Bihar Polytechnic key terms

The shortest straight-line distance from an object's starting point to its final position, together with the direction. It is a vector quantity measured in metres and can be zero even when distance travelled is not.

The rate of change of displacement with respect to time. Because displacement has direction, velocity is a vector; average velocity divides total displacement by total time, while instantaneous velocity is its value at one moment.

The rate at which velocity changes with time, measured in metres per second squared. It occurs whenever speed changes, direction changes, or both change, and it is a vector pointing along the change in velocity.

The net force on a body equals the rate of change of its momentum, which for constant mass reduces to force equals mass times acceleration. It links cause (force) to effect (acceleration) in mechanics.

The product of a body's mass and its velocity, a vector quantity measured in kilogram metres per second. In an isolated system the total momentum stays constant during collisions, which is the law of conservation of momentum.

The product of a force and the time for which it acts, equal to the change in momentum it produces. Extending the time of impact reduces the force, which is why airbags and cushions soften collisions.

The statement that the net work done on a body by all forces equals the change in its kinetic energy. It allows problems to be solved by tracking energy rather than forces and accelerations at every point.

The energy a body possesses because of its motion, equal to one half of mass times the square of speed. It is a scalar measured in joules and is always zero for a body at rest.

The principle that when only conservative forces such as gravity or spring force act, the sum of kinetic and potential energy remains constant. Energy may shift between the two forms but the total does not change.

A scalar is a quantity with magnitude only, such as mass, time, or temperature. A vector has both magnitude and direction, such as force or velocity, and vectors are added by the triangle or parallelogram rule.

For a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it, so voltage equals current times resistance. Devices that do not obey this relation are called non-ohmic.

The opposition a material offers to the flow of electric current, measured in ohms. For a uniform wire it increases with length, decreases with cross-sectional area, and depends on the material's resistivity and temperature.

The rate at which electrical energy is transferred or dissipated in a circuit, measured in watts. It equals voltage times current, and for a resistor also equals current squared times resistance or voltage squared divided by resistance.

In a series circuit components are joined end to end, share one current, and their resistances add. In a parallel circuit they share the same voltage and the reciprocals of their resistances add.

The bending of light as it passes from one transparent medium into another because its speed changes. Light bends towards the normal when entering a denser medium and away from it when leaving.

The ratio of the speed of light in vacuum to its speed in a given medium, a dimensionless number greater than one for ordinary materials. It determines how strongly a ray bends at a boundary and controls critical angle.

The complete reflection of light back into a denser medium when it strikes the boundary at an angle greater than the critical angle. It is the principle behind optical fibres and the sparkle of diamonds.

The amount of substance containing exactly 6.022 times ten to the power twenty-three elementary entities, such as atoms or molecules. This number is the Avogadro constant and links particle counts to measurable masses.

The mass of one mole of a substance in grams per mole, numerically equal to its formula mass in atomic mass units. It converts between moles and grams in stoichiometric calculations.

The quantitative study of the amounts of reactants and products in a balanced chemical equation. Mole ratios from the coefficients allow prediction of the mass or volume of any substance involved.

The simplest whole-number ratio of the atoms of each element present in a compound. It is found from percentage composition, while the molecular formula is a whole-number multiple of it.

Oxidation is loss of electrons and reduction is gain of electrons; the two always occur together. A useful memory aid is OIL RIG, and the oxidising agent itself is reduced while the reducing agent is oxidised.

The formal charge an atom would carry if the electrons in each bond were assigned entirely to the more electronegative atom. Tracking its change reveals which species is oxidised and which is reduced.

The potential developed when an element is in contact with a solution of its own ions, measured relative to the standard hydrogen electrode. A more positive value indicates a greater tendency to be reduced.

A logarithmic measure of the hydrogen ion concentration in a solution, defined as the negative logarithm to base ten of that concentration. Values below seven are acidic, seven is neutral, and above seven is basic.

An acid donates a proton and a base accepts one, according to the Bronsted-Lowry view; Lewis theory instead treats them as electron-pair acceptors and donors. Acids turn litmus red and react with bases to form salt and water.

A solution that resists a change in pH when small amounts of acid or base are added, usually containing a weak acid with its conjugate base or a weak base with its conjugate acid. Blood is a natural example.

The mixing of atomic orbitals of similar energy to form new equivalent orbitals that give the observed molecular geometry. Common types are sp linear, sp2 trigonal planar, and sp3 tetrahedral.

The existence of compounds with the same molecular formula but different structures or arrangements. Structural isomers differ in connectivity, while stereoisomers differ only in the spatial arrangement of atoms.

A chemical bond formed by the sharing of one or more pairs of electrons between atoms, usually non-metals. The shared pair is attracted to both nuclei, which holds the atoms together.

A single number computed from a square array of numbers that indicates whether the corresponding matrix is invertible and gives the scale factor of the associated linear transformation. A zero value means the matrix has no inverse.

A rectangular arrangement of numbers in rows and columns, used to represent linear transformations and to solve systems of linear equations. Matrices are added element-wise and multiplied by the row-column rule.

A square matrix that, when multiplied by the original, gives the identity matrix. It exists only when the determinant is non-zero and is found from the adjoint divided by the determinant.

The instantaneous rate of change of a function with respect to its variable, defined as the limit of the difference quotient. Geometrically it is the slope of the tangent to the curve at a point.

The reverse process of differentiation, used to find a function whose derivative is known or to compute the area under a curve between two limits. The definite integral is evaluated using the fundamental theorem of calculus.

Points where a function reaches a local highest or lowest value, found by setting the first derivative to zero. The second derivative test then shows whether each such point is a maximum or a minimum.

A sequence in which each term after the first is obtained by adding a fixed constant called the common difference. The nth term is a plus n minus one times d, and the sum has a standard formula.

A sequence in which each term after the first is obtained by multiplying by a fixed constant called the common ratio. The nth term is a times r to the power n minus one, and the sum formula depends on whether r equals one.

A permutation counts arrangements where order matters, while a combination counts selections where order does not. Their formulas use factorials, and the number of combinations is always at most the corresponding permutations.

A number between zero and one expressing how likely an event is, calculated for equally likely outcomes as favourable outcomes divided by total outcomes. The probabilities of all mutually exclusive outcomes sum to one.

Basic freedoms guaranteed to citizens by Part Three of the Indian Constitution, including equality, freedom of speech, and protection from exploitation. They are enforceable in courts through writ petitions.

Guidelines in Part Four of the Indian Constitution that direct the state towards social and economic welfare, such as fair wages and public health. They are not enforceable in courts but are fundamental to governance.

The opening statement of the Indian Constitution declaring the source of its authority and the ideals of justice, liberty, equality, and fraternity. It is used as an aid in interpreting the Constitution.

The system of local self-government in rural India established by the 73rd Constitutional Amendment, with three tiers at village, block, and district level. Its aim is to bring decision-making closer to citizens.