SRMJEEE flashcards

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

Projectile maximum range

For launch speed u on level ground, range R = u²sin2θ/g, which peaks at θ = 45° giving R_max = u²/g; complementary angles give equal ranges.

Centripetal force direction

It always points toward the centre of the circular path, has magnitude mv²/r, and changes velocity direction without changing speed for uniform circular motion.

Banking angle formula

For a vehicle on a frictionless banked curve, tanθ = v²/(rg); the angle depends on design speed and radius, not on vehicle mass.

Work-energy theorem

The net work done by all forces on a body equals its change in kinetic energy, W_net = ½mv² − ½mu², valid even when forces vary.

Ohm's law and resistance

At constant temperature, V = IR for a conductor; resistance rises with length and falls with cross-sectional area, R = ρL/A.

Series versus parallel resistors

Series resistances add directly and share the same current; parallel resistances add as reciprocals and share the same voltage across each branch.

Lens and mirror formulas

Thin lens: 1/v − 1/u = 1/f. Spherical mirror: 1/v + 1/u = 1/f. Sign conventions decide whether images are real or virtual.

Snell's law of refraction

n₁sin i = n₂sin r at an interface; light bends toward the normal when entering a denser medium and total internal reflection occurs beyond the critical angle.

First law of thermodynamics

ΔQ = ΔU + ΔW: heat supplied to a system raises internal energy and/or does work by it. In an isothermal process ΔU = 0 for an ideal gas.

Adiabatic process relation

No heat exchange occurs (ΔQ = 0), so PV^γ = constant where γ = Cp/Cv; the gas cools on expansion and heats on compression.

Bond order from MO theory

Bond order equals half the difference between bonding and antibonding electrons; higher bond order means shorter, stronger bonds, and zero order implies instability.

Aromaticity criteria

A ring is aromatic if it is cyclic, planar, fully conjugated, and holds 4n+2 π electrons (Hückel rule); 4n π electrons in the same setting give antiaromatic behaviour.

Ideal gas equation

PV = nRT links pressure, volume, moles, and absolute temperature; at constant T, P₁V₁ = P₂V₂ (Boyle) and at constant P, V/T is fixed (Charles).

pH and pOH relation

pH = −log[H⁺] and pOH = −log[OH⁻]; at 25 °C, pH + pOH = 14, so a solution with pH below 7 is acidic.

Le Chatelier's principle

A system at equilibrium shifts to oppose a change: adding reactant shifts forward, raising pressure favours the side with fewer gas moles, and catalysts do not shift position.

Oxidation number rules

Elements in free state are 0, oxygen is usually −2, hydrogen +1, and the sum of oxidation numbers equals the overall charge of the species or ion.

Hybridisation from steric number

Steric number = sigma bonds + lone pairs on the central atom: 2 gives sp, 3 gives sp², 4 gives sp³, 5 gives sp³d, 6 gives sp³d².

Quadratic roots relations

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

Arithmetic progression formulas

nth term aₙ = a + (n−1)d and sum Sₙ = n/2[2a + (n−1)d]; for a geometric progression, aₙ = ar^(n−1) and Sₙ = a(rⁿ−1)/(r−1).

Straight line slope and forms

Slope m = (y₂ − y₁)/(x₂ − x₁); point-slope form y − y₁ = m(x − x₁); parallel lines share slope, perpendicular slopes multiply to −1.

Limits and L'Hôpital's rule

For 0/0 or ∞/∞ indeterminate forms, differentiate numerator and denominator separately and take the limit of the resulting quotient, repeating if needed.

Derivative of standard functions

d/dx(sin x) = cos x, d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x, and d/dx(xⁿ) = nx^(n−1); chain rule handles composite functions.

Definite integral property

∫ from a to b of f(x)dx = F(b) − F(a) where F is an antiderivative; reversing limits flips the sign, and splitting intervals preserves additivity.

Binomial expansion term

(a + b)ⁿ = Σ C(n,r) a^(n−r) b^r; the general term is C(n,r) a^(n−r) b^r, and the middle term has the largest binomial coefficient.

Vector dot and cross product

a·b = |a||b|cosθ gives a scalar and is zero for perpendicular vectors; a×b = |a||b|sinθ n̂ gives a vector perpendicular to both.

Probability complement rule

P(A') = 1 − P(A); for mutually exclusive events P(A∪B) = P(A) + P(B), and for independent events P(A∩B) = P(A)P(B).

Permutations and combinations

nPr = n!/(n−r)! counts ordered arrangements of r items from n; nCr = n!/[r!(n−r)!] counts unordered selections and equals nC(n−r).

Dimensional analysis check

Both sides of a physical equation must have identical dimensions; this verifies formulas and derives relations, but cannot fix dimensionless constants.

SI units of key quantities

Force in newton (kg·m/s²), energy in joule (N·m), power in watt (J/s), pressure in pascal (N/m²), and frequency in hertz (s⁻¹).

Mole concept and molarity

One mole holds 6.022×10²³ particles; molarity M = moles of solute per litre of solution, and moles = mass/molar mass.

Series and parallel capacitors

Capacitors in parallel add directly (C = C₁ + C₂); in series the reciprocals add, so total capacitance is smaller than any individual capacitance.

Quantitative aptitude ratio rule

If a:b = c:d then ad = bc; in mixtures and alligation, the mean value lies between the two component values weighted by their quantities.