Maharashtra SSC Science and Technology (MSBSHSE) cheat sheet

Newton's law of gravitation: F = G m1 m2 / r^2, with G ≈ 6.67 × 10^-11 N m^2 kg^-2.

Acceleration due to gravity: g = GM/R^2; near Earth's surface g ≈ 9.8 m/s^2.

g decreases with altitude and depth; at Earth's centre g = 0, and g is slightly greater at the poles than at the equator.

Free-fall equations with downward positive: v = u + gt; s = ut + (1/2)gt^2; v^2 = u^2 + 2gs.

Mass is a scalar and constant; weight W = mg is a force measured in newtons and changes with g.

Kepler's laws: planetary orbits are ellipses; equal areas are swept in equal times; T^2 ∝ r^3.

Gravitational potential energy near Earth: U = mgh; escape velocity v_e = √(2GM/R) ≈ 11.2 km/s for Earth.

Satellite orbital speed: GMm/r^2 = mv^2/r, so v = √(GM/r); gravity provides the centripetal force.

Distance is scalar; displacement is vector. Speed = distance/time; velocity = displacement/time.

Acceleration a = (v − u)/t, SI unit m/s^2; for uniform acceleration: v = u + at, s = ut + (1/2)at^2, v^2 = u^2 + 2as.

Newton's first law: a body remains at rest or in uniform motion unless acted on by a net external force; this property is inertia.

Newton's second law: F_net = ma; 1 N = 1 kg m/s^2.

Newton's third law: forces occur in equal and opposite pairs acting on different bodies.

Momentum p = mv; impulse FΔt = Δp; total momentum is conserved when the net external force is zero.

Friction opposes relative motion; static friction ≤ μ_sN; kinetic friction = μ_kN.

Uniform circular motion: centripetal acceleration a = v^2/r directed towards the centre; force = mv^2/r.

On a distance-time graph slope = speed; on a velocity-time graph slope = acceleration and area under the graph = displacement.

Temperature measures the average kinetic energy of particles; SI unit kelvin; 0 °C = 273.15 K.

Heat is energy transferred because of a temperature difference; SI unit joule; 1 cal ≈ 4.18 J.

Specific heat capacity: Q = mcΔT; for water c ≈ 4200 J kg^-1 °C^-1.

Latent heat: Q = mL; for water, latent heat of fusion ≈ 334 kJ/kg and vaporization ≈ 2260 kJ/kg.

Heat transfers by conduction, convection and radiation; radiation requires no medium.

Thermal expansion: ΔL = LαΔT; water shows anomalous expansion between 0 °C and 4 °C and has maximum density at 4 °C.

Newton's law of cooling: rate of heat loss is proportional to the temperature difference from the surroundings for small differences.

Good absorbers are good emitters; black surfaces absorb and emit more radiation than shiny surfaces.

Refraction is the bending of light due to a change in speed when it passes from one medium to another.

Snell's law: n1 sin i = n2 sin r; refractive index n = c/v, and for light entering from air n = sin i / sin r.

Light bends towards the normal when entering a denser medium (higher n) and away from the normal when entering a rarer medium.

Convex lens converges light and has positive focal length; concave lens diverges light and has negative focal length in the Cartesian sign convention.

Lens formula: 1/f = 1/v − 1/u; magnification m = v/u = h_i/h_o.

Lens power P = 1/f with f in metres; SI unit dioptre (D); convex positive, concave negative.

A convex lens forms a real inverted image when object distance > f; it forms a virtual erect image when object distance < f.

Total internal reflection occurs when light travels from denser to rarer medium and angle of incidence exceeds critical angle C, where sin C = 1/n.

Eye defects: myopia corrected by concave lens; hypermetropia corrected by convex lens.

Ohm's law: V = IR at constant temperature; resistance R = ρL/A.

Series resistance: R = R1 + R2 + ...; parallel resistance: 1/R = 1/R1 + 1/R2 + ...

Electric power: P = VI = I^2R = V^2/R; electrical energy in kWh = power in kW × time in h.

Heating effect of current: H = I^2Rt; used in electric heaters, fuses and filament lamps.

Magnetic field lines run from north to south outside a magnet and form closed loops; the field is strongest where lines are closest.

Right-hand thumb rule: thumb along current, curled fingers give the direction of the magnetic field around a straight conductor.

Force on a current-carrying conductor: F = BIL sin θ; Fleming's left-hand rule gives its direction.

Electromagnetic induction: a changing magnetic flux induces an emf; Fleming's right-hand rule gives induced current direction.

Electric motor converts electrical energy to mechanical energy; generator converts mechanical energy to electrical energy.

A balanced chemical equation has equal numbers of each kind of atom on both sides, conserving mass.

Combination: A + B → AB; decomposition: AB → A + B (thermal, electrolytic or photolytic).

Displacement: a more reactive element displaces a less reactive one from its compound; the reactivity series decides feasibility.

Double displacement: ions exchange, often forming a precipitate, e.g. AgNO3 + NaCl → AgCl↓ + NaNO3.

Oxidation is loss of electrons or gain of oxygen; reduction is gain of electrons or loss of oxygen; both occur in redox reactions.

Exothermic reactions release heat; endothermic reactions absorb heat; bond breaking absorbs and bond making releases energy.

Corrosion is slow oxidation of metals; rancidity is oxidation of fats/oils; antioxidants slow rancidity.

Reaction rate increases with higher concentration, higher temperature, greater surface area and presence of a suitable catalyst.

Arrhenius acid releases H+ in water; Arrhenius base releases OH− in water; Brønsted acid is a proton donor.

pH = −log[H+]; pH < 7 acidic, pH = 7 neutral, pH > 7 basic at 25 °C.

Acid + metal → salt + hydrogen; acid + metal carbonate/bicarbonate → salt + water + carbon dioxide.

Acid + base → salt + water (neutralization); acid + metal oxide → salt + water.

Strong acids ionize almost completely in water; weak acids ionize partially; dilution lowers H+ concentration and raises pH.

Common acids: HCl, H2SO4, HNO3; common bases: NaOH, KOH, Ca(OH)2.

Salts: NaCl (common salt), NaHCO3 (baking soda), Na2CO3·10H2O (washing soda), CaSO4·½H2O (plaster of Paris).

Water of crystallization is fixed water molecules in a crystal; heating can remove it and change colour, as in blue CuSO4·5H2O to white CuSO4.

Modern periodic law: properties are periodic functions of atomic number; elements are arranged by increasing atomic number.

Periods 1–7 are horizontal rows; groups 1–18 are vertical columns; main-group valence electrons relate to group number.

Metals lie on the left and centre; nonmetals on the right; metalloids along the staircase line.

Across a period, atomic radius decreases and electronegativity increases; down a group, atomic radius increases and electronegativity decreases.

Group 1 alkali metals, group 2 alkaline earth metals, group 17 halogens, group 18 noble gases.

Metallurgy steps: concentration of ore, roasting or calcination, reduction to metal, refining.

Roasting heats a sulphide ore in excess air; calcination heats a carbonate or hydrated ore in limited air.

Ores: bauxite Al2O3·2H2O (aluminium), haematite Fe2O3 (iron), galena PbS (lead).

Highly reactive metals are extracted by electrolytic reduction; moderately reactive by carbon reduction; unreactive metals occur free.

Carbon is tetravalent and forms four covalent bonds; it shows catenation and forms chains, branches and rings.

Allotropes of carbon include diamond (tetrahedral network), graphite (layers) and fullerene (C60 cage).

Alkanes are saturated: C_nH_2n+2; alkenes have one C=C: C_nH_2n; alkynes have one C≡C: C_nH_2n−2.

Functional groups: alcohol −OH, aldehyde −CHO, ketone −CO−, carboxylic acid −COOH, ester −COO−.

Isomers have the same molecular formula but different structural arrangements and often different properties.

Ethanol C2H5OH is produced by fermentation; ethanoic acid CH3COOH is a weak acid and gives vinegar.

Esterification: carboxylic acid + alcohol ⇌ ester + water, usually with an acid catalyst.

Addition reactions occur at double/triple bonds; alkanes mainly undergo substitution; combustion gives CO2 and H2O.

Homologous series: same functional group and general formula; successive members differ by CH2 (14 u).

General formulas: alkanes C_nH_2n+2, alkenes C_nH_2n, alkynes C_nH_2n−2, alcohols C_nH_2n+1OH.

In a homologous series, boiling point generally rises with chain length; water solubility generally falls.

Polymers are large molecules made by joining many small monomer units; polymerization can be addition or condensation.

Addition polymers: polyethylene from ethene, PVC from vinyl chloride, polystyrene from styrene.

Condensation polymers: nylon and polyester form with loss of a small molecule such as water.

Natural polymers include cellulose, starch, proteins and natural rubber; synthetic polymers include polythene, PVC and bakelite.

Thermoplastics soften on heating and can be remoulded; thermosetting plastics set permanently and char on strong heating.

Cell theory: all living organisms are made of cells; the cell is the structural and functional unit of life; new cells arise from existing cells.

Prokaryotic cells lack a membrane-bound nucleus; eukaryotic cells have a nucleus and membrane-bound organelles.

Plant cells have a cellulose cell wall, chloroplasts and a large vacuole; animal cells lack these and have centrioles.

Nucleus contains chromosomes and controls cell activities; mitochondria release energy as ATP by aerobic respiration.

Chloroplasts carry out photosynthesis; ribosomes synthesize proteins; lysosomes contain digestive enzymes.

Cell membrane is selectively permeable; diffusion and osmosis move substances without energy input.

Mitosis produces two genetically identical diploid cells for growth and repair; meiosis produces four haploid gametes.

Osmosis: solvent moves through a selectively permeable membrane from higher water potential to lower water potential.

Photosynthesis: 6CO2 + 6H2O → C6H12O6 + 6O2, using chlorophyll and sunlight; occurs in chloroplasts.

Aerobic respiration releases more ATP than anaerobic respiration; anaerobic respiration in muscles produces lactic acid.

Xylem transports water and minerals upward; phloem transports food, mainly sucrose, in both directions.

The human excretory unit is the nephron; kidneys filter blood and form urine; dialysis removes wastes artificially.

Reflex action is a rapid involuntary response through a reflex arc; brain and spinal cord form the central nervous system.

Hormones are chemical messengers secreted by endocrine glands into blood and act on target organs.

Biotechnology uses living organisms or their parts to make products; examples include insulin, vaccines and antibiotics.

Tissue culture grows cells on sterile nutrient medium; genetic engineering transfers DNA between organisms.

Mendel's law of dominance: in a heterozygote, the dominant allele masks the recessive allele.

Law of segregation: two alleles of a gene separate during gamete formation, so each gamete carries one allele.

Law of independent assortment: alleles of different genes assort independently during gamete formation when genes are on different chromosomes.

Genotype is genetic makeup (TT, Tt, tt); phenotype is observable trait; homozygous has identical alleles, heterozygous has different alleles.

DNA carries hereditary information; a gene is a segment of DNA; chromosomes are packaged DNA-protein structures.

Human sex determination: XX female, XY male; the father's sperm determines the offspring's sex.

Evolution is change in inherited traits of populations over generations; Darwin proposed natural selection.

Homologous organs have similar structure but different functions; analogous organs have different structure but similar functions; both indicate evolution.

Binomial nomenclature uses genus and species; classification order is kingdom, phylum, class, order, family, genus, species.

Ecosystem includes the biotic community and abiotic factors; producers, consumers and decomposers form trophic levels.

Food chain transfers energy; only about 10% of energy passes to the next trophic level.

Biogeochemical cycles include carbon, nitrogen, water and oxygen cycles; decomposers return nutrients to soil.

Greenhouse gases include CO2, methane, nitrous oxide and water vapour; they trap infrared radiation and cause global warming.

Ozone layer absorbs ultraviolet radiation; CFCs destroy ozone in the stratosphere.

Biomagnification increases concentration of non-biodegradable pollutants at higher trophic levels.

Waste management hierarchy: reduce, reuse, recycle; segregation at source improves composting and recycling.

Biodiversity conservation includes national parks, wildlife sanctuaries, biosphere reserves and seed banks.

Sustainable development meets present needs without compromising future generations' ability to meet their needs.

Renewable energy sources include solar, wind, hydro, biomass, geothermal and tidal; fossil fuels are non-renewable.

Solar photovoltaic cells convert sunlight directly to electricity; solar water heaters use solar thermal energy.

Wind turbines convert kinetic energy of wind to electricity; hydroelectric plants convert potential energy of stored water.

Biogas is produced by anaerobic digestion of organic waste and contains mainly methane and carbon dioxide.

Energy conservation: use LED lamps, switch off unused appliances, use public transport and efficient appliances.

Earthquake terms: focus is underground origin; epicentre is surface point directly above; magnitude is measured on the Richter scale.

Disaster preparedness includes early warning, evacuation plans, first-aid kits, and safe construction practices.

Cyclone safety: move to a safe shelter, stay away from windows and the coast, and follow official warnings.

Flood management includes embankments, drainage improvement, afforestation and rainwater harvesting.