MECEE-BL Nepal cheat sheet

Cell theory: all living organisms are made of cells, the cell is the basic unit of life, and all cells arise from pre-existing cells by division.

Mitosis produces two genetically identical diploid daughter cells; meiosis produces four genetically distinct haploid cells through two divisions.

DNA base pairing: adenine pairs with thymine (two hydrogen bonds), guanine pairs with cytosine (three hydrogen bonds).

Mendel's law of segregation: the two alleles of a gene separate during gamete formation, so each gamete carries only one allele.

Photosynthesis light reaction occurs in the thylakoid membrane and produces ATP and NADPH; the Calvin cycle fixes CO2 in the stroma.

Human blood groups follow ABO codominance: IA and IB are codominant, and both are dominant over i (O).

Enzymes lower activation energy without altering the equilibrium constant; they are not consumed in the reaction they catalyse.

Binomial nomenclature gives each species a two-part Latin name: genus capitalised, species lowercase, both italicised.

Mole concept: one mole contains 6.022 x 10^23 particles; moles = mass in grams / molar mass.

Ideal gas equation PV = nRT, with R = 0.0821 L atm mol^-1 K^-1 or 8.314 J mol^-1 K^-1.

pH = -log[H+]; for a strong monoprotic acid pH equals -log of its concentration, and pH + pOH = 14 at 25 degrees C.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons (decrease in oxidation number).

Le Chatelier's principle: increasing pressure shifts equilibrium toward the side with fewer moles of gas; increasing temperature favours the endothermic direction.

Molarity = moles of solute / volume of solution in litres; dilution follows M1V1 = M2V2.

Alkanes follow CnH2n+2, alkenes and cycloalkanes CnH2n, and alkynes CnH2n-2.

Bond order from molecular orbital theory = (bonding electrons - antibonding electrons) / 2.

Kinematics: v = u + at, s = ut + (1/2)at^2, and v^2 = u^2 + 2as, valid for constant acceleration only.

Newton's second law: net force equals rate of change of momentum, F = ma when mass is constant.

Work-energy theorem: net work done equals change in kinetic energy, W = (1/2)mv^2 - (1/2)mu^2.

Ohm's law V = IR; resistors in series add, and in parallel 1/R = 1/R1 + 1/R2.

Snell's law: n1 sin(theta1) = n2 sin(theta2); total internal reflection occurs only when light travels from denser to rarer medium beyond the critical angle.

Lens and mirror formula 1/f = 1/v + 1/u, with magnification m = -v/u for mirrors and m = v/u for lenses (sign conventions applied).

Period of a simple pendulum T = 2 pi sqrt(L/g), independent of the bob mass for small oscillations.

Half-life relation for radioactive decay: N = N0 (1/2)^(t/T), and activity A = lambda N.

Quadratic formula: roots of ax^2 + bx + c = 0 are x = [-b +/- sqrt(b^2 - 4ac)] / (2a); the discriminant b^2 - 4ac decides real, equal, or complex roots.

Sum of roots = -b/a and product of roots = c/a for a quadratic ax^2 + bx + c = 0.

Arithmetic progression: nth term a + (n-1)d, sum of n terms (n/2)[2a + (n-1)d].

Geometric progression: nth term ar^(n-1), sum of n terms a(r^n - 1)/(r - 1) for r not equal to 1; infinite sum a/(1-r) when |r| < 1.

Derivative rules: d/dx(x^n) = nx^(n-1), product rule (uv)' = u'v + uv', quotient rule (u/v)' = (u'v - uv')/v^2.

Integration by parts: integral u dv = uv - integral v du; choose u by the ILATE order (inverse, log, algebraic, trig, exponential).

Binomial theorem: (a + b)^n = sum from r=0 to n of C(n,r) a^(n-r) b^r.

Distance between points (x1,y1) and (x2,y2) is sqrt[(x2-x1)^2 + (y2-y1)^2]; slope m = (y2-y1)/(x2-x1).

Number series: check successive differences first, then ratios, then alternating or two interleaved series before trying squares and cubes.

Letter series: convert letters to positions A=1 to Z=26; a jump of +5 then -2 repeating signals an alternating pattern.

Coding-decoding: test a fixed shift, then reversal, then letter-position arithmetic; verify the rule on every given pair before applying it.

Blood relations: draw a family tree with gender symbols; 'brother of my father' is uncle, 'daughter of my sister' is niece.

Direction sense: fix north upward, track net displacement with vectors, and use Pythagoras for shortest distance after turns.

Clock problems: angle between hands = |30H - 5.5M| degrees; hands coincide 11 times in 12 hours.

Calendar: a normal year shifts the weekday by 1 day, a leap year by 2; century years are leap only if divisible by 400.

Ratio and average shortcuts: if a quantity is increased by x% then decreased by x%, the net change is a decrease of x^2/100 percent.

The human heart has four chambers; oxygenated blood returns via pulmonary veins to the left atrium and leaves the left ventricle through the aorta.

Normal adult resting heart rate is about 60-100 beats per minute; normal body temperature is about 37 degrees C (98.6 F).

Blood components: plasma, red blood cells (haemoglobin, oxygen transport), white blood cells (immunity), and platelets (clotting).

Deficiency diseases: vitamin C causes scurvy, vitamin D causes rickets, iodine deficiency causes goitre, and iron deficiency causes anaemia.

Vaccines produce active acquired immunity by stimulating antibody formation without causing the disease.

Nepal facts: Mount Everest (Sagarmatha) at 8,848.86 m, capital Kathmandu, and the Constitution of Nepal promulgated in 2015.

World Health Organization defines health as complete physical, mental, and social well-being, not merely absence of disease.

Vector-borne diseases: malaria is transmitted by female Anopheles mosquitoes and dengue by Aedes aegypti.