Patterns, Series, Coding and Analogies PYQs for GATE CS

Solve 5+ Patterns, Series, Coding and Analogies previous year questions for GATE CS with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Patterns, Series, Coding and Analogies

Chapter Journey

Letter Coding and Decoding

Master positional logic, shift patterns, and reverse coding rules.

Number Series and Array Patterns

Identify arithmetic, geometric, and hybrid progression rules in sequences.

Word and Functional Analogies

Decode semantic relationships, cause-and-effect, and functional dependencies.

Letter Coding and Decoding: The Core Idea

In analytical reasoning, a code is a deterministic transformation of a given string of characters.

The fundamental principle is consistency: the rule that transforms the given word into its code will apply identically to the target word.

To decode any pattern, you must shift your mindset from reading words phonetically to analyzing them as sequences of numerical positions in the English alphabet.

Patterns, Series, Coding and Analogies: Solved Questions with Step-by-Step Explanations (5 Problems)

Question 1 · Analytical Aptitude · 2025_Set2 MCQ

If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH ?

A.
CEADP
B.
IDBFC
C.
JGIBC
D.
IBCEC

Correct Answer:

Step-by-Step Solution

Insight: The coding rule involves reversing the original word and then applying a uniform forward shift of +1 to each letter.

Exam route: Reverse BEACH to get HCAEB. Shift each letter forward by 1: H→I, C→D, A→B, E→F, B→C. Result is IDBFC.

Learning route:

Step 1: Test direct left-to-right shift for IMAGE → FHBNJ. I(9) to F(6) is -3, M(13) to H(8) is -5. Inconsistent.

Step 2: Apply the Reverse Test. Reverse IMAGE to get EGAMI.

Step 3: Calculate shift: E(5)→F(6) [+1], G(7)→H(8) [+1], A(1)→B(2) [+1], M(13)→N(14) [+1], I(9)→J(10) [+1]. The rule is confirmed: Reverse +1.

Step 4: Verify with FIELD. Reverse to DLEIF. Shift +1: D→E, L→M, E→F, I→J, F→G. Result EMFJG. Matches perfectly.

Step 5: Apply to BEACH. Reverse to HCAEB. Shift +1: H→I, C→D, A→B, E→F, B→C. Final code is IDBFC.

Question 2 · Analytical Aptitude · 2024_Set2 MCQ

In the

4 \times 4

array shown below, each cell of the first three rows has either a cross (X) or a number.

The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is

A.
11
B.
10
C.
12
D.
9

Correct Answer:

Step-by-Step Solution

Insight: This is an array/grid logic problem where a cell's value equals the count of its immediate neighbors (including diagonals) that do NOT contain an 'X'.

Exam route: The last row has no 'X's. Evaluate each bottom-row cell's non-'X' neighbors:

Cell (4,1): Neighbors are (3,1)=3, (3,2)=X, (4,2)=B. Non-X count = 2. So A = 2.
Cell (4,2): Neighbors are (3,1)=3, (3,2)=X, (3,3)=6, (4,1)=A, (4,3)=C. Non-X count = 4. So B = 4.
Cell (4,3): Neighbors are (3,2)=X, (3,3)=6, (3,4)=X, (4,2)=B, (4,4)=D. Non-X count = 3. So C = 3.
Cell (4,4): Neighbors are (3,3)=6, (3,4)=X, (4,3)=C. Non-X count = 2. So D = 2.

Sum = 2 + 4 + 3 + 2 = 11.

Learning route:

Step 1: Verify the rule with a known cell. Take Row 3, Col 1 (value 3). Its neighbors are (2,1)=X, (2,2)=5, (3,2)=X, (4,1), (4,2). Since the last row has no X, (4,1) and (4,2) are not X. The non-X neighbors are (2,2), (4,1), and (4,2). Count = 3. This matches the given value, confirming our understanding.

Step 2: Apply the rule to Row 4, Col 1 (let's call it A). Neighbors: (3,1)=3, (3,2)=X, (4,2)=B. Non-X neighbors: (3,1) and (4,2). Total = 2. Thus, A = 2.

Step 3: Apply to Row 4, Col 2 (B). Neighbors: (3,1)=3, (3,2)=X, (3,3)=6, (4,1)=A, (4,3)=C. Non-X neighbors: (3,1), (3,3), (4,1), (4,3). Total = 4. Thus, B = 4.

Step 4: Apply to Row 4, Col 3 (C). Neighbors: (3,2)=X, (3,3)=6, (3,4)=X, (4,2)=B, (4,4)=D. Non-X neighbors: (3,3), (4,2), (4,4). Total = 3. Thus, C = 3.

Step 5: Apply to Row 4, Col 4 (D). Neighbors: (3,3)=6, (3,4)=X, (4,3)=C. Non-X neighbors: (3,3), (4,3). Total = 2. Thus, D = 2.

Step 6: Sum the last row: A + B + C + D = 2 + 4 + 3 + 2 = 11.

Question 3 · Analytical Aptitude · 2024_Set2 MCQ

In the sequence $6, 9, 14, x, 30, 41$ , a possible value of $x$ is

A.
25
B.
21
C.
18
D.
20

Correct Answer:

Step-by-Step Solution

Insight: This is a second-order difference sequence where the first differences form a progression of consecutive odd numbers.

Exam route: Calculate first differences: $9 - 6 = 3$ , $14 - 9 = 5$ , and $41 - 30 = 11$ . The missing differences between 5 and 11 in an odd number sequence are 7 and 9. Thus, $x = 14 + 7 = 21$ . Verify: $21 + 9 = 30$ .

Learning route:

Step 1: Calculate the first differences ( $Δ_{1}$ ) between consecutive terms:

$9 - 6 = 3$

$14 - 9 = 5$

$x - 14 = ?$

$30 - x = ?$

$41 - 30 = 11$

Step 2: Analyze the known differences: $3, 5, \dots, 11$ . This strongly suggests a sequence of consecutive odd numbers: $3, 5, 7, 9, 11$ .

Step 3: Solve for the missing terms using this pattern. Assume the next difference is $7$ :

$x = 14 + 7 = 21$

Step 4: Verify with the next term. If $x = 21$ , then the next difference is $30 - 21 = 9$ . This perfectly matches the expected odd number $9$ .

Conclusion: $x = 21$ .

Question 4 · Analytical Aptitude · 2021_Set2 MCQ

Pen : Write :: Knife : _________

Which one of the following options maintains a similar logical relation in the above?

A.
Vegetables
B.
Sharp
C.
Cut
D.
Blunt

Correct Answer:

Step-by-Step Solution

Insight: This is a Tool-to-Function analogy. The relationship is "A [Tool] is primarily used to [Action]".

Exam route: A Pen is used to Write. Applying the same bridge sentence, a Knife is used to Cut.

Learning route:

Step 1: Isolate the given pair: Pen : Write.

Step 2: Formulate the Bridge Sentence: "A [Pen] is a tool used to [Write]."

Step 3: Test this exact sentence structure on the target: "A [Knife] is a tool used to [?]."

Step 4: Evaluate options. "Cut" fits perfectly. "Vegetables" is the object acted upon, not the action. "Sharp" is an attribute, not a function. "Blunt" is the opposite attribute.

Step 5: Verify directionality. Tool $\to$ Function. Pen $\to$ Write. Knife $\to$ Cut. The logical relation is perfectly maintained.

Question 5 · Analytical Aptitude · 2021_Set1 MCQ

_____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

A.
Plan, outline
B.
Hospital, library
C.
Doctor, book
D.
Medicine, grammar

Correct Answer:

Step-by-Step Solution

Insight: This is a Worker-to-Product/Action analogy. The logical relationship is "A [Professional] performs/produces [Action/Product]".

Exam route: A Writer produces a Book. Following the same directional relationship, a Doctor performs Surgery. Therefore, the missing pair is Doctor, book.

Learning route:

Step 1: Isolate the known contiguous pair: "writer" and the blank. We know a writer's primary output is a "book".

Step 2: Formulate the Bridge Sentence: "A [Worker] produces/performs [Product/Action]".

Step 3: Apply to the first part: "A [Worker] performs surgery". The professional who performs surgery is a "Doctor".

Step 4: Verify directionality. Doctor $\to$ Surgery (Worker $\to$ Action). Writer $\to$ Book (Worker $\to$ Product). The logical relation is perfectly maintained.

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Patterns, Series, Coding and Analogies PYQs for GATE CS

Chapter Roadmap: Patterns, Series, Coding and Analogies

Chapter Journey

Letter Coding and Decoding: The Core Idea

Letter Coding and Decoding: The Core Idea

Patterns, Series, Coding and Analogies: Solved Questions with Step-by-Step Explanations (5 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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