Assam CEE flashcards

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

Projectile maximum range

For a projectile on level ground, range R = u²sin2θ/g is greatest at a launch angle of 45 degrees, giving R_max = u²/g.

Centripetal acceleration

In uniform circular motion the speed is constant but velocity changes direction, so acceleration a = v²/r points toward the centre of the circle.

Work–energy theorem

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

Elastic collision, equal masses

When a moving body strikes an identical stationary body elastically in one dimension, the two exchange velocities: the first stops, the second moves off with the original speed.

Pendulum time period

A simple pendulum has period T = 2π√(l/g), independent of mass and, for small swings, independent of amplitude; length and gravity alone set the period.

Lens formula sign convention

For a thin lens, 1/v − 1/u = 1/f with distances measured from the optical centre; real images have positive v under the Cartesian convention.

Photoelectric threshold frequency

Emission occurs only when incident light frequency exceeds ν₀ = φ/h; the stopping potential rises with frequency but is unchanged by increasing intensity.

Half-life relation

Radioactive half-life T½ = 0.693/λ, where λ is the decay constant; after n half-lives the undecayed fraction is (1/2)ⁿ.

Molar volume at STP

One mole of any ideal gas occupies about 22.4 litres at standard temperature and pressure (273 K, 1 atm), a direct consequence of PV = nRT.

Le Chatelier pressure rule

Increasing pressure on a gaseous equilibrium shifts it toward the side having fewer moles of gas; the shift is nil when gaseous mole counts are equal.

Buffer pH equation

For a weak acid buffer, pH = pKa + log([salt]/[acid]); the mixture resists pH change on adding small amounts of strong acid or base.

Hybridisation from steric number

Steric number 2, 3 and 4 correspond to sp, sp² and sp³ hybridisation; 5 and 6 give sp³d and sp³d² geometries such as trigonal bipyramidal and octahedral.

Tollens' test

Warming an aldehyde with ammoniacal silver nitrate deposits a silver mirror as the aldehyde is oxidised; ketones give no such reaction.

SN1 versus SN2

SN1 is two-step via a carbocation, first order, favoured by tertiary halides; SN2 is one-step backside attack, second order, favoured by primary halides.

Colligative property formula

Boiling-point elevation ΔTb = i·Kb·m and freezing-point depression ΔTf = i·Kf·m depend on molality m and van't Hoff factor i, not solute identity.

Aromatic substitution preference

Benzene prefers electrophilic substitution over addition because substitution restores the stable aromatic sextet; typical reactions include nitration and Friedel–Crafts alkylation.

Quadratic root relations

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

Standard limit sin x over x

As x approaches zero in radians, sin x/x tends to 1; this limit underlies the derivatives of sine and cosine.

Integration by parts

∫u dv = uv − ∫v du; pick u using ILATE order (inverse trig, log, algebraic, trig, exponential) so the remaining integral is simpler.

Perpendicular line slopes

Two non-vertical lines are perpendicular exactly when the product of their slopes is −1; parallel lines share the same slope and never intersect.

Point-to-line distance

The perpendicular distance from (x₁, y₁) to ax + by + c = 0 is |ax₁ + by₁ + c| divided by √(a² + b²).

Binomial general term

In the expansion of (a + b)ⁿ, the term containing bʳ is C(n,r)·aⁿ⁻ʳ·bʳ, where C(n,r) = n!/(r!(n − r)!).

Addition rule of probability

For any two events, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); when independent, P(A ∩ B) = P(A)·P(B).

Definite integral symmetry

The identity ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a − x) dx converts many trigonometric definite integrals into simpler, directly evaluable forms.

Light reaction products

Thylakoid light reactions split water, releasing oxygen and producing ATP and NADPH, which the stroma Calvin cycle uses to fix carbon dioxide.

Glycolysis net yield

In the cytoplasm, one glucose yields two pyruvate with a net gain of 2 ATP and 2 NADH, without requiring oxygen.

Dihybrid F2 ratio

Crossing two heterozygotes for independently assorting genes gives a 9:3:3:1 phenotypic ratio in the F2 generation.

Base pairing rules

In DNA, adenine pairs with thymine via two hydrogen bonds and guanine pairs with cytosine via three; the two strands run antiparallel.

ABO blood group alleles

Three alleles Iᴬ, Iᴵ and i produce four phenotypes; Iᴬ and Iᴵ are codominant, and genotype ii gives blood group O.

Nephron reabsorption site

Most glucose and water are selectively reabsorbed in the proximal convoluted tubule, while the loop of Henle builds the medullary gradient for urine concentration.

Insulin action

Insulin lowers blood glucose by promoting glucose uptake into cells and glycogen formation; glucagon and adrenaline oppose it by stimulating glycogen breakdown.

Ten percent energy rule

Only roughly 10 percent of energy at one trophic level is transferred to the next, so food chains are short and top consumers receive little energy.