JEE B.Arch key terms

The natural or trained ability to perceive, reason about, and mentally manipulate spatial forms, patterns, and structures. B.Arch. admission tests measure it through diagrams, folding, and pattern-completion items rather than factual recall.

The capacity to understand and reason about objects in two and three dimensions, including their positions, orientations, and relationships. It underpins tasks such as identifying which 3D solid a flat net will produce.

Imagining how a shape looks after being turned in space, without physically moving it. Candidates compare a target figure with rotated versions and reject mirrored or distorted copies.

A reasoning task where a sheet is folded one or more times, punched or cut, then unfolded. You must deduce the pattern of holes or cuts from the symmetry of the folds.

A flat, unfolded pattern that can be creased and joined to form a 3D solid. Questions ask which net folds into a given cube, prism, or pyramid, or which faces end up adjacent.

A method of representing a 3D object by separate flat views, usually front, top, and side, with parallel lines of sight. Each view shows true shape but only two dimensions of the object.

An orthographic view of an object seen from the front or side, showing height and width but not depth. Elevations are paired with plans to fully describe a building or block form.

The view of an object or building seen from directly above, showing layout, width, and depth. In architectural drawing, the plan is the primary drawing from which other views are derived.

A pictorial drawing in which the three axes are equally inclined at 120 degrees, so vertical edges stay vertical and horizontal edges slope at 30 degrees. It shows three faces of an object at once without perspective convergence.

A family of parallel projections, including isometric, dimetric, and trimetric, that shows a 3D object without vanishing points. Parallel edges stay parallel, so true lengths can be scaled along the axes.

The point on the horizon where parallel lines receding from the viewer appear to converge in a perspective drawing. One-point and two-point perspective each use a different number of these points.

A drawing that mimics how the eye sees space, with distant objects appearing smaller and parallel lines meeting at vanishing points. It conveys depth more naturally than orthographic or isometric views.

The horizontal line in a perspective drawing that represents the viewer's eye level. Its height relative to objects determines whether they are seen from above, at eye level, or from below.

A line that divides a figure into two halves that are mirror images of each other. Counting and locating these lines is a common shortcut in folding, pattern, and figure-completion problems.

A property of a figure that looks unchanged after being rotated by less than a full turn about a centre. The order of symmetry equals the number of distinct positions that match the original.

The reversed reflection of a figure across a line, where left and right are swapped but distances from the mirror line are preserved. Candidates must distinguish a true reflection from a mere rotation.

A simple shape hidden inside a more complex drawing, which you must locate or count. These items test visual scanning and the ability to separate a target outline from distracting lines.

A task where a partly drawn figure or pattern must be finished by choosing the option that continues it correctly. Success depends on detecting the underlying rule of the pattern.

Identifying the rule that governs a sequence or arrangement of shapes, colours, or numbers so the next element can be predicted. Rules may involve rotation, alternation, counting, or progressive addition.

A reasoning item in which a sequence of figures or numbers follows a hidden rule and the missing or next term must be supplied. The rule is often a repeated transformation applied step by step.

A relationship item of the form A is to B as C is to D, where the link may be functional, causal, or categorical. In aptitude tests it checks relational reasoning with words rather than figures.

A classification task in which all but one item share a common property, and the exception must be identified. The shared property may concern shape, symmetry, number of sides, or meaning.

Problems involving folded cubes or dice where opposite and adjacent faces must be deduced from given views. The key rule is that faces separated by one face in a net end up opposite each other.

The proportion approximately 1.618, written as phi, where a line is divided so the whole is to the longer part as the longer part is to the shorter. It appears in classical proportion systems and design theory.

The relationship between the size of drawn elements and their real size, and the harmonious size relationships among parts of a design. Questions test reading scales and judging balanced proportions.

A single number computed from a square matrix that indicates whether the matrix is invertible and gives the scaling factor of the associated linear transformation. A zero determinant means the matrix has no inverse.

A rectangular array of numbers arranged in rows and columns, used to represent linear transformations and systems of equations. Matrix multiplication is defined only when the column count of the first equals the row count of the second.

A matrix that, when multiplied by the original square matrix, yields the identity matrix. It exists only when the determinant is non-zero and is computed using the adjugate divided by the determinant.

The value a function approaches as its input approaches a given point, regardless of whether the function is defined there. Limits are the foundation for defining continuity and the derivative.

A property of a function that has no breaks, jumps, or holes at a point, meaning the limit there equals the function's value. Checking continuity requires comparing one-sided limits with the function value.

The instantaneous rate at which a function changes with respect to its variable, equal to the limit of the difference quotient. Geometrically it gives the slope of the tangent to the curve.

The property that a function has a well-defined derivative at a point, implying it is smooth there. Differentiability at a point implies continuity there, but continuity does not guarantee differentiability.

A straight line that touches a curve at a point and has the same slope as the curve there. Its slope equals the derivative of the function at that point.

The line perpendicular to the tangent at a point on a curve. Its slope is the negative reciprocal of the derivative at that point.

The limit of a sum of areas of thin rectangles under a curve between two bounds, interpreted as signed area. It is evaluated using the fundamental theorem of calculus with an antiderivative.

The region between a function's graph and the horizontal axis over an interval, computed by definite integration. Regions below the axis contribute negative signed area.

A number between zero and one expressing how likely an event is, calculated as favourable outcomes divided by total equally likely outcomes in simple cases. Conditional probability updates this value given extra information.

Counting methods for arrangements where order matters (permutations) and selections where order does not (combinations). Their formulas use factorials and underpin many probability calculations.

The probability of an event given that another event has already occurred, written as P(A|B) and equal to P(A and B) divided by P(B). It underlies Bayes' theorem and tree-diagram problems.

A rule that reverses a conditional probability, updating the probability of a cause given observed evidence. It combines prior probabilities with likelihoods to produce posterior probabilities.

A curve obtained by cutting a cone with a plane: circle, ellipse, parabola, or hyperbola. Each has a standard equation and characteristic eccentricity that determine its shape.

A number describing how much a conic section deviates from a circle, equal to the distance from a point to the focus divided by its distance to the directrix. Circles have zero, ellipses less than one, parabolas exactly one, hyperbolas more than one.

The set of all points satisfying a given geometric condition, such as all points equidistant from two fixed points. Deriving a locus equation is a standard coordinate-geometry skill.

A quantity with both magnitude and direction, represented by an arrow or an ordered triple of components. Vectors support addition, scalar multiplication, dot products, and cross products.

A scalar obtained by multiplying corresponding components of two vectors and summing them, equal to the product of magnitudes times the cosine of the angle between them. It is zero for perpendicular vectors.

A vector perpendicular to two given vectors, with magnitude equal to the product of their magnitudes times the sine of the angle between them. It gives the area of the parallelogram they span.

The straight, unobstructed path between a viewer's eye and an object, used in perspective construction and in drawing what is actually visible. Hidden edges are omitted or dashed when the line of sight is blocked.

A light preliminary guideline drawn to establish proportions, axes, or vanishing points before final lines are made. These lines are usually kept faint or erased in a finished drawing.

The relative thickness of lines in a drawing, used to show depth, importance, and separation of elements. Foreground and outline edges are drawn heavier than construction or hidden lines.

A shading technique using closely spaced parallel lines to suggest tone, shadow, or material. Varying line spacing and direction creates the illusion of depth and curvature.

The process of adding shading, texture, colour, or light effects to a drawing so it reads as a believable three-dimensional scene. It communicates materials and mood as well as form.

The arrangement of elements within a drawing's frame, balancing visual weight, focus, and negative space. A strong composition guides the viewer's eye and gives the image coherence.

A freehand or scaled drawing showing the external face of a building or object, including openings and surface details. It is judged on proportion, alignment, and clarity of features.