Defense Reasoning - Non-Verbal & Visuals

Figure Series and Pattern Completion

Figure series are the backbone of non-verbal reasoning: a row of boxes changes by a rule and you must supply the next box. Almost every other question type in this book — analogies, matrices, odd-one-out — reuses the same idea of a rule acting on a figure, so the vocabulary built here (six attributes, clockwise degrees, numbered border positions) carries through the rest of the book. The chapter opens by locating figure reasoning in the defence entrance papers from their official notices, then works through rotation, movement, counting and compound rules, and ends with completing symmetric designs.

KarmSakha preparation topics covered

• Where figure (non-verbal) reasoning appears in AFCAT, Agniveervayu, SSC Constable (GD) and Territorial Army papers, read from the official notices
• The six attributes of a figure element: element, count, position, orientation, shading, size
• Rotation rules: constant, growing and alternating turns, measured clockwise in degrees
• Movement rules on the eight-position border, including two elements moving in opposite directions
• Counting, adding and cyclic (period-two and period-three) rules
• Compound rules, the four-step routine and option elimination
• Pattern completion using mirror, rotational and diagonal symmetry

Where figure reasoning appears in defence entrance tests

Non-verbal reasoning is the part of a reasoning paper in which the question is a picture rather than a sentence: a row of figures that changes by a rule, a figure and its mirror image, a sheet of paper folded and punched, a die seen from two sides. The skill tested is the same across exams — noticing exactly what changes between figures and carrying that change forward — but the weight it carries differs sharply from one defence entrance to the next, so it is worth reading your own notification before deciding how much time this book deserves in your plan.

The Indian Air Force's AFCAT is the clearest case. The AFCAT 01/2026 notification lists four subject areas in one two-hour online paper of 100 questions carrying 300 marks, with three marks for a correct answer and one mark deducted for a wrong one, and it describes the Reasoning and Military Aptitude Test component in four words: verbal and non-verbal reasoning. The later AFCAT 02/2026 notification repeats the same pattern and wording. The same notification says that testing at the Air Force Selection Board begins with Stage-I, an Officer Intelligence Rating test along with a picture perception and discussion test, and that Stage-I is a screening test. The notification does not publish the item types of the Officer Intelligence Rating test, so this book does not claim to reproduce it; it trains the figure skills that intelligence-rating tests of this kind commonly draw on.

For Airmen, the syllabus sheet for the Agniveervayu Reasoning and General Awareness (RAGA) paper, published on the CASB portal in 2022, lists sixteen reasoning topics under the heading Reasoning (Verbal and Non-Verbal), and item 14 of that list is non-verbal reasoning. The model paper released with it includes a figure odd-one-out question built from four drawings and five figure-series questions in which you choose the answer figure that completes a series. Check the CASB portal for the sheet that applies to your own intake. For the Central Armed Police Forces constable route, the Staff Selection Commission's notice for Constable (GD) 2026 goes furthest: Part A, General Intelligence and Reasoning, has 20 of the paper's 80 questions, and the notice says analytical aptitude will be tested through questions principally of non-verbal type, naming analogies, similarities and differences, spatial visualisation, spatial orientation, visual memory, discrimination, figural classification and non-verbal series.

The Territorial Army Commission 2026 notice sets a 40-question reasoning part (Part 1, 40 of the paper's 100 questions) and describes it as testing the ability to complete sequences and draw logical conclusions from simple patterns of numbers, statements, figures and letters, with one-third of a question's marks deducted for a wrong answer. The Indian Army's syllabus sheet for Agniveer General Duty (10th) lists five Logical Reasoning questions in a 50-question paper without breaking them into verbal and non-verbal types, so treat this book as one part of that preparation rather than the whole of it. Pattern figures such as question counts and penalties are quoted here from the named notifications only to show where the topic sits; they change between cycles, and the live notification for your own cycle always governs.

The six things that can change in a figure

Every figure question in this book, however complicated it looks, is built from a small number of elements — an arrow, a dot, a triangle, a line, a flag-like motif — and each element carries a handful of attributes. When a series moves from one box to the next, one or more of these attributes changes by a fixed rule. The single most useful habit you can build is to stop looking at the figure as a whole and start reading it as a list: which elements are present, and for each element, what are its six attributes right now.

The six attributes are: the element itself (is it still a triangle, or has it become a square); the count (how many dots, lines or sides); the position (where in the box the element sits); the orientation (which way it points, measured as a turn from pointing up); the shading (black, white, or occasionally hatched); and the size. A rule may change one attribute or several, and different elements in the same box may follow different rules. What never happens in a well-set question is a change with no rule at all, so if you find an attribute that changes erratically, you have almost certainly mis-read the figure or paired the wrong elements across boxes.

Direction and turning need a fixed vocabulary, because an ambiguous word such as 'rotates' hides the two facts you actually need: how far and which way. In this book every turn is measured as it appears on the page. Clockwise means the direction the hands of a wall clock move; a quarter turn is 90 degrees, a half turn 180, and an eighth of a turn 45 degrees. An arrow that points up and then points right has turned 90 degrees clockwise; the same final position could also be reached by turning 270 degrees anticlockwise, and a question may deliberately describe the move either way. Always convert both descriptions to clockwise degrees before comparing them.

Position needs the same discipline. For elements that move around the edge of a box, number the eight border positions clockwise from the top-left corner: top-left corner, top edge centre, top-right corner, right edge centre, bottom-right corner, bottom edge centre, bottom-left corner and left edge centre. Moving 'one step' then means moving to the next number, and moving 'corner to corner' means jumping two numbers. With that numbering, a dot's journey through a series becomes a sequence such as 1, 2, 3, 4, which you can extend without looking at the pictures again.

Rotation rules: constant, growing and alternating turns

Rotation is the most common rule in figure series, and it comes in three flavours. In a constant rotation the element turns by the same angle every step — 45 degrees clockwise each time, say — so after four steps an arrow that started pointing up points down. In a growing rotation the angle itself increases, typically 45, then 90, then 135 degrees, so the element seems to speed up. In an alternating rotation the direction flips, for example 90 degrees clockwise, then 45 degrees anticlockwise, then 90 clockwise again, which makes the element drift slowly round rather than march.

To identify the flavour, write down the orientation of the element in each box as an angle from pointing up: 0 for up, 90 for right, 180 for down and 270 for left, with the diagonals at 45, 135, 225 and 315. Then take differences between neighbours, always counting clockwise and always reducing to the range 0 to 359. A list of differences such as 45, 45, 45, 45 is a constant rule; 45, 90, 135, 180 is a growing rule; 90, 315, 90, 315 is an alternating rule, because 315 degrees clockwise is the same as 45 degrees anticlockwise. The next difference in the list gives you the next orientation directly.

Rotation has a trap that catches careful candidates too. A figure with rotational symmetry looks the same after certain turns — a square after 90 degrees, an equilateral triangle after 120 degrees, a circle after any turn at all — so the rotation of such an element cannot be seen, and a question setter will only use it to rotate something asymmetric. When you track rotation, track an asymmetric feature: the tip of an arrow, the cloth of a flag, the open end of a hook, or the one black dot attached to a shape. If the only thing in a box is a square, its rotation is not the rule; look at count, position or shading instead.

A second trap is confusing rotation with reflection. Turning a flag that points up with its cloth on the right through 180 degrees gives a flag pointing down with its cloth on the left. Reflecting the same flag in a horizontal line gives a flag pointing down with its cloth still on the right. The two results look similar at a glance and are placed side by side in the options precisely because of that. The test is handedness: rotation never changes which side the cloth is on relative to the direction the pole points, while a single reflection always does. Chapter 7 develops this test in detail; for series questions it is enough to check the side of the cloth or hook in the final option.

Movement rules: stepping round the border

When an element changes position rather than orientation, it almost always moves along a track, and in a square box the track is nearly always the border. Using the clockwise numbering from position 1 at the top-left corner to position 8 at the left edge centre, a movement rule is simply a step size and a direction. A dot moving 'one step clockwise' goes 1, 2, 3, 4; a dot moving 'two steps clockwise' visits only corners, 1, 3, 5, 7; a dot moving one step anticlockwise goes 1, 8, 7, 6. Because there are eight positions, a step of three clockwise is the same as five anticlockwise, and the arithmetic wraps round after 8.

The border numbering also handles several elements at once, which is where movement questions become difficult. A harder item might have a black dot moving one step clockwise and a white dot moving two steps anticlockwise in the same boxes. Taken together the picture looks chaotic; taken one dot at a time each is trivial. Write two short lists — black: 1, 2, 3, 4; white: 6, 4, 2, 8 — extend each list by one, and only then look for the option that has the black dot at position 5 and the white dot at position 6. Solved example 7 works through exactly this item.

Some movement questions use corners only (a track of four positions) or the centre and the four edge midpoints. The method does not change: number the track, find the step, extend. What does change is how you count 'one step', so settle the track first by listing every position the element occupies in the given boxes. If it only ever sits on corners, the track has four positions and a jump from top-left to bottom-right is two steps, not four.

Movement can combine with rotation inside the same element: a flag that walks round the border while also turning. Separate the two. Its position follows the border list and its orientation follows the angle list, and each list has its own rule. Many candidates try to find one rule that explains both at once — for instance, 'the flag always points towards the centre' — and that sometimes works, but the two-list method always works, and it is faster to apply under time pressure because each list needs only one subtraction.

Counting, adding and alternating rules