Series Completion

From figure 1st to 2nd the element at top left corner shifted to the top right corner in the clockwise direction. Similarly, all the element at corner are shifted one place in clockwise direction, but arrow in the middle shifted $45^{\circ}$ in anti-clockwise direction. The same pattern follow in the next steps. Hence, option

(d) is the correct answer.

Pattern of the given series is as follows,

Hence, option (c) is the correct answer.

In the series,

Hence, option (c) is the correct answer.

In the given series,

Hence, option (a) is the correct answer.

In the given series,

Hence, option (b) is the correct answer.

In the first step, the dot (.) moves two spaces (each space is equal to half-a-side of the square boundary) in an anti-clockwise direction. In the second step, the equal $ (=) $ moves three spaces in anticlockwise. In the third step, the plus ( + ) sign moves four spaces anti-clockwise. This three steps are repeated tocontinue the series.

The pattern of the series is as shown below.

$ \therefore \quad ?=183 $

Pattern of the series is as follows.

$ \therefore ?= $ HANK

The pattern of the series is as follows,

Hence, 281 will replace the question mark.

On observing the given pattern, the arrow moving $90^{\circ}$ in clockwise direction along with the pointed shape in each step. So, figure of option (a) will replace the question mark.

The pattern of the series is as follow,

So, 'GDWWI' will replace the question mark.

The pattern of the series is as follows

$\therefore$ ? = FIBQ

1. The first letter of each cluster decreases by 3 positions in the alphabet: T (20th letter) to Q (17th letter) to N (14th letter) to K (11th letter), so the next should be H (8th letter).

2. The second letter of each cluster decreases by 1 position in the alphabet: X (24th letter) to W (23rd letter) to V (22nd letter) to U (21st letter), so the next should be T (20th letter).

3. The third letter of each cluster increases by 3 positions in the alphabet: B (2nd letter) to E (5th letter) to H (8th letter) to K (11th letter), so the next should be N (14th letter).

Therefore, the next letter cluster in the sequence should indeed be HTN, which is Option C.

The pattern is as following

So, V185J will replace the question mark.

To find the wrong number in the sequence, we need to look for some pattern that the other numbers follow which the wrong number does not. Let's examine the sequence given:

2, 6, 12, 72, 865, 62208

At first glance, there doesn't seem to be a simple arithmetic progression or geometric progression. Therefore, we need to look for alternative patterns. One method is to examine the ratios of successive terms to see if they follow a certain pattern:

• 6 / 2 = 3
• 12 / 6 = 2
• 72 / 12 = 6
• 865 / 72 ≈ 12.01
• 62208 / 865 ≈ 71.91

The pattern isn't immediately clear from these ratios. Another approach is to look at how each number could be generated from the previous one using any mathematical operations (such as addition, subtraction, multiplication, division, powers, factorials, etc.). A more complex pattern may involve factorials or powers, given how the numbers increase rapidly. But looking at the jumps between the numbers, another idea might be to examine multiplicative factors increased by non-constant additive increments:

• The jump from 2 to 6 is by multiplying by 3 (2 * 3).
• The jump from 6 to 12 is by multiplying by 2 (6 * 2).

If the pattern is based on multiplying by natural numbers and each time we increase the multiplier by 1, we would expect:

2 (multiplied by 3) = 6

6 (multiplied by 2) = 12

12 (multiplied by 3) should be 36, but we have 72.

At this stage, there is a clear discrepancy since 72 is not obtainable by multiplying 12 by 3. Let's continue to see if there is a different pattern:

12 (multiplied by 6) = 72

72 (multiplied by 12) = 864

According to the second part of the pattern, the term after 72 should be 864 if we multiply by 12. But instead, we have 865. This suggests that 865 is the number that does not fit in the pattern. We would expect a multiplication sequence by consecutive natural numbers (2, 3, 4, ...) or some similar pattern. Either way, 865 is incorrect because it is one more than what the pattern suggests (864).

Given the choices:

• Option A: 72 - This fits with our pattern when using a multiplier of 6.
• Option B: 12 - This fits with our pattern when using a multiplier of 2.
• Option C: 62208 - It doesn’t fit the pattern if we extend it, but keep in mind 865 is already incorrect and should be 864.
• Option D: 865 - This number is one more than what the pattern suggests, so it is the incorrect number in the sequence.

Therefore, the answer is:

Option D: 865