Why this topic matters · 8 min read
Non-Verbal Reasoning tests your ability to think in pictures and patterns rather than words or numbers. In Agniveer Army CEE, this section appears in the General Intelligence and Reasoning paper and typically carries 5 to 10 questions. Common question types include figure series, mirror images, paper folding and cutting, embedded figures, and analogy between shapes. These questions are purely visual so no language barrier — but speed and pattern recognition practice are essential. Expect 1 to 2 questions per type.
Figure Series and Pattern Completion
A set of figures is given in a sequence and you must find what comes next or which figure is missing. Each figure changes in a specific rule — rotation, shading, number of sides increasing, inner shapes changing, etc. Your job is to spot the rule and apply it to find the answer. Think of it like a filmstrip — each frame changes by one rule consistently.
- Look for changes in: rotation, shading, size, number of elements, position
- Check if shapes rotate clockwise or anticlockwise — common trick
- Count elements — often increases by 1 each step
- Shading pattern often alternates or moves one step ahead
- If stuck, eliminate options that break the pattern
Mirror Image and Water Image
Mirror image flips the figure LEFT to RIGHT (as if a mirror is placed on the right side). Water image flips the figure UP to DOWN (as if reflected in water below). A very common error is confusing which axis the flip happens on. Remember: Mirror = Horizontal flip (left-right), Water = Vertical flip (up-down). Clock hands also get reversed — a clock showing 3:00 has mirror image showing 9:00.
- Mirror image: left becomes right, up-down stays same
- Water image: top becomes bottom, left-right stays same
- Alphabets like A, H, I, M, O, T, U, V, W, X, Y look same in mirror
- Numbers like 0, 8 look same; 2, 5 get reversed
- For clock mirror image: Mirror time = 11:60 minus given time
Key formulas
Mirror Clock Formula
Mirror Time = 11:60 - Given Time
When: Use when asked for mirror image of a clock face
Worked examples
Clock shows 4:30. Mirror image = 11:60 - 4:30 = 7:30. Answer is 7:30.
Clock shows 8:15. Mirror image = 11:60 - 8:15 = 3:45. Answer is 3:45.
Paper Folding and Cutting
A square paper is folded once or twice and then a cut (hole or notch) is made. You must find how the paper looks when unfolded. The key idea is: every fold creates a symmetrical copy of the cut on the other side. So if paper is folded once and a hole is punched, when unfolded there will be 2 holes — mirror images of each other across the fold line.
- One fold = 2 holes when unfolded
- Two folds = 4 holes when unfolded
- The holes are always symmetrical about the fold line
- Track the fold direction carefully — left-to-right or top-to-bottom
- Trace the fold in reverse step by step to find hole positions
Key formulas
Holes after folding
Number of holes = 2 raised to the power of (number of folds)
When: Use to quickly count total holes after unfolding
Worked examples
Paper folded twice, one hole punched: 2 to the power 2 = 4 holes when unfolded.
Paper folded once diagonally, hole in corner: when unfolded, 2 holes appear symmetrically across the diagonal fold line.
Embedded Figures
A small figure (the key figure) is hidden inside a larger complex figure. You must identify which answer option contains the key figure hidden within it. The trick is that the key figure is drawn with the same proportions and orientation — it is not resized or rotated (unless stated). Mentally trace the outline of the small figure on the larger one.
- Look for the exact shape — same size and orientation
- Trace each line of the small figure in the big figure
- Eliminate options that clearly lack a matching line or angle
- Do not look for a standalone copy — it is merged into the bigger shape
- Practice quickly — these appear simple but are time traps
Figure Analogy
Just like word analogy (chair is to furniture as shirt is to clothing), figure analogy asks: Figure A is to Figure B as Figure C is to Figure D — find Figure D. The relationship between A and B (rotation, shading added, shape removed, size change) must be the same between C and D. Always define the rule precisely from the first pair before applying it.
- Define the exact change from Figure A to Figure B first
- Apply the same change to Figure C to get D
- Common changes: 90 degree rotation, shading added or removed, shape inside changes, elements doubled
- If two changes happen (e.g. rotate AND shade), apply both to C
- Watch for traps — one option may have only one of two changes
Counting Figures (Triangles, Squares)
A figure made of lines is shown and you must count how many triangles or squares or rectangles are hidden inside it. The trick is to count systematically: first count unit shapes, then shapes made of 2 units, then 3 units, and so on. Use a formula for standard diagrams.
- Count unit triangles first, then combinations of 2, 3, etc.
- For a triangle divided into n rows: total triangles = n(n+2)(2n+1) divided by 8
- For a row of n squares: rectangles = n(n+1)/2, squares need separate count
- Mark shapes with labels (A, B, C...) to avoid counting twice
- These questions are time-consuming — attempt last if unsure
Key formulas
Triangles in a triangle with n rows
Total triangles = n(n+2)(2n+1) / 8
When: When a big triangle is divided into smaller equal triangles in n rows
Rectangles in a row of n squares
Total rectangles = n(n+1) / 2
When: When n unit squares are placed in a single row
Worked examples
Triangle divided into 3 rows: 3 x 5 x 7 / 8 = 105/8 = 13 triangles (nearest whole number using this formula gives 13).
4 squares in a row: rectangles = 4 x 5 / 2 = 10 rectangles total.
⚠ Common mistakes to avoid
- Confusing mirror image with water image — mirror is left-right flip, water is up-down flip. Remember: Mirror = M for Matching left-right sides.
- In paper folding, forgetting that 2 folds give 4 holes not 2 — candidates only trace one fold and miss the second symmetry.
- In figure series, assuming rotation is always clockwise — always check anticlockwise too before choosing answer.
- In counting figures, counting the same combination twice — always label each unit with a letter and list combinations systematically.
- Spending too long on embedded figures — if you cannot spot it in 30 seconds, mark and move on. These are time traps in the exam.
🧠 Memory aids
- MIRROR = M stands for Match Left-Right (horizontal flip). WATER = W stands for Wave going Up-Down (vertical flip).
- For paper folding holes: Folds make holes multiply. 1 fold = 2 holes, 2 folds = 4 holes, 3 folds = 8 holes. Think of it as doubling each time you fold.
- Figure Series rule-check order: RSSEN — Rotation, Size, Shading, Elements, Number. Check each one in this order so you miss nothing.
- For mirror clock: Think of 12 as a wall. The mirror pushes the time to the other side of 12. Formula 11:60 minus given time does this mathematically.
🎯 AGNIVEER ARMY exam tips
- Agniveer Army CEE typically has 4 to 8 non-verbal questions. Mirror images and figure series are the most repeated — master these two first.
- Mirror image of clock and letters/numbers appears almost every year. Practice 10 clocks daily for 3 days and you will never miss these.
- Paper folding questions have increased in recent years — expect 1 to 2 questions. They look scary but are solved fast once you learn the symmetry trick.
- Non-verbal questions should take you 30 to 45 seconds each at most. If you are spending more than 1 minute on any one figure, skip and return.
- Embedded figures and counting triangles are lower frequency but higher difficulty — attempt them last within the reasoning section to protect your score.
Q1 · hard · AI-verified
A cube is painted red on all faces and then cut into 27 smaller cubes of equal size. How many small cubes will have exactly two faces painted?
- 24
- 8
- 12
- 6
Q2 · hard · AI-verified
A cube is painted red on all faces and then cut into 64 smaller cubes of equal size. How many small cubes will have exactly two faces painted?
- 28
- 20
- 16
- 24
Q3 · hard · AI-verified
In a certain code, if △ means +, □ means -, ○ means ×, and ◇ means ÷, then what is the value of: 15 ○ 3 △ 8 ◇ 2 □ 6?
- 41
- 39
- 45
- 43
Q4 · hard · AI-verified
In a sequence of figures showing a clock, if the hour hand moves 3 hours forward and minute hand moves 15 minutes backward each step, and it starts at 12:00, what time is shown after 4 steps?
- 11:00
- 12:00
- 1:00
- 11:45
Q5 · hard · AI-verified
In a 4×4 grid, if you start from top-left corner and can only move right or down, visiting each cell exactly once, and must end at bottom-right corner, how many different paths are possible?
- 16
- 20
- 24
- 28