JEE Main flashcards

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

Projectile maximum range angle

For a projectile launched over level ground with fixed speed, the horizontal range R = u²sin2θ/g is greatest when θ = 45°, giving R_max = u²/g.

Work–energy theorem

The net work done by all forces on a body equals the change in its kinetic energy: W_net = ΔK = ½mv² − ½mu².

Parallel-axis theorem

The moment of inertia about any axis equals that about a parallel axis through the centre of mass plus Md², where d is the separation of the axes.

Rolling without slipping condition

A body rolls without slipping when its contact point has zero velocity, so v_cm = ωR; static friction acts but does no work, conserving mechanical energy.

SHM acceleration relation

In simple harmonic motion the restoring acceleration is proportional and opposite to displacement: a = −ω²x, with angular frequency ω = 2π/T.

Carnot efficiency formula

The maximum efficiency of a heat engine between reservoirs is η = 1 − T_c/T_h, with both temperatures expressed in kelvin; no real engine exceeds it.

Capacitor stored energy

The energy stored in a capacitor of capacitance C at voltage V is U = ½CV² = ½QV = Q²/(2C), where Q is the charge on either plate.

Kirchhoff's circuit rules

The junction rule states that charge entering a node equals charge leaving; the loop rule states that the algebraic sum of potential changes around a closed loop is zero.

Snell's law and critical angle

Refraction obeys n₁sinθ₁ = n₂sinθ₂. Total internal reflection occurs when light travels from denser to rarer medium and the incidence angle exceeds θ_c, where sinθ_c = n₂/n₁.

Young's double slit fringe width

In Young's double-slit interference the spacing between adjacent bright fringes on a screen is β = λD/d, where D is slit-to-screen distance and d is slit separation.

Photoelectric equation

Einstein's photoelectric relation is hν = φ + K_max, where φ is the work function and K_max is the maximum kinetic energy of emitted electrons.

Bohr energy levels

For hydrogen-like atoms the nth energy level is E_n = −13.6 Z²/n² electronvolts, so the ground state of hydrogen is −13.6 eV.

Radioactive half-life relation

Radioactive decay follows N = N₀e^(−λt), and the half-life is t½ = ln2/λ ≈ 0.693/λ, independent of the initial number of nuclei.

Molarity and dilution

Molarity is moles of solute per litre of solution. On dilution the moles of solute stay constant, so M₁V₁ = M₂V₂.

Gibbs free energy criterion

ΔG = ΔH − TΔS; a reaction is spontaneous at constant temperature and pressure when ΔG is negative, non-spontaneous when positive, and at equilibrium when zero.

Buffer pH equation

For a weak acid buffer, pH = pKa + log([A⁻]/[HA]); the buffer resists pH change best when the acid and conjugate base concentrations are nearly equal.

SN1 versus SN2 preference

SN1 proceeds via a carbocation and is favoured by tertiary substrates and polar protic solvents; SN2 is a single-step backside attack favoured by primary substrates and polar aprotic solvents.

Quadratic roots relations

For ax² + bx + c = 0 the roots satisfy sum = −b/a and product = c/a; the discriminant D = b² − 4ac decides whether roots are real and distinct, equal, or complex.

Circle from general equation

The equation x² + y² + 2gx + 2fy + c = 0 represents a circle with centre (−g, −f) and radius √(g² + f² − c), real only when g² + f² − c > 0.

Bayes' theorem statement

Bayes' theorem gives the conditional probability P(A|B) = P(B|A)P(A)/P(B), updating a prior probability P(A) with the likelihood of the observed evidence.

Euler's polyhedron formula

For any convex polyhedron the number of vertices minus edges plus faces equals two: V − E + F = 2. A cube satisfies 8 − 12 + 6 = 2.

First-angle projection layout

In first-angle orthographic projection the object lies between observer and plane, so the top view is drawn below the front view and the left-side view appears on the right.

Isometric scale factor

In isometric drawing the three axes are 120° apart and true lengths are multiplied by √(2/3) ≈ 0.816 to obtain the isometric length, giving equal foreshortening on all axes.

Representative fraction of scale

The representative fraction equals drawing length divided by actual length in the same units; an RF of 1:50 means one unit on paper represents fifty units on the ground.

Two-point perspective basics

In two-point perspective, two vanishing points lie on the horizon line and represent two horizontal directions of the object; vertical edges remain vertical when the picture plane is vertical.

Complementary colours rule

Complementary colours sit opposite each other on the colour wheel, such as red and green or blue and orange, and produce maximum contrast when placed side by side.

Cone total surface area

The total surface area of a right circular cone is πr(l + r), where r is the base radius and l = √(r² + h²) is the slant height.

Regular polygon symmetry order

A regular polygon with n sides has rotational symmetry of order n, meaning it maps onto itself under rotation by 360°/n about its centre.

Net versus gross density

Net residential density divides population by net residential land only, while gross density uses total area including roads and open space, so net density is higher.

Neighbourhood unit radius

Clarence Perry's neighbourhood unit is organised around a primary school within roughly a quarter-mile, about 400 metres, walking distance, bounded by arterial streets.

Gravity model of trip distribution

Trip interchange between zones is modelled as proportional to the product of their attractions and inversely proportional to the square of the distance between them.

Rule of 70 for doubling

For a population growing at r percent per year, the doubling time is approximately 70/r years; at 2 percent annual growth the population doubles in about 35 years.