COMEDK UGET flashcards

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

Projectile maximum range

For a projectile launched and landing at the same level, range is maximum at 45 degrees, giving R = u squared divided by g, independent of mass.

Escape velocity formula

Minimum speed to escape Earth's gravity from the surface: v = square root of (2GM/R), about 11.2 km/s for Earth, derived from equating kinetic and potential energy.

Doppler effect

Apparent frequency shifts when source and observer move relative to each other: f' = f(v ± v_observer)/(v ∓ v_source), with approach raising pitch and recession lowering it.

Kirchhoff circuit rules

Junction rule: total current entering a node equals total leaving. Loop rule: algebraic sum of potential differences around any closed loop equals zero.

Photoelectric threshold

Electrons are emitted only when incident light frequency exceeds the threshold frequency; maximum kinetic energy equals hf minus the work function.

Half-life decay law

After n half-lives, remaining radioactive nuclei equal N0 times (1/2) to the power n; activity also halves every half-life.

Molarity versus molality

Molarity is moles of solute per litre of solution and varies with temperature; molality is moles per kilogram of solvent and is temperature-independent.

Ideal gas molar volume

At standard temperature and pressure, one mole of an ideal gas occupies 22.4 litres, following from PV = nRT with R = 0.0821 L atm per mol K.

Markovnikov addition rule

When HX adds to an unsymmetrical alkene, hydrogen attaches to the carbon with more hydrogens, placing the halogen on the more substituted carbon.

Hybridisation geometry map

sp gives linear 180 degrees; sp2 gives trigonal planar 120 degrees; sp3 gives tetrahedral 109.5 degrees; sp3d gives trigonal bipyramidal and sp3d2 octahedral.

Entropy and spontaneity

Gibbs free energy change ΔG = ΔH − TΔS; a reaction is spontaneous when ΔG is negative, which favours exothermic and entropy-increasing processes.

Limits L'Hôpital rule

For indeterminate forms like 0/0 or infinity/infinity, differentiate numerator and denominator separately and take the limit of the quotient.

Derivative of inverse tangent

The derivative of arctan x with respect to x is 1 divided by (1 + x squared), a standard result used in integration and differential equation problems.

Straight line slope form

Line through (x1, y1) with slope m: y − y1 = m(x − x1). Two lines are perpendicular when the product of their slopes equals negative one.

Parabola standard elements

For y squared = 4ax: vertex at origin, focus at (a, 0), directrix x = −a, axis along the x-axis, latus rectum length 4a.

Binomial coefficient symmetry

In the expansion of (a + b) to the power n, coefficients are symmetric: nCr equals nC(n−r), and the general term is nCr a^(n−r) b^r.

Probability addition rule

P(A or B) = P(A) + P(B) − P(A and B); for mutually exclusive events the intersection term is zero, so probabilities simply add.

Matrix inverse condition

A square matrix has an inverse only when its determinant is non-zero; the inverse equals the adjugate divided by the determinant.

Definite integral area

The definite integral of a function from a to b gives the signed area between the curve and the x-axis; areas below the axis count negative.

Relative velocity

Velocity of A relative to B equals vector vA minus vector vB; use it for river-boat and rain-man problems to find resultant speeds and directions.

Centre of mass formula

For discrete masses, x_cm = sum of (m_i x_i) divided by sum of m_i; the centre of mass moves as if all external forces act there.

Lens maker equation

1/f = (n − 1)(1/R1 − 1/R2) for a thin lens in air; combine with 1/f = 1/v − 1/u using the Cartesian sign convention.

Architectural scale conversion

Scale 1:100 means one unit on the drawing represents 100 units in reality, so 1 cm on paper equals 1 m on site.

Golden ratio value

φ is approximately 1.618, satisfying φ squared = φ + 1; used in proportion problems for rectangles, facades and classical composition.

Stair riser-tread rule

Comfort rule: 2 times riser plus tread approximately equals 600 mm; typical riser is 150 to 190 mm and tread 250 to 300 mm.

First-angle projection

The object sits between observer and plane, so the top view is placed below the front view and the left view appears on the right.

Cantilever bending moment

A cantilever under uniform load w over length L has maximum bending moment wL squared divided by 2 at the fixed support, where shear is also greatest.

Simply supported beam moment

Under uniform load w over span L, maximum bending moment is wL squared divided by 8 at midspan, with zero moment at both supports.

Plinth and parapet

Plinth is the projecting base of a wall above ground; parapet is the low protective wall continuing above the roof edge.

Chajja and lintel

Lintel is a horizontal beam spanning an opening to carry the wall above; chajja is a projecting slab over openings for sun and rain protection.

Hot-dry climate strategy

Design uses thick massive walls, small shaded openings, light-coloured surfaces, courtyards and night ventilation to reduce daytime heat gain.

Warm-humid climate strategy

Design maximises cross-ventilation with large openings, raised floors, deep verandahs and shading, since cooling by air movement matters more than thermal mass.

One-point perspective

A drawing with a single vanishing point on the horizon, used when the viewer faces one plane of the object directly, as in a straight corridor view.