÷ 4) = 16

Total = 1 + 0 + 6 + 66 + 16 = 89

Remainder of 89 ÷ 7 = 5

Day code 5 corresponds to Friday.

Hence, the correct answer is Friday.

Given the conditions for the runs scored by five boys R, B, C, L, and Q:

1. Runs of B are less than Q but more than C: 

Q > B > C.

2. Runs of L are more than R but less than C:

C > L > R.

By combining these two relationships, we get the complete descending sequence of runs:

Q > B > C > L > R

Now, let us evaluate the given sequences based on the combined chain:

I. Q > L > R → Correct (From the combined sequence Q > B > C > L > R, it is clear that Q is greater than L, and L is greater than R.)

II. B > L > C → Incorrect (From the combined sequence, we see that B > C and C > L, which means the order should be B > C > L.)

Since only the first sequence holds true, Only I is the correct conclusion.

Hence, the correct answer is 'Option 1'.

Given that there are 6 boys with different heights: M, N, O, P, Q, and R.

From the clues, we can deduce the following relationships:

1. Height of M is less than only Q and O.

→ So, the order is: O/Q > O/Q > M > _ > _ > _

2. O is the tallest boy among all.

→ Therefore, O > Q > M > _ > _ > _

3. Height of P is more than R but less than N.

→ N > P > R

4. Since M is already the 3^rd tallest, the remaining three positions below M must be occupied by N, P, and R.

Combining all the facts gives the final order from tallest to shortest:

→ O > Q > M > N > P > R

The boy whose height is less than M but more than P is N.

Hence, the correct answer is "Option 4".

Given Word: EAGLES

1. SAGE → The letters required are S, A, G, E. All these letters are available in EAGLES. Thus, SAGE can be formed.

2. LEGS → The letters required are L, E, G, S. All these letters are available in EAGLES. Thus, LEGS can be formed.

3. GALE → The letters required are G, A, L, E. All these letters are available in EAGLES. Thus, GALE can be formed.

Hence, the correct answer is “Option 4”.

Given:

'Pooja is older than Neha but younger than Rina':

Rina > Pooja > Neha.

'Seema is younger than Neha but older than Kiran': 

Neha > Seema > Kiran.

By combining both logical chains, we get the following sequence:

Rina > Pooja > Neha > Seema > Kiran.

Therefore, Kiran is the youngest person among them.

Hence, the correct answer is 'Option 4'.

Least possible Venn diagram,

​

Conclusions:

I. All the trains are bikes → Does not follow (The statements only tell us that all trains are cats. There is no information that all trains are bikes.)

II. Some bikes are trains → Does not follow (Although some bikes are cats and all trains are cats, there is no definite information that bikes and trains overlap.)

Neither conclusion I nor II follows.

Hence, the correct answer is "Option 4".

The logic followed in this pattern is based on specific alphabetical shifts for each letter in the group.

For 'CFI' related to 'HMO':

Applying the same logic to 'BDF':

Thus, CFI is related to HMO in the same way BDF is related to GKL.

Hence, the correct answer is 'Option 4'.

BEG : CFH

 

Similarly,

DFH : ?

 

Hence, the correct answer is 'Option 1'.