MHT-CET flashcards

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

Projectile range formula

For launch speed u and angle θ on level ground, range R = u² sin 2θ / g; maximum range occurs at θ = 45° when air resistance is ignored.

Centripetal acceleration

For uniform circular motion, centripetal acceleration has magnitude a_c = v²/r = ω²r and points toward the circle's centre; speed is constant but velocity direction changes.

Work-energy theorem

The net work done by all forces on a particle equals its change in kinetic energy: W_net = ΔK = ½mv_f² − ½mv_i².

Rolling without slipping

A round body rolls without slipping when v = ωR at contact; total kinetic energy is ½mv²(1 + I/mR²), combining translation and rotation.

Simple pendulum period

For small angular amplitude, a simple pendulum has period T = 2π√(L/g), independent of bob mass; g is gravitational acceleration and L is effective length.

Snell law

At an interface, n₁ sin i = n₂ sin r, where angles are measured from the normal; light bends toward the normal when entering a higher refractive index medium.

Carnot efficiency

The maximum efficiency of a heat engine operating between hot and cold reservoirs at absolute temperatures T_h and T_c is η = 1 − T_c/T_h.

Wheatstone bridge balance

A Wheatstone bridge is balanced when the galvanometer current is zero; then P/Q = R/S, so unknown resistance can be found from three known arms.

Molarity

Molarity is moles of solute per litre of solution: M = n_solute / V_solution(L). It changes with temperature because solution volume expands or contracts.

Ideal gas equation

For an ideal gas, PV = nRT, where P is pressure, V volume, n moles, R the gas constant, and T absolute temperature; STP molar volume is about 22.4 L.

Le Chatelier principle

If a system at equilibrium is disturbed by concentration, pressure, or temperature change, the equilibrium shifts in the direction that partially opposes the disturbance.

Buffer pH equation

For an acidic buffer, pH = pKa + log([A⁻]/[HA]); for a basic buffer, pOH = pKb + log([BH⁺]/[B]).

First-order half-life

A first-order reaction has half-life t₁/₂ = 0.693/k, independent of initial reactant concentration; k is the first-order rate constant.

SN2 reaction

SN2 is a one-step bimolecular substitution with backside attack; it gives inversion of configuration and is favoured by primary alkyl halides and polar aprotic solvents.

Nernst equation

At 298 K, E = E° − (0.059/n) log Q for a cell reaction; n is electrons transferred and Q is the reaction quotient.

Faraday constant

One faraday equals about 96,500 coulombs per mole of electrons; it converts charge to moles in electrolysis using n = Q/F.

Quadratic roots

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

Derivative of sine

d/dx(sin x) = cos x and d/dx(cos x) = −sin x when x is in radians; chain rule multiplies by the derivative of the inner angle.

Integration by parts

∫u dv = uv − ∫v du; choose u by LIATE preference usually, and apply repeatedly when the new integral is simpler.

Standard limit sinx/x

As x approaches zero in radians, lim(sin x/x) = 1; related limits include lim((1 − cos x)/x²) = 1/2.

Conditional probability

P(A|B) = P(A ∩ B)/P(B), provided P(B) > 0; it gives the probability of A after knowing B has occurred.

Vector dot product

a·b = |a||b|cosθ, a scalar equal to the sum of component products; perpendicular vectors have dot product zero.

Circle centre and radius

For x² + y² + 2gx + 2fy + c = 0, centre is (−g, −f) and radius is √(g² + f² − c), requiring positive radicand.

Sine rule

In any triangle, a/sin A = b/sin B = c/sin C = 2R, where R is the circumradius and side a is opposite angle A.

DNA replication semiconservative

Each parental DNA strand acts as a template, so every daughter double helix contains one old strand and one newly synthesized strand.

Calvin cycle location

The Calvin cycle occurs in the chloroplast stroma; RuBisCO fixes CO₂ onto RuBP, and ATP and NADPH from light reactions reduce the product to sugar.

Glycolysis net ATP

Glycolysis in the cytoplasm converts one glucose to two pyruvate, with a net gain of 2 ATP and 2 NADH before pyruvate oxidation.

Law of segregation

During meiosis, the two alleles of a gene separate into different gametes, so each gamete carries only one allele for that gene.

Start codon

AUG is the usual start codon in translation; it codes for methionine and sets the reading frame on mRNA.

SA node

The sinoatrial node in the right atrium sets the heart's rhythm; it depolarizes spontaneously and acts as the natural pacemaker.

Competitive inhibition

A competitive inhibitor binds the enzyme's active site, blocking substrate; increasing substrate concentration can overcome it, and apparent Km rises while Vmax is unchanged.

Ten percent energy law

In an ecosystem, only about 10% of energy at one trophic level is transferred to the next; the rest is lost mainly as heat and through metabolism.