Assam CEE key terms

An expression showing how a physical quantity is built from the base dimensions mass, length, time, electric current, temperature, amount of substance and luminous intensity. Used to check equation consistency and convert units between systems.

Motion of an object launched into the air that then moves only under gravity, with constant horizontal velocity and constant vertical acceleration. Its path is a parabola when air resistance is neglected.

The velocity of one body measured from a frame attached to another moving body, found by vector subtraction of the two velocities. Central to river-boat and rain-man problems.

A dimensionless ratio between the limiting or kinetic friction force and the normal reaction between two surfaces in contact. It depends on the nature of the surfaces, not on the area of contact.

The net inward force that keeps a body moving on a circular path, directed toward the centre and equal to mass times speed squared divided by radius. It changes direction of velocity, not speed.

A measure of rotational motion equal to the cross product of position vector and linear momentum, or moment of inertia times angular velocity. It stays constant when no external torque acts.

A body's resistance to change in its rotational motion, equal to the sum of mass times squared distance from the axis for all particles. Its value depends on the chosen axis.

The minimum speed an object needs at a planet's surface to move away and never return, ignoring air resistance. It equals the square root of twice gravitational parameter divided by radius.

The speed required for a satellite to stay in a stable circular orbit at a given radius, equal to the square root of gravitational parameter divided by that radius. It falls as orbital radius increases.

Oscillation in which restoring acceleration is directly proportional to displacement from equilibrium and directed opposite to it. Its displacement follows a sinusoidal function of time with fixed angular frequency.

A large-amplitude response that occurs when a driving frequency approaches a system's natural frequency, provided damping is small. It explains tuning circuits and some mechanical failures.

The quantity of heat absorbed or released per unit mass when a substance changes phase at constant temperature, such as melting or boiling. It does not raise the temperature during the change.

A statement of energy conservation for thermal processes: heat supplied to a system equals the increase in internal energy plus work done by the system. It fixes the sign conventions used in problems.

A change in a gas carried out at constant temperature, so internal energy stays fixed for an ideal gas and all heat supplied becomes work done. The pressure-volume curve is a hyperbola.

A change in which no heat crosses the system boundary, so work done comes at the expense of internal energy. For an ideal gas, pressure times volume raised to gamma stays constant.

The apparent change in observed frequency of a wave when source and observer move relative to each other, rising on approach and falling on separation. It applies to sound and to light.

Periodic variation in loudness heard when two sound waves of slightly different frequencies superpose, with beat frequency equal to the difference of the two frequencies.

Complete return of light into a denser medium when it strikes the boundary with a rarer medium beyond the critical angle. It requires travel from denser to rarer medium and underlies optical fibres.

The angle of incidence in the denser medium for which the refracted ray grazes the boundary between two media. Beyond it, total internal reflection occurs instead of refraction.

Superposition of two coherent light waves producing alternate bright and dark fringes where path differences equal whole or half multiples of wavelength. It demonstrates the wave nature of light.

Spreading of waves around obstacles and through apertures, producing fringes when light passes a narrow slit. Its extent grows when wavelength is comparable to the obstacle size.

Emission of electrons from a metal surface when light of sufficiently high frequency falls on it. Maximum kinetic energy depends on frequency, not on intensity, supporting the photon model.

The minimum energy needed to remove an electron from the surface of a particular metal. It sets the threshold frequency below which no photoelectric emission occurs.

The idea that one mole contains Avogadro's number of particles and has a mass in grams equal to the relative molecular mass. It converts between particle counts, mass and gas volume.

The simplest whole-number ratio of atoms of each element present in a compound, obtained from percentage composition. It may be a submultiple of the actual molecular formula.

Concentration expressed as moles of solute dissolved per litre of solution. It changes slightly with temperature because solution volume expands or contracts.

Concentration expressed as gram equivalents of solute per litre of solution, where the equivalent weight depends on the reaction involved. It is used in acid-base and redox titrations.

When a system at equilibrium is disturbed by changes in concentration, pressure or temperature, it shifts in the direction that partly opposes the disturbance. Used to predict yields in reversible reactions.

A ratio of product concentrations to reactant concentrations, each raised to its stoichiometric coefficient, at equilibrium for a given temperature. Its size indicates whether products or reactants dominate.

A logarithmic scale of hydrogen ion concentration, defined as the negative logarithm to base ten of that concentration in moles per litre. Values below seven are acidic at ordinary temperature.

A solution that resists large changes in pH when small amounts of acid or base are added, usually a weak acid with its salt or a weak base with its salt. Its pH follows the Henderson-Hasselbalch relation.

The mixing of atomic orbitals of similar energy to form equivalent new orbitals with fixed geometry, such as sp, sp2 and sp3. It explains observed bond angles and shapes of molecules.

One of several equivalent Lewis representations of a molecule in which electrons are delocalised, such as the structures of benzene or the carbonate ion. The real molecule is a hybrid of them.

A species that is electron-deficient and accepts an electron pair from a nucleophile to form a new bond. Common examples are carbocations, carbonyl carbon and halonium ions.

A species with a lone pair or negative charge that donates electrons to an electron-deficient centre. It attacks electrophiles in substitution and addition reactions.

When a hydrogen halide adds to an unsymmetrical alkene, the hydrogen attaches to the carbon already bearing more hydrogens, giving the more stable carbocation intermediate.

The value a function approaches as its argument approaches a given point, whether or not the function is defined there. It underlies continuity and differentiation.

A property of a function at a point where the limit exists, the function is defined there, and the two values agree. A function continuous on an interval has no breaks in its graph.

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

The property that a function has a finite derivative at a point, which implies continuity there but not the converse. Corner points and cusps are typical places where it fails.

The limit of a sum of products of function values and small interval widths over a stated range, interpreted as signed area under a curve. It is evaluated using antiderivatives.

A single number computed from the entries of a square matrix that tells whether the matrix is invertible and scales areas or volumes under the associated linear transformation.

A rectangular array of numbers arranged in rows and columns, supporting operations of addition, scalar multiplication and multiplication when dimensions are compatible.

An arrangement of objects in which order matters, counted using factorials or products of successive choices. The number of arrangements of r objects chosen from n distinct objects is n factorial divided by (n minus r) factorial.

A selection of objects in which order does not matter, counted by dividing the corresponding permutation count by the factorial of the number selected.

The probability distribution of the number of successes in a fixed number of independent trials, each with the same two possible outcomes and the same success probability.

Net movement of water across a semipermeable membrane from a region of higher water potential to one of lower water potential. It drives absorption of water by roots and cell turgidity.

Shrinking of the protoplast away from the cell wall when a plant cell loses water in a hypertonic solution. It shows that the cell membrane is selectively permeable.

Loss of water vapour mainly through stomata of leaves, creating the pull that moves water up the xylem. Rate rises with temperature, wind and light and falls with humidity.

The light-driven synthesis of carbohydrates from carbon dioxide and water in chloroplasts, releasing oxygen. It converts light energy into chemical energy stored in glucose.

The light-dependent splitting of water molecules in the chloroplast, releasing oxygen and supplying electrons and protons for the light reactions of photosynthesis.

The characteristic proportion of phenotypes among offspring of known crosses, such as 3:1 from a monohybrid cross or 9:3:3:1 from a dihybrid cross, assuming independent assortment and dominance.

The genetic constitution of an organism at one or more loci, describing which alleles are present. It interacts with environment to produce the observable phenotype.

A bacterial enzyme that cuts DNA at a specific recognition sequence, producing fragments with sticky or blunt ends. It is a basic tool in recombinant DNA technology.

A small circular extrachromosomal DNA molecule in bacteria that replicates independently. It is widely used as a vector to carry inserted genes into host cells.

A protein produced by plasma cells that binds specifically to an antigen and helps neutralise or mark it for destruction. Its Y-shaped structure has variable antigen-binding sites.

Any substance, usually a foreign protein or polysaccharide, that triggers an immune response and can be bound specifically by antibodies or T-cell receptors.

A diagram showing numbers, biomass or energy at successive trophic levels, with producers at the base. Energy pyramids are always upright because energy is lost at each transfer.