JEE Main Paper 2B - B.Planning key terms

A rectangular arrangement of numbers or expressions in rows and columns, written inside brackets. Matrices can be added, multiplied or inverted under set rules and are used to solve systems of linear equations.

A single number computed from the entries of a square matrix. It tells whether the matrix has an inverse and is used in solving linear equations, finding areas and checking consistency of systems.

An ordered arrangement of a fixed set of objects in which the sequence matters. The number of permutations of n distinct objects taken r at a time is written nPr and equals n! divided by (n−r)!.

A selection of objects from a group in which order does not matter. The number of ways to choose r items from n distinct items is written nCr and equals n! divided by r!(n−r)!.

A sequence in which each term after the first is obtained by adding a fixed constant called the common difference. Its nth term is a+(n−1)d and the sum of n terms follows a standard formula.

A sequence in which each term after the first is found by multiplying the previous term by a fixed non-zero number called the common ratio. Terms grow or shrink geometrically and the sum formula depends on the ratio.

A formula that expands a power of a two-term expression, (a+b)^n, as a sum of terms involving binomial coefficients. It gives each coefficient as nCr and applies for positive integer n.

The value that a function's output approaches as its input approaches a chosen point, even if the function is not defined at that point. Limits underpin continuity and are the base for defining derivatives.

The instantaneous rate at which a function changes with respect to its variable. Geometrically it gives the slope of the tangent line, and it is obtained as the limit of a difference quotient.

The signed area between a curve and the horizontal axis over a stated interval, computed as a limit of sums. It is evaluated using antiderivatives and yields totals such as distance or accumulated quantity.

A measure of how spread out a set of observations is around its mean. It is the square root of the average squared deviation, so a larger value means greater variability.

The probability that an event occurs given that another event has already happened. It equals the probability of both events divided by the probability of the given event, provided that is not zero.

An operation on two vectors producing a single number equal to the product of their magnitudes and the cosine of the angle between them. It tests perpendicularity and gives projections.

A ratio compares two quantities of the same kind by division, while a proportion states that two ratios are equal. These ideas are used to scale quantities and solve sharing and mixing problems.

A way of expressing a number as a fraction of one hundred. It is used to compare quantities of different sizes and to compute increases, decreases, discounts and marks.

The sum of a set of values divided by the number of values, also called the arithmetic mean. It gives a single representative value and is the starting point for studying spread.

A class of problems about how long people or machines take to finish a task when working alone or together. Work rates are added and the total job is usually taken as one unit.

Commercial arithmetic dealing with the gain or loss made when an item is sold, measured against its cost price. Results are usually expressed as a percentage of the cost price.

Interest calculated only on the original principal for the whole period, without adding earlier interest to it. The formula is principal multiplied by rate multiplied by time, divided by one hundred.

Interest calculated on the principal plus any interest already added, so the amount grows faster than with simple interest. It may be compounded yearly, half-yearly or quarterly.

A sequence of numbers following a hidden rule, in which the candidate must find the missing or next term. Rules may involve differences, ratios, squares, primes or alternating patterns.

The skill of reading tables, bar charts, line graphs and pie charts, then calculating totals, averages, percentages and comparisons from them. Answers must rest only on the data shown.

A reasoning task in which a person moves through a series of turns and the solver must determine the final position or facing direction. A rough compass diagram usually makes it simple.

The process of deciding how land, buildings, transport and services in a town or city should be arranged and used, now and in the future, balancing growth with livability.

A long-range statutory document that sets out a city's broad goals for land use, transport, housing and infrastructure, usually with a horizon of twenty years or more.

The purpose for which a parcel of land is put to work or reserved, such as residential, commercial, industrial, agricultural or recreational. Planning maps assign categories to guide where development may occur.

The division of a city into districts where rules specify which activities are permitted and what building size is allowed. Zoning separates incompatible uses and gives developers predictable rules.

The total floor area of all storeys in a building divided by the area of the plot on which it stands. Higher values permit taller or denser construction and are capped by local regulations.

The minimum distance that a building must be kept from the plot boundary, road or neighbouring structure. Setbacks protect light, air, privacy and safety and are fixed in local rules.

Local rules that control the design and construction of buildings, covering setbacks, heights, floor area, staircases, ventilation and fire safety. Approval for new construction depends on complying with them.

The outward, often low-density spread of a city into surrounding farmland and open land. It increases travel distances and the cost of providing roads, water and sewerage.

A continuous built-up area formed by a central city together with its adjoining towns and outgrowths, treated as one unit for planning and census purposes. People live and work across its boundaries.

A planning approach that concentrates housing, shops and offices within easy walking distance of a public transport station. It aims to reduce car dependence and make better use of existing transport.

Development that satisfies present needs without preventing future generations from meeting theirs. It balances economic growth, social equity and environmental protection over the long term.

Computer software for storing, mapping and analysing information that has a location on the earth. Planners use it to overlay maps of land use, roads and services and to test site options.

A formal study done before a major project that predicts how it will affect air, water, soil, ecology and nearby communities, and lists steps to reduce harm. Clearance may depend on it.

The area at the core of a city where shops, offices, banks and other commercial activities cluster most densely. It usually has the highest land values and the heaviest daytime footfall.

The maximum population or level of activity that an area can support without lasting damage to its land, water, air and services. Planners compare it with projected growth to judge sustainability.