Figure Matrix
Figure Matrix – RRB Reasoning Guide
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Row/Column Rule | The change (rotation, shading, addition, deletion) that happens along a row is exactly repeated along every row; same for columns. |
| 2 | 90° Clockwise Rule | If a figure turns 90° clockwise in each step, the next figure is the previous one rotated right by 90°. |
| 3 | Mirror-Image Rule | One figure in each row/column is the water-image (vertical flip) of the other; the third is the mirror-image (horizontal flip). |
| 4 | Counting Elements | Total number of lines, circles, arrows or shaded parts increases/decreases by a fixed number (±1, ±2 …) as you move right or down. |
| 5 | Odd-One-Out | The matrix contains 8 identical transformations and 1 odd; locate the odd box to pick the missing figure. |
| 6 | Super-imposition | The third figure in a row/column is obtained by super-imposing the first two and cancelling common lines (XOR logic). |
| 7 | Position Arithmetic | Position of a dot, arrow-head or small square moves (row +1, column +2) etc.; apply the same arithmetic to find the blank box. |
10 Practice MCQs
Q1. (Easy)
Row-1: 🚂→🚃→?
Row-2: 🚞→🚋→?
Row-3: 🚄→🚅→?
Which figure completes Row-3?
A) 🚆 B) 🚇 C) 🚈 D) 🚉
Answer: C) 🚈
Solution: Each row is a train with engine + coach; Row-3 follows the same pattern.
Shortcut: Look for matching “pair” type; pick the un-used rail symbol.
Concept: Pattern completion by analogy.
Q2. (Easy)
In every row the circle count increases by 1.
Row-3 has 2, 3, ?
A) 3 B) 4 C) 5 D) 6
Answer: B) 4
Solution: 2→3→4 (arithmetic +1).
Shortcut: Count only circles; ignore other shapes.
Concept: Quantitative progression.
Q3. (Easy)
Arrow direction: ↑ → ↓ → ?
A) ← B) → C) ↑ D) ↓
Answer: A) ←
Solution: Rotating 90° clockwise each step.
Shortcut: Remember cycle: ↑→↓→←→↑.
Concept: Rotation matrix.
Q4. (Medium)
In each row the second figure is the mirror of the first; the third is the mirror of the second.
If Row-3 starts with “P”, the missing figure is
A) q B) P C) d D) b
Answer: B) P
Solution: Mirror twice = original.
Shortcut: Even number of mirrors = no change.
Concept: Mirror-image rule.
Q5. (Medium)
The number of railway tracks (parallel lines) in each box is 3, 5, 7 in Row-1 and 4, 6, ? in Row-2.
A) 7 B) 8 C) 9 D) 10
Answer: B) 8
Solution: Arithmetic +2; 6+2=8.
Shortcut: Spot odd/even sequences separately.
Concept: Linear count progression.
Q6. (Medium)
Super-imposition rule: Box3 = Box1 ⊕ Box2 (cancel common lines).
Box1 has “+”, Box2 has “×”; missing figure is
A) ◆ B) ⊗ C) ☒ D) ○
Answer: C) ☒
Solution: Super-impose gives 8-vertex star; common lines cancel → square with diagonals.
Shortcut: Draw on rough sheet; erase common strokes.
Concept: XOR super-imposition.
Q7. (Medium)
Dot moves (row+1, col+2) each step. Starting at (1,1) it reaches (3,5) in the blank; choose the figure with dot at
A) top-left B) top-right C) bottom-left D) bottom-right
Answer: D) bottom-right
Solution: 3rd row → bottom, 5th column → right.
Shortcut: Map matrix rows to bottom→top, columns left→right.
Concept: Coordinate tracking.
Q8. (Hard)
In every row the outside shape rotates 45° clockwise, inside shape 90° anti-clockwise.
Row-3 outside: pentagon→?
Inside: ▽→▷
Missing figure has
A) pentagon+▷ B) hexagon+▷ C) pentagon+△ D) hexagon+△
Answer: C) pentagon+△
Solution: Outside 45° still pentagon; inside 90° anti-clockwise ▽→▷→△.
Shortcut: Track two separate rotation tables.
Concept: Dual rotation.
Q9. (Hard)
Shaded area follows A, A√2, 2A in each row.
If 1st box area = 5 cm², 3rd box area is
A) 5√2 B) 10 C) 10√2 D) 20
Answer: B) 10
Solution: 5→5√2→10 (multiply √2 each step).
Shortcut: Write 5, 5√2, 10 as 5×(√2)⁰, 5×(√2)¹, 5×(√2)².
Concept: Geometric progression of area.
Q10. (Hard)
Figure codes: 1-line=1, 2-circle=2, 3-shade=4 (binary weight).
Row-3 codes: 3, 5, ?
Choose figure whose code is
A) 6 B) 7 C) 8 D) 9
Answer: B) 7
Solution: Pattern +2; 3→5→7.
Shortcut: Treat codes as decimal; apply same arithmetic.
Concept: Weighted attribute coding.
5 Previous Year Questions
PYQ 1.
Figure Matrix: Row-1: 1 arrow, 2 arrows, 3 arrows. Row-2: 2,3,?. Row-3: 3,4,?.
RRB NTPC 2021 CBT-1
Answer: Row-2: 4 arrows (Option C)
Solution: Arithmetic +1 horizontally; same vertically.
Exam Tip: When both row & column obey same rule, fill arithmetic progression.
PYQ 2.
Mirror-image row: first symbol is ‘b’, second is ‘d’; missing symbol is
RRB Group-D 30-08-2022 Shift-2
Answer: ‘b’
Solution: Mirror applied twice returns original.
Exam Tip: Even number of reflections → original figure.
PYQ 3.
Dot moves like a knight (2½ steps) in chessboard matrix. Start centre; after two moves dot is in
RRB ALP 2018 Stage-I
Answer: Top-right corner box
Solution: Knight vector (+2,+1) twice → (4,2) i.e. top-right in 4×4 matrix.
Exam Tip: Translate move to (row, col) vector; matrix size matters.
PYQ 4.
Super-imposition: rails ∩ tunnels = cancelled lines; find remaining track layout
RRB JE CBT-1 26-05-2019
Answer: Parallel tracks with gap at centre
Solution: Common portion (overlap) erased → gap.
Exam Tip: Draw both figures lightly; erase intersection before choosing.
PYQ 5.
Shade fraction: ¼ → ½ → ?; choose ¾ shaded square
RPF SI 2019
Answer: ¾ shaded box
Solution: Arithmetic +¼ progression.
Exam Tip: Convert shades to like denominator; count smallest squares.
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Rotation only | Write “90°CW = +1” on finger; bend finger each step to track turns | ▶→▼→◀→▲ cycle |
| Counting figures | Tick each element with pencil dot while counting; prevents re-count | 8 triangles spotted in 5 s |
| Mirror confusion | Stretch right hand—mirror shows left; apply same to arrow direction | → mirror → ← |
| Super-imposition | Slide two transparent sheets (rough) over each other; common lines vanish | + and × → ☒ |
| Row + Column both given | Apply row rule first; if blank still ambiguous, verify with column rule—takes 5 s | Row: +1 circle, Col: +2 lines → intersection gives both attributes |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Ignoring column rule | Focus only on rows | Cross-verify one column before final answer |
| Counting same element twice | Overlapping shares | Use separate tally marks for each attribute |
| Clockwise vs anti-clockwise | Mental rotation error | Always rotate paper (90° physically) |
| Assuming colour = shade | Colour-blind quick look | Check question: “shade” means filled, colour may be decorative |
| Forgetting 3×3 centre | Centre box influences both row & column | Give centre double weight while verifying |
Quick Revision Flashcards
| Front | Back |
|---|---|
| 90°CW 3 times | 270°CW or 90°ACW |
| Mirror twice | Original figure |
| Super-impose common lines | Cancel (XOR) |
| Row rule fails | Check column rule |
| Knight move vector | (±2, ±1) or (±1, ±2) |
| Shade fraction sequence | ¼, ½, ¾, full |
| Rotation cycle of arrow | 4 steps → 360° |
| Even number of reflections | Back to start |
| Attribute code: line=1, circle=2, shade=4 | Sum gives unique code |
| Dot position arithmetic | (row+c, col+d) → apply same c,d |
Topic Connections
- Direct Link: Series Completion (same rotation/count rules), Analogy (1-step relation), Classification (odd-one-out logic)
- Combined Questions: Coding-Decoding + Matrix (attributes assigned letters), Direction-Sense + Knight-move matrix
- Foundation For: Complex 3-D rotation cubes, Machine input-output flowcharts, Diagrammatic data interpretation in RRB JE signal & system diagrams
Master these matrix logics to secure 3-4 definite reasoning marks within 2 minutes in any RRB CBT!
BETA
