JEE B.Arch flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Orthographic projection views

Front view gives length and height, top view gives length and depth, side view gives depth and height. Missing lines are found by projecting each edge into the other two views.

Painted cube corner count

A cuboid painted on all faces and cut into unit cubes always has exactly 8 cubes with three painted faces, since only the eight corners touch three faces.

Vertical mirror image rule

A vertical mirror swaps left and right while keeping top and bottom unchanged. Letters symmetric about a vertical axis, such as A, H, I, M, O, T, U, V, W, X, Y, look the same.

Water image reversal

A horizontal or water mirror reverses up and down but preserves left and right. Letters with horizontal symmetry, such as B, C, D, E, H, I, K, O, X, stay unchanged.

Cube net opposite faces

In a cube net, two squares separated by exactly one square in a straight strip become opposite faces when folded, so they can never be adjacent on the cube.

Chandigarh Capitol Complex

Designed by Le Corbusier in Chandigarh, it includes the Secretariat, Legislative Assembly, and High Court, and is a UNESCO World Heritage site noted for exposed concrete and the Open Hand monument.

Jawahar Kala Kendra architect

Charles Correa designed the Jawahar Kala Kendra in Jaipur, planning it on a nine-square navagraha grid that echoes the original nine-square plan of the city.

Lotus Temple designer

The Lotus Temple in New Delhi, a Bahá'í House of Worship completed in 1986, was designed by Iranian-born architect Fariborz Sahba as 27 marble-clad petals in nine groups.

Opposite letters in alphabet

Letters whose positions sum to 27 are opposite pairs: A–Z, B–Y, C–X, D–W, up to M–N. This is used in coding, analogy, and letter-series questions.

Quadratic discriminant meaning

For ax²+bx+c=0 with D=b²−4ac: D>0 gives two distinct real roots, D=0 gives equal real roots, and D<0 gives a conjugate complex pair.

Parabola focus and directrix

For y²=4ax the focus is (a,0) and the directrix is x=−a. Every point on the parabola is equidistant from the focus and the directrix.

Ellipse eccentricity formula

For x²/a²+y²/b²=1 with a>b, eccentricity e=√(1−b²/a²), which lies between 0 and 1. A circle is the limiting case with e=0.

Hyperbola eccentricity

For x²/a²−y²/b²=1, eccentricity e=√(1+b²/a²), always greater than 1. Its asymptotes are the lines y=±(b/a)x.

Point-to-line distance

The perpendicular distance from point (x₁,y₁) to line ax+by+c=0 equals |ax₁+by₁+c| divided by √(a²+b²), with the line in general form.

Angle between two lines

For slopes m₁ and m₂, tanθ=|(m₁−m₂)/(1+m₁m₂)|. Lines are perpendicular when m₁m₂=−1 and parallel when m₁=m₂.

Standard limit sin x over x

As x approaches 0, sin x divided by x tends to 1. This underlies derivatives of trigonometric functions and many JEE limit problems.

L'Hôpital applicability condition

L'Hôpital's rule may be applied only to indeterminate forms 0/0 or ∞/∞. Forms like 0·∞ or ∞−∞ must first be rewritten into a ratio before differentiating.

Derivative of tan x

The derivative of tan x is sec²x, equivalently 1+tan²x. The derivative of cot x is −cosec²x, and of sec x is sec x tan x.

Definite integral symmetry rule

∫₀^a f(x)dx equals ∫₀^a f(a−x)dx. This identity converts many awkward definite integrals into simpler equivalent forms before evaluation.

Dot and cross product

a·b=|a||b|cosθ is a scalar; a×b has magnitude |a||b|sinθ and is perpendicular to both vectors. Dot product zero means perpendicular vectors.

Scalar triple product meaning

a·(b×c) equals the volume of the parallelepiped with edges a, b, c. It equals zero exactly when the three vectors are coplanar.

Conditional probability formula

P(A|B) equals P(A∩B)/P(B) for P(B)>0. Rearranged, it gives the multiplication rule P(A∩B)=P(B)·P(A|B) for dependent events.

Inverse matrix existence

A square matrix has an inverse A⁻¹=adj(A)/det(A) only when det(A)≠0. A zero determinant makes the matrix singular and non-invertible.

Determinant product rule

For square matrices of the same order, det(AB)=det(A)·det(B). Consequently det(A⁻¹)=1/det(A) and det(kA)=kⁿdet(A) for order n.

Human figure head-height rule

An average adult stands about 7.5 head-heights tall. This proportion keeps figures in architectural sketches believable against doors and furniture.

Standard architectural dimensions

Typical values used in sketches: door height about 2.1 m, ceiling about 3.0 m, eye level about 1.6 m, chair seat about 0.45 m, stair riser about 0.15 m.

One-point perspective rule

In one-point perspective, all edges receding into depth converge at a single vanishing point on the horizon, while front-facing surfaces keep their true shape.

Two-point perspective rule

Two-point perspective uses two vanishing points on the horizon line, one for each receding direction. Vertical edges stay vertical and parallel to each other.

Isometric drawing axes

Isometric drawings use three axes spaced 120° apart, with true lengths measured along each axis. Circles appear as ellipses, and no vanishing points are used.

Rule of thirds composition

Divide the frame into a 3×3 grid and place the focal mass near a grid intersection rather than at centre, leaving breathing space around the subject.

Line weight hierarchy

Outlines are heaviest, visible edges medium, hidden edges dashed, and construction or centre lines lightest. Consistent weights make a freehand drawing read clearly.

Light and shade terms

A rendered form shows highlight, mid-tone, core shadow, and reflected light, with one fixed light source. Hatch lines follow the surface direction to describe curvature.