MP PAT cheat sheet

Wheat irrigation is most critical at crown root initiation (about 20–25 days after sowing), tillering, flowering and milk stage; water stress at CRI sharply reduces tiller number and final yield.

Classic deficiency-disorder pairs: khaira of rice = zinc; whiptail of cauliflower = molybdenum; brown heart of turnip and hollow stem of cauliflower = boron; chlorosis of young leaves = iron.

Seed rate (kg/ha) = (target plant population per ha × test weight in g) ÷ (1000 × germination fraction × purity fraction); test weight is the 1000-grain weight.

Average gestation lengths: cattle about 280 days, buffalo about 310 days, goat about 150 days, sheep about 147 days, pig about 114 days.

Propagating material: mango by veneer grafting or inarching, banana by sucker, sugarcane by three-bud setts, potato by tuber, rose by T-budding.

Economics: net return = gross return − total cost of cultivation; B:C ratio = gross return ÷ total cost, so any ratio above 1.0 means the enterprise is profitable.

Plant protection decision rule: apply insecticide only when the pest population reaches the economic threshold level (ETL), not at first appearance, to protect natural enemies and delay resistance.

Extension set-up: Krishi Vigyan Kendra (KVK) works at district level for technology assessment and demonstration; ATMA prepares bottom-up district extension plans through block-level Farm Information and Advisory Centres.

Equations of uniformly accelerated motion: v = u + at; s = ut + ½at²; v² = u² + 2as; distance in nth second = u + a(n − ½).

Newton's second law in momentum form F = dp/dt; for constant mass this reduces to F = ma, and impulse equals change in momentum.

Work–energy theorem: net work done = change in kinetic energy = ½mv² − ½mu²; potential energy near the earth is mgh.

Mirror and lens formula 1/f = 1/v − 1/u with the Cartesian sign convention; magnification m = −v/u for mirrors and m = v/u for lenses.

Ohm's law V = IR; power P = VI = I²R = V²/R; series R = R₁ + R₂ + …, parallel 1/R = 1/R₁ + 1/R₂ + …

Escape velocity from the earth's surface = √(2gR) ≈ 11.2 km/s and is independent of the projectile's mass; orbital velocity near the surface ≈ 7.9 km/s.

Photoelectric equation hν = φ + Kmax, with h = 6.63 × 10⁻³⁴ J·s; no emission occurs below the threshold frequency whatever the intensity.

Dimensional formulae to memorise: force [MLT⁻²], work and energy [ML²T⁻²], power [ML²T⁻³], pressure [ML⁻¹T⁻²], Planck's constant [ML²T⁻¹].

One mole contains 6.022 × 10²³ particles; moles = mass in g ÷ molar mass, and for gases at STP 1 mol occupies 22.4 L.

Molarity (M) = moles of solute per litre of solution and changes with temperature; molality (m) = moles of solute per kg of solvent and is temperature independent.

pH = −log[H⁺]; pOH = −log[OH⁻]; at 25 °C pH + pOH = 14, and pH < 7 is acidic, pH > 7 basic.

Buffer pH by Henderson–Hasselbalch: pH = pKa + log([salt]/[acid]); maximum buffering occurs when pH = pKa.

Le Chatelier's principle: raising pressure shifts equilibrium towards the side with fewer gaseous moles; raising temperature favours the endothermic direction.

Colligative properties: ΔTb = i·Kb·m, ΔTf = i·Kf·m, π = iCRT, where i is the van't Hoff factor (2 for NaCl, 3 for CaCl₂, 1 for glucose).

Hybridisation from steric number (sigma bonds + lone pairs): 2 → sp, 3 → sp², 4 → sp³, 5 → sp³d, 6 → sp³d².

Group tests: Tollens' and Fehling's reagents detect aldehydes; yellow iodoform with I₂/NaOH indicates a methyl ketone or ethanol; Baeyer's reagent decolourises with unsaturation.

Nernst equation at 298 K: E = E° − (0.0591/n)·log Q; a positive E°cell means the cell reaction is spontaneous.

Quadratic ax² + bx + c = 0: roots x = [−b ± √(b² − 4ac)]/2a; discriminant D > 0 gives real distinct roots, D = 0 equal roots, D < 0 complex roots.

Root relations: α + β = −b/a and αβ = c/a; the equation with given roots is x² − (α + β)x + αβ = 0.

AP: nth term a + (n − 1)d and sum Sn = n/2[2a + (n − 1)d]; GP: nth term ar^(n−1) and sum Sn = a(rⁿ − 1)/(r − 1), with S∞ = a/(1 − r) for |r| < 1.

Binomial theorem: (a + b)ⁿ general term T(r+1) = nCr·a^(n−r)·b^r; number of terms is n + 1.

Trigonometric identities: sin²θ + cos²θ = 1; sin 2θ = 2 sin θ cos θ; cos 2θ = 1 − 2sin²θ = 2cos²θ − 1.

Derivatives: d/dx(xⁿ) = nx^(n−1), d/dx(sin x) = cos x, d/dx(cos x) = −sin x, d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x; product rule (uv)' = u'v + uv'.

Straight line: slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines have m₁ = m₂, perpendicular lines have m₁m₂ = −1; point-slope form y − y₁ = m(x − x₁).

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); for independent events P(A ∩ B) = P(A)·P(B); P(A') = 1 − P(A).

Circle with centre (h, k) and radius r: (x − h)² + (y − k)² = r²; the general form x² + y² + 2gx + 2fy + c = 0 has centre (−g, −f) and radius √(g² + f² − c).

Photosynthesis has light reactions in the thylakoid (producing ATP, NADPH and O₂ from water) and the Calvin cycle in the stroma, where RuBisCO fixes CO₂; each CO₂ costs 3 ATP and 2 NADPH.

C4 plants (maize, sugarcane) show Kranz anatomy and have no photorespiration; CAM plants (opuntia, pineapple) fix CO₂ at night and open stomata in darkness.

Aerobic respiration yield: glycolysis gives a net 2 ATP and 2 NADH; the complete oxidation of one glucose yields about 36–38 ATP in eukaryotes.

Mendelian ratios: monohybrid F₂ phenotypic ratio 3:1 with genotypic ratio 1:2:1; dihybrid F₂ phenotypic ratio 9:3:3:1; test cross with the recessive parent reveals genotype.

Plant hormones: auxin causes apical dominance and rooting, gibberellin causes stem elongation and bolting, cytokinin promotes cell division, abscisic acid closes stomata and induces dormancy, ethylene ripens fruit.

Human blood groups (ABO): A has antigen A and anti-B, B has antigen B and anti-A, AB has both antigens and no antibodies (universal recipient), O has no antigens and both antibodies (universal donor).

Nephron parts in order: Bowman's capsule → proximal convoluted tubule → loop of Henle → distal convoluted tubule → collecting duct; glomerular filtration rate is about 125 mL/min.

Ecology: the 10% law states only about 10% of energy passes to the next trophic level, so food chains rarely exceed 4–5 trophic levels; pyramids of energy are always upright.

Central dogma: DNA → RNA (transcription) → protein (translation); DNA is a double helix with A–T and G–C base pairing, and the two strands run antiparallel.