VITEEE flashcards

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

Quadratic formula

For ax² + bx + c = 0 with a ≠ 0, x = [−b ± √(b² − 4ac)]/(2a). The discriminant b² − 4ac decides whether roots are real, equal, or complex.

Discriminant rule

For ax² + bx + c = 0, D = b² − 4ac. D > 0 gives two distinct real roots, D = 0 gives equal real roots, and D < 0 gives complex conjugate roots.

Derivative of sin x

The derivative of sin x with respect to x is cos x. For a composite sin(g(x)), the chain rule gives cos(g(x))·g′(x).

Integration by parts

∫u dv = uv − ∫v du. Choose u using the LIATE order (logarithmic, inverse trig, algebraic, trig, exponential) to simplify the remaining integral.

Mendelian monohybrid ratio

A cross between two heterozygotes (Tt × Tt) gives a phenotype ratio of 3 dominant : 1 recessive and a genotype ratio of 1 TT : 2 Tt : 1 tt.

Photosynthesis light reactions

In thylakoid membranes, photosystems use light to split water, release oxygen, and produce ATP and NADPH, which then power the Calvin cycle in the stroma.

Nephron reabsorption site

Most glucose, amino acids, and sodium are reabsorbed in the proximal convoluted tubule. The loop of Henle creates a medullary osmotic gradient for water reabsorption.

Ribosome function

Ribosomes translate mRNA into polypeptide chains. Free ribosomes make cytosolic proteins, while ribosomes on rough endoplasmic reticulum make proteins for secretion or membranes.

Equations of motion

For constant acceleration a: v = u + at, s = ut + ½at², and v² = u² + 2as, where u is initial velocity and v is final velocity.

Ohm's law

At constant temperature, the current through a conductor is directly proportional to the potential difference: V = IR, where R is resistance in ohms.

Simple pendulum period

For small oscillations, T = 2π√(l/g). The period depends on length and gravitational acceleration, not on the mass of the bob.

Coulomb's law

The force between two point charges is F = kq₁q₂/r², where k ≈ 9 × 10⁹ N·m²/C². Like charges repel; opposite charges attract.

Thin lens formula

1/f = 1/v − 1/u for a thin lens using the Cartesian sign convention. Focal length is positive for a converging convex lens.

Photoelectric equation

The maximum kinetic energy of emitted electrons is Kmax = hf − φ, where hf is photon energy and φ is the work function of the metal.

de Broglie wavelength

A particle of momentum p has wavelength λ = h/p. For an electron accelerated through voltage V, λ ≈ 1.227/√V nanometres.

Mole concept

One mole contains 6.022 × 10²³ particles and has mass equal to the molar mass in grams. At STP, one mole of ideal gas occupies 22.4 litres.

pH definition

pH = −log₁₀[H⁺]. A neutral aqueous solution at 25 °C has pH 7; pH below 7 is acidic and pH above 7 is basic.

Nernst equation

At 298 K, E = E° − (0.0591/n) log Q, where n is electrons transferred and Q is the reaction quotient. It corrects cell potential for non-standard concentrations.

Gibbs free energy

ΔG = ΔH − TΔS. A reaction is spontaneous at constant temperature and pressure when ΔG is negative; ΔG = 0 means the system is at equilibrium.

Markovnikov's rule

When HX adds to an unsymmetrical alkene, hydrogen attaches to the carbon with more hydrogens, and the halogen attaches to the more substituted carbon.

Le Chatelier's principle

If a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, the equilibrium shifts to oppose the change and restore equilibrium.

First-order half-life

For a first-order reaction, t½ = 0.693/k. Half-life is independent of initial concentration, unlike zero-order reactions where t½ = [A]₀/(2k).

Successive percentage change

For successive changes of a% and b%, net change = a + b + ab/100 percent. A 20% increase then a 10% decrease gives 1.2 × 0.9 = 1.08, an 8% net increase.

Average formula

Average = sum of observations ÷ number of observations. If every value is increased by k, the average rises by k; multiplying all values by k multiplies the average by k.

Relative speed

When two bodies move in opposite directions, relative speed is the sum of their speeds; in the same direction, it is the difference. Meeting time = distance ÷ relative speed.

Letter coding position

Alphabet positions run A = 1 to Z = 26. Reverse position = 27 − forward position. Coding questions often shift each letter by a fixed number of places.

Syllogism Venn method

Draw circles for each category. A conclusion is valid only if it must be true in every possible diagram consistent with the given statements.

Blood relation decoding

Decode symbols first: father's sister is aunt, mother's brother is uncle, brother's son is nephew. Build a family tree before answering relationship questions.

Subject-verb agreement

A singular subject takes a singular verb and a plural subject takes a plural verb. Phrases between subject and verb, such as 'along with', do not change verb number.

Present perfect with since

Use present perfect (has/have + past participle) with 'since' for a starting point and 'for' for a duration: She has worked here since 2019.

Active to passive

Move the object to subject position, use the correct form of 'be' plus the past participle, and add 'by' plus the original subject when relevant.

Conditional sentences

First conditional uses if + present simple, will + base verb for real future possibilities. Second conditional uses if + past simple, would + base verb for unreal present situations.