Class 12 questions with answers

15 questions · Flower as the reproductive structure of angiosperms · Ovule, megasporogenesis, and female gametophyte · Agents of pollination and floral adaptations · Anther, microsporogenesis, and male gametophyte · Modes of pollination and outbreeding devices · Pollen-pistil interaction and controlled hybridisation · Double fertilisation, syngamy, and triple fusion · Endosperm and embryo development · Seeds, fruits, dormancy, and germination · Apomixis, polyembryony, and hybrid-seed value

15 questions · Male reproductive system and sperm transport · Female reproductive system and mammary glands · Spermatogenesis and sperm structure · Menstrual cycle and hormonal coordination · Oogenesis, follicular growth, and ovulation · Cleavage, blastocyst formation, and implantation · Fertilisation and prevention of polyspermy · Pregnancy, placenta, and embryonic development · Parturition and neuroendocrine control · Lactation and colostrum

15 questions · Reproductive health, education, and public-health strategy · Population growth and stabilisation · Natural contraceptive methods · Barrier methods and intrauterine devices · Hormonal and emergency contraception · Surgical contraception · Medical termination of pregnancy · Sexually transmitted infections · Assisted reproductive technologies · Infertility and clinical evaluation

15 questions · Law of segregation and test crosses · Mendelian experiments, monohybrid crosses, and dominance · Incomplete dominance, codominance, and multiple alleles · Dihybrid crosses and independent assortment · Chromosomal theory, linkage, and recombination · Polygenic inheritance and pleiotropy · Sex determination systems · Mutation and mutagens · Pedigree analysis and Mendelian disorders · Chromosomal disorders and nondisjunction

15 questions · DNA and RNA polynucleotide structure · DNA packaging in prokaryotes and eukaryotes · Experimental identification of genetic material and RNA world · Semiconservative DNA replication · Transcription units and RNA processing · Genetic code and coding mutations · tRNA, ribosomes, and translation · Regulation of gene expression and lac operon · Human Genome Project and genome features · DNA fingerprinting and VNTR polymorphism

15 questions · Major transitions in the history of life · Origin of life and chemical evolution · Evidence from fossils, homology and analogy · Adaptive radiation and convergent evolution · Darwinian natural selection and fitness · Evolutionary forces and modes of selection · Natural selection observed in real time · Mutation, variation and speciation · Hardy-Weinberg genetic equilibrium · Origin and evolution of humans

15 questions · Common bacterial and viral infections · Health, disease and host factors · Malaria and vector-borne disease · Innate immunity and barriers · Acquired humoral and cell-mediated immunity · Vaccination and passive immunity · Allergy and autoimmunity · HIV infection and AIDS · Cancer, detection and treatment · Drug and alcohol dependence

15 questions · Microbes in household food production · Industrial fermentation products · Antibiotics and responsible use · Activated sludge and anaerobic digestion · Methanogens and renewable energy · Microbial biocontrol · Primary and secondary sewage treatment · Scaling microbial welfare processes · Biofertilisers and nitrogen fixation · Mycorrhiza and plant benefit

15 questions · Core principles of biotechnology · Gel electrophoresis and elution · Restriction enzymes and recognition sites · Cloning-vector architecture · Competent hosts and DNA uptake · DNA isolation and controlled cutting · Polymerase chain reaction · Bioreactor design and control · Downstream processing and quality · Ligation, transformation and screening

15 questions · Bt crops and insect specificity · GM agriculture: benefits and limits · RNA interference · Recombinant human insulin · Gene therapy for ADA deficiency · Molecular diagnosis · Transgenic animals · Biosafety and ethical evaluation · Biopatents and biopiracy · Recombinant therapeutics and vaccines

15 questions · Exponential and logistic growth · Organisms and abiotic environment · Adaptations to deserts and extremes · Density dependence and population regulation · Population attributes · Life-history strategies · Competition and predation · Parasitism and host relations · Mutualism and commensalism · Regulation, conformity, migration and suspension

15 questions · Ecosystem structure and components · Carbon cycle · Primary productivity · Decomposition process and controls · Food chains and food webs · Ecological pyramids · Energy flow and transfer efficiency · Ecological succession · Phosphorus cycle · Ecosystem services

15 questions · Biodiversity, productivity and stability · Latitudinal and species-area patterns · Levels of biodiversity · Extinction rates and the current crisis · Habitat loss and fragmentation · Overexploitation, invasions and coextinction · Ex-situ conservation · In-situ conservation and hotspots · Conservation decisions and global cooperation · Sacred groves and community stewardship

15 questions · Types of solutions and concentration measures · Solubility and Henry's law for gases · Raoult's law and vapour pressure of liquid solutions · Ideal solutions, non-ideal deviations, and azeotropes · Colligative properties and relative lowering of vapour pressure · Depression of freezing point and molar-mass calculation · Elevation of boiling point and molar-mass calculation · Osmosis, osmotic pressure, tonicity, and reverse osmosis · Abnormal molar masses and the van't Hoff factor

15 questions · Electrochemical cells, electrode processes, and cell notation · Electrochemical corrosion and its prevention · Standard electrode potentials and the electrochemical series · Nernst equation, Gibbs energy, and equilibrium · Conductivity, conductance, cell constant, and dilution trends · Kohlrausch law and ionic-conductivity applications · Electrolysis and Faraday laws · Primary cells, secondary batteries, and fuel cells

15 questions · Reaction rate and stoichiometric rate expression · Rate law, order, and molecularity · Arrhenius equation and catalysis · Integrated rate equations and half-life · Collision theory and effective collisions

15 questions · Position and electronic configuration of d-block elements · Physical properties and variable oxidation states · Potassium dichromate chemistry · Potassium permanganate chemistry · Actinoids and comparison with lanthanoids · Lanthanoids and lanthanoid contraction

15 questions · Werner theory and coordination terminology · Nomenclature and formulae of coordination compounds · Valence bond theory and magnetic behaviour · Crystal-field splitting, colour, and spin · Metal carbonyls, stability, and applications · Structural and stereoisomerism

15 questions · Classification, nomenclature, and the carbon–halogen bond · Preparation of haloalkanes and haloarenes · Nucleophilic substitution and stereochemistry · Elimination, organometallic formation, and coupling · Haloarene reactivity and orientation · Polyhalogen compounds and environmental effects

15 questions · Classification, nomenclature, and structure · Commercial alcohols and safe application · Preparation of alcohols · Phenol acidity, preparation, and electrophilic substitution · Reactions and oxidation of alcohols · Ether preparation and cleavage

15 questions · Carbonyl nomenclature, structure, and physical properties · Carboxylic-acid preparation, acidity, and reactions · Preparation of aldehydes and ketones · Nucleophilic addition and carbonyl derivatives · Oxidation, reduction, and distinguishing tests · Alpha-hydrogen reactions and disproportionation

15 questions · Amine classification, structure, nomenclature, and basicity · Preparation of amines · Chemical reactions and tests of amines · Diazonium salts: preparation and replacement reactions · Azo coupling and synthetic applications

15 questions · Carbohydrate classification and structure · Amino acids and protein structure · Enzymes and biochemical catalysis · Vitamins and deficiency · Nucleic acids and genetic information · Hormones and chemical signalling

15 questions, 1 with pictures · A relation is a set of ordered pairs · Counting relations and extending one to a required type · Reflexive relations · Symmetric relations · Transitive relations · Equivalence classes and the partition they create · Equivalence relations: all three properties together · One-one (injective) functions · Onto (surjective) functions and choosing the codomain · Bijections, and what changes on a finite set · Composition of functions and invertibility

15 questions, 2 with pictures · Evaluating a sum or difference of several principal values · Evaluating a trigonometric function applied to an inverse trigonometric value · Reading and identifying the graph of an inverse trigonometric function · Simplifying $\sin^{-1}(\sin x)$ and its relatives when $x$ is outside the branch · The domain and principal value branch of each inverse trigonometric function · Finding the principal value of a single inverse trigonometric ratio · Why a trigonometric function needs a restricted domain before it has an inverse · Finding the domain of an expression built on an inverse trigonometric function · Finding the range of an inverse function that has been scaled or shifted · Writing an inverse trigonometric expression in its simplest form by substitution · Solving an equation or inequality that contains inverse trigonometric functions

15 questions, 2 with pictures · Computing a matrix product: row against column · Constructing a matrix from a rule $a_{ij} = f(i, j)$ · Solving a matrix equation for an unknown matrix · What a matrix is: its order, its element count and the entry $a_{ij}$ · Adding, subtracting and scaling matrices · Equality of matrices, and the system of equations it produces · Types of matrices: row, column, square, diagonal, scalar, identity and zero · Powers of a matrix and equations such as $A^2 - kA + mI = O$ · Properties of matrix multiplication: what carries over from numbers and what does not · Transpose of a matrix and its properties · When a matrix product is defined, and the order of the result · Building symmetric and skew symmetric matrices, and splitting a square matrix into its two parts · Symmetric and skew symmetric matrices · Invertible matrices

15 questions · Collinear points and the line through two points, by determinant · Reading a zero determinant off the shape of the array · Rules the inverse obeys: products, scalars, sums and determinants · Singular or not: when $A^{-1}$ exists and how the adjoint gives it · What a determinant is, and the rule for a $2 \times 2$ · Expanding a $3 \times 3$ determinant along a row or a column · What scaling a matrix and multiplying matrices do to the determinant · Finding an unknown when a determinant is given a value · The area of a triangle as a determinant · A row against its own cofactors, and against another row's · Minors and cofactors of the elements of a determinant · The adjoint of a matrix and the identity $A(\text{adj }A) = |A|I$ · Getting $A^{-1}$ out of an equation that $A$ satisfies · Deciding whether a system is consistent · Solving a system of equations by the matrix method

15 questions · What it means for a function to be differentiable at a point · Building continuous functions: sums, quotients and composites · Choosing the constant that makes a function continuous · Differentiable implies continuous, and why the converse fails · What it means for a function to be continuous at a point · Where a function is discontinuous, and where the question does not arise · Differentiating a curve given through a parameter · The chain rule for a composite function · Derivatives of the inverse trigonometric functions · Differentiating a relation that is not solved for $y$ · Testing a function where its formula changes · The exponential and the logarithm: domains, graphs and laws · Logarithmic differentiation for a variable base and a variable exponent · The second order derivative and relations it satisfies · Differentiating $e^x$, $\log x$ and what is built from them

15 questions, 1 with pictures · Optimisation of a geometric quantity: boxes, rectangles, cylinders, cones and distances · The derivative as the rate of change of one quantity with respect to another · Two quantities changing with time: related rates through the Chain Rule · Two rates linked through a third: eliminating the intermediate rate · Finding the intervals on which a function increases or decreases · Functions with a gap in the domain: increasing on each piece, not across the gap · Increasing and decreasing on a bounded interval: the trigonometric cases · Finding the values of a parameter for which a function is increasing or decreasing · Increasing and decreasing functions, and the sign of the derivative · Local maxima and minima, and the critical points where they can occur · The first derivative test: reading the sign change of $f'$ through a critical point · The second derivative test, and what to do when it fails · Absolute maximum and minimum values on a closed interval · Maximum and minimum values of a function, and when they do not exist · Optimisation: two numbers with a fixed sum, and cost, revenue and profit

15 questions · Integration as the inverse of differentiation: the standard table, the constant of integration, and the algebra done before integrating · Integration by parts: choosing the first function, the second-function integral without a constant, and the loop that returns the original integral · Properties $P_5$-$P_7$: even and odd functions on $[-a, a]$, and $\int_0^{2a}$ in terms of $f(2a - x)$ · Substituting the inner function: linear arguments, composite arguments, and the change of variable $dx = g'(t)\,dt$ · Substitution when the derivative of the inside function is present: the $\int \frac{f'(x)}{f(x)}dx$ and $\int [f(x)]^n f'(x)\,dx$ forms · The form $\int e^x[f(x) + f'(x)]\,dx = e^x f(x) + C$: splitting the bracket into a function and its derivative · Properties $P_0$-$P_2$ and integrands with a modulus: split the interval where the expression changes sign · Substitution in a definite integral: change the limits with the variable and never return to $x$ · Substitutions that clear a radical or a fractional power: $x + 2 = t^2$, $x = t^6$, $t = \frac{1}{x}$, and rationalising · Properties $P_3$ and $P_4$: replacing $x$ by $a + b - x$ (or $a - x$), and adding the two forms of $I$ · Reducing even powers, cubes and products of sines and cosines with the double-angle, triple-angle and product-to-sum identities · A linear numerator over a quadratic or its root: $px + q = A\frac{d}{dx}(ax^2 + bx + c) + B$ · An identity that turns a trigonometric quotient or root into a standard form: half angles, $1 \pm \sin 2x$ as a perfect square, $\sec^2 - 1$, and $\sec^2 + \operatorname{cosec}^2$ splits · Completing the square: $\int \frac{dx}{ax^2 + bx + c}$ and $\int \frac{dx}{\sqrt{ax^2 + bx + c}}$ reduced to the standard forms · The six standard integrals of Section 7.4 and their use with a scaled or substituted variable

15 questions · Area of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ by integration: $\frac{4b}{a}\int_0^a\sqrt{a^2 - x^2}\,dx = \pi ab$ · Area under a curve by vertical strips: $A = \int_a^b y\,dx$ between two ordinates · Area with horizontal strips: $A = \int_c^d x\,dy$ when the region is bounded by the $y$-axis and $y = c$, $y = d$ · A region bounded by a line and a curve, or described by inequalities: intersection points, then upper boundary minus lower on each piece · Regions below the $x$-axis: the integral is negative there, so the area is $|A_1| + A_2$ split at the crossing · Area of a circle and of its parts by integration: $4\int_0^a\sqrt{a^2 - x^2}\,dx = \pi a^2$ · Using the symmetry of a region: integrate one congruent piece and multiply by their number · Area under a modulus graph $y = |x + a|$ or $y = c + |x + a|$: write the V piecewise and cut at its vertex

15 questions · Degree of a differential equation: defined only when it is a polynomial in the derivatives, and then the power of the highest-order derivative · Order of a differential equation: the order of the highest-order derivative present, whatever surrounds it · Particular solutions of separable equations: fix the constant from the given condition after integrating, and translate a slope condition into the equation of a curve · Solutions of a differential equation: a function that satisfies it; the general solution carries as many arbitrary constants as the order, a particular solution none · Variables separable: $\frac{dy}{dx} = g(x)\,h(y)$ becomes $\int\frac{dy}{h(y)} = \int g(x)\,dx$, and the general solution is $H(y) = G(x) + C$ · A rate proportional to the quantity: $\frac{dP}{dt} = kP$ and its relatives -- continuous interest, bacteria, cooling, a changing volume · Homogeneous functions of degree $n$ -- $F(\lambda x, \lambda y) = \lambda^n F(x, y)$ -- and the homogeneous differential equation $\frac{dy}{dx} = g\left(\frac{y}{x}\right)$ · Solving a homogeneous equation: $y = vx$ gives $\frac{dy}{dx} = v + x\frac{dv}{dx}$, then $\frac{dv}{g(v) - v} = \frac{dx}{x}$, integrate, and put back $v = \frac{y}{x}$ · First order linear equations $\frac{dy}{dx} + Py = Q$ and $\frac{dx}{dy} + P_1x = Q_1$: reading $P$ from the standard form and the integrating factor $e^{\int P\,dx}$ · Solving a linear equation: $y\,(\text{I.F.}) = \int Q\,(\text{I.F.})\,dx + C$, then divide through by the integrating factor, constant included

15 questions · Multiplying a vector by a scalar: the magnitude of lambda a, collinear vectors and collinear points · Component form, the magnitude of a vector and the vector joining two points · The vector product in components (the determinant) and a unit vector perpendicular to two given vectors · Unit vectors, direction cosines and ratios, and a vector of a given magnitude along a direction · The section formula: internal and external division, midpoints and points on a produced segment · Magnitudes and angles from dot-product identities: expanding |a + b|^2, (a + b).(a - b) and three vectors summing to zero · Perpendicular vectors: the zero dot product test and solving for an unknown from a dot-product condition · Scalars and vectors; zero, unit, coinitial, collinear, equal and negative vectors · The scalar (dot) product: definition, component formula, the angle between two vectors and its bounds · The vector (cross) product: definition, right-hand rule, non-commutativity, unit-vector products and the Lagrange identity · Projection of a vector on another: the scalar formula, the projection vector and projections along a line or an axis · Areas of triangles and parallelograms from the vector product: sides, diagonals and vertices · The triangle and parallelogram laws: sums of sides, medians, diagonals and resultants

15 questions · Direction angles and direction cosines of a line; $l^2 + m^2 + n^2 = 1$ · Direction ratios; direction cosines from direction ratios and from a Cartesian equation · The angle between two lines; the conditions for perpendicular and for parallel lines · Equation of a line through a point in a given direction: vector, Cartesian and parametric forms · The image (reflection) of a point in a line and the line joining a point to its image · The line through two points: direction ratios, direction cosines, collinear points and points on a segment · Parallel, intersecting and skew lines; finding the point of intersection · The shortest distance between two skew lines and between two parallel lines · A line perpendicular to two given lines: the cross product of their directions · The foot of the perpendicular from a point on a coordinate axis and the distance of the point from the axis · The foot of the perpendicular from a point to a line and the perpendicular distance · Finding a point on a line: the general point, a distance condition, a coordinate condition

15 questions, 2 with pictures · Linear programming problems and their mathematical formulation · The Corner Point Method on a bounded feasible region · The feasible region: graphing the constraints, corner points and boundedness · Unbounded feasible regions and the open half-plane test · Multiple optimal solutions and conditions on the objective coefficients

15 questions, 1 with pictures · Bayes' theorem and reversing a conditional probability · Computing a conditional probability inside a listed sample space · Conditional probability and its defining formula · Properties of conditional probability · The multiplication rule for the probability of a joint event · Complements, "at least one", and repeated independent trials · Independent events and the product rule · Independent events are not mutually exclusive events · A partition of a sample space · The theorem of total probability · A random variable and the values it takes

15 questions, 2 with pictures · Charge quantisation and counting carriers · Charging, conduction and charge conservation · Coulomb force and inverse-square comparisons · Vector superposition and symmetry · Electric field, test charge and particle motion · Meaning and consistency of electric field lines · Oriented area and electric flux · Axial and equatorial dipole fields · Electric dipole moment and its direction · A dipole in a uniform electric field · Continuous charge distributions · Gauss law for spherical charge distributions · Gauss law: enclosed charge, net flux and symmetry · Gauss law for a plane sheet and parallel sheets · Gauss law for an infinite charged wire

15 questions, 2 with pictures · Potential of an isolated point charge · Scalar addition and zero-potential locations · Stored energy and electric energy density · Potential difference, work and charge sign · Connected and isolated capacitor changes · Equipotentials and the potential gradient · Dipole potential and the zero-potential plane · Interaction energy and dipole orientation · Conductors, charge redistribution and shielding · Dielectrics and bound-charge polarisation · Partial dielectric and metallic slabs · Capacitance and the charge on a capacitor · Parallel-plate geometry and capacitance · Series and parallel capacitor networks · Charge sharing and loss of capacitor energy

15 questions, 1 with pictures · Charge flow and conventional current · Resistance, resistivity and wire geometry · Drift speed, current density and continuity · Microscopic conduction and mobility · Ohmic behaviour and graph interpretation · Temperature dependence of resistance · Electrical power, energy and rated appliances · Combinations of real cells · Emf, terminal voltage and internal resistance · Series and parallel resistor networks · Kirchhoff rules and signed branch currents · Wheatstone bridge balance

15 questions, 1 with pictures · Force on a current-carrying conductor · Magnetic and Lorentz forces · Circular and helical motion · Circular-coil fields and superposition · Ampere law and straight-wire fields · Biot–Savart law and source-element geometry · Long-solenoid magnetic field · Force between parallel currents · Magnetic moment and torque of a loop · Moving-coil galvanometer and meter conversion

15 questions, 1 with pictures · Magnetic Gauss law and absence of monopoles · Magnetic poles and field-line meaning · Far axial and equatorial dipole fields · Torque and force on a magnetic dipole · Magnetic potential energy, equilibrium and work · Magnetisation and magnetic intensity · Susceptibility, permeability and classification · Diamagnetic response and perfect diamagnetism · Paramagnetic moments and thermal disorder · Domains, remanence and temperature

15 questions, 1 with pictures · Magnetic flux and oriented area · Faraday law: rates, turns and transported charge · Induced emf versus closed-circuit current · Lenz law and energy conservation · Motional emf in translating and rotating conductors · Mutual inductance and shared magnetic flux · Self-induction and solenoid geometry · Magnetic energy of an inductor · AC generator amplitude, phase and rotation

15 questions, 1 with pictures · Sinusoidal current, effective values and resistor heating · Ideal capacitor: phase and frequency response · Ideal inductor: phase and frequency response · Series LCR impedance and phasor addition · Series resonance and natural angular frequency · Average power, wattless current and power factor · Transformers, energy conservation and transmission

15 questions, 3 with pictures · Displacement current and time-varying electric flux · Radiation sources and propagation without matter · Transverse field directions and phase · Vacuum speed and passage into a medium · Wave amplitudes, frequency and wave number · Energy sharing, intensity and radiation momentum · Infrared and ultraviolet sources, absorption and uses · Spectrum ordering, photon energy and overlapping bands · Radio waves, microwaves and directional beams · X-ray and gamma-ray production and applications · Ampere-Maxwell continuity and capacitor geometry

15 questions, 2 with pictures · Reflection and the local normal · Refracting telescope in normal adjustment · Refraction at a spherical interface · Spherical mirrors and Cartesian image signs · Apparent depth and plane parallel slabs · Refractive index, speed and frequency · Critical angle, escape cone and optical fibres · Lens shape, curvature signs and surrounding medium · Thin lens imaging and virtual objects · Lens power and combinations in contact · Sequential imaging by separated lenses · Dispersion and wavelength dependence · Prism geometry and minimum deviation · Compound microscope and focal-plane tube length · Image formation and aperture

15 questions, 1 with pictures · Wavefronts, rays and Huygens construction · Wave refraction: speed, wavelength and frequency · Coherence and persistent interference · Initial phase and a plate in one path · Interference amplitudes, contrast and energy · Path difference and interference intensity · Coincident fringes of two wavelengths · Young experiment in a uniform medium · Young fringe width, angles and order · Single-slit diffraction and the central maximum · Polarisation, Malus law and transverse light

15 questions, 1 with pictures · Photocurrent, collection and intensity · Einstein energy balance and stopping potential · Photoelectric graph slopes and material thresholds · Surface escape, threshold and prompt photoemission · Photon energy, momentum and photon flux · de Broglie wavelength and mechanical state · Matter-wave evidence and macroscopic limits

15 questions, 1 with pictures · Evidence for the nuclear atom · Head-on distance of closest approach · Impact parameter and scattering angle · Classical instability and Bohr stationary states · Bohr radii and unequal radial spacing · Quantised angular momentum · Speed and period of orbital revolution · Kinetic, potential and total atomic energy · Photon energy and transition comparisons · Hydrogen spectral series and line counts · Selective absorption and excitation thresholds · de Broglie standing-wave condition · Limits of the Bohr model

15 questions, 1 with pictures · Atomic versus nuclear masses · Nuclide composition and related species · Nuclear radius and density · Mass defect and binding energy · Mass-energy balance and reaction Q · Binding energy per nucleon and the curve · Short-range nuclear force and potential energy · Nuclear decay and particle bookkeeping · Fission, fusion and binding-energy gains · Coulomb barrier for light-nucleus fusion · Counting nuclear events and macroscopic energy

15 questions, 2 with pictures · Energy bands and material classification · Electron-hole pairs, conventional currents and temperature · Donors, acceptors, neutrality and carrier equilibrium · Diffusion, depletion ions and equilibrium drift · Bias polarity, barrier width and reverse current · Diode characteristics and circuit models · Half-wave and full-wave rectification and capacitor filtering