# CBSE Class 12 Board Exam (Science Stream NCERT): Electrostatics, Optics, Coordination Compounds, Name Reactions, Molecular Basis of Inheritance & Calculus

> High-yield NCERT Class 12 Science Stream (Physics, Chemistry, Biology, Mathematics) flashcards covering Gauss's Law, Optics, Electrochemistry, Coordination Compounds, Organic Name Reactions, Molecular Genetics, and Calculus.

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- **Total Cards:** 32

## Flashcards (32 Cards)

| # | Front (Term / Prompt) | Back (Definition / Answer) | Example | Multiple-Choice Options |
| :--- | :--- | :--- | :--- | :--- |
| 1 | In Current Electricity, what are the drift velocity relation I = n*e*A*v_d, Kirchhoff's Two Rules, and the Wheatstone Bridge balance condition? | Current I = n*e*A*v_d, where drift velocity v_d = (e*E/m)*tau and mobility mu = v_d / E = e*tau/m. Kirchhoff's First Rule (Junction Rule): Sum of currents at a node = 0 (Conservation of Charge). Kirchhoff's Second Rule (Loop Rule): Algebraic sum of changes in potential around a closed loop = 0 (Conservation of Energy). Balanced Wheatstone Bridge (I_g = 0): P / Q = R / S. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Intrinsic semiconductor (pure Si/Ge): n_e = n_h = n_i.; B) Rosenmund Reduction: R-COCl + H2 (Pd-BaSO4) -> R-CHO; Stephen: R-CN + SnCl2/HCl -> R-CHO; Etard: Toluene + CrO2Cl2 -> Benzaldehyde; Clemmensen Reduction: >C=O + Zn-Hg / conc.; C) Current I = n*e*A*v_d, where drift velocity v_d = (e*E/m)*tau and mobility mu = v_d / E = e*tau/m. Kirchhoff's First Rule (Junction Rule): Sum of currents at a node = 0 (Conservation of Charge). Kirchhoff's Second Rule (Loop Rule): Algebraic sum of changes in potential around a closed loop = 0 (Conservation of Energy). Balanced Wheatstone Bridge (I_g = 0): P / Q = R / S. ✓; D) Every differentiable function is continuous, but a continuous function need not be differentiable (e.g., f(x) = \|x\| at x = 0). |
| 2 | In Class 12 Physics (Electrostatics), state Gauss's Law and give the electric field expressions for an infinite line charge, an infinite plane sheet, and a thin spherical shell. | Gauss's Law: Total electric flux through any closed surface S is Phi_E = oint E . dA = q_enclosed / epsilon_0. Applications: 1) Infinite line charge (linear charge density lambda): E = lambda / (2*pi*epsilon_0*r); 2) Infinite thin plane sheet (surface density sigma): E = sigma / (2*epsilon_0) (independent of distance r); 3) Thin spherical shell of radius R: E = kQ / r^2 for r >= R, and E = 0 inside the shell (r < R). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Faraday-Lenz Law: Induced EMF e = -N * (dPhi_B / dt), where the negative sign (Lenz's Law) obeys Conservation of Energy.; B) Spectrochemical Series (increasing crystal field splitting Delta_0): I- < Br- < SCN- < Cl- < F- < OH- < H2O < NCS- < EDTA4- < NH3 < en < CN- < CO.; C) Restriction Endonucleases ('Molecular Scissors', e.g., EcoRI recognizes palindromic sequence 5'-GAATTC-3' and produces sticky ends).; D) Gauss's Law: Total electric flux through any closed surface S is Phi_E = oint E . dA = q_enclosed / epsilon_0. Applications: 1) Infinite line charge (linear charge density lambda): E = lambda / (2*pi*epsilon_0*r); 2) Infinite thin plane sheet (surface density sigma): E = sigma / (2*epsilon_0) (independent of distance r); 3) Thin spherical shell of radius R: E = kQ / r^2 for r >= R, and E = 0 inside the shell (r < R). ✓ |
| 3 | How does the capacitance of a parallel-plate capacitor change when a dielectric slab of constant K is inserted with the battery disconnected vs remains connected? | Initial Capacitance C_0 = epsilon_0 * A / d. With dielectric (C = K * C_0): 1) Battery Disconnected (Charge Q remains constant): C becomes K*C_0, Voltage V = V_0/K, Electric Field E = E_0/K, and Stored Energy U = U_0/K (decreases). 2) Battery Connected (Voltage V remains constant): C becomes K*C_0, Charge Q = K*Q_0, Electric Field E = E_0, and Stored Energy U = K*U_0 (increases). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Einstein's Photoelectric Equation: K_max = e*V_0 = h*nu - phi_0 = h*(nu - nu_0) (stopping potential V_0 depends on frequency nu, NOT intensity).; B) Finkelstein: R-X + NaI (in dry acetone) -> R-I + NaX; Swarts: R-Br + AgF -> R-F; Wurtz: 2 R-X + 2 Na (dry ether) -> R-R; Reimer-Tiemann Reaction: Phenol + CHCl3 + aq.; C) Initial Capacitance C_0 = epsilon_0 * A / d. With dielectric (C = K * C_0): 1) Battery Disconnected (Charge Q remains constant): C becomes K*C_0, Voltage V = V_0/K, Electric Field E = E_0/K, and Stored Energy U = U_0/K (decreases). 2) Battery Connected (Voltage V remains constant): C becomes K*C_0, Charge Q = K*Q_0, Electric Field E = E_0, and Stored Energy U = K*U_0 (increases). ✓; D) For \|A\| = n: Total relations = 2^(n^2); Reflexive relations = 2^(n(n-1)); Symmetric relations = 2^(n(n+1)/2). |
| 4 | In Class 12 Differential Calculus, what are the conditions for Continuity, Differentiability, Rolle's Theorem, Lagrange's Mean Value Theorem (LMVT), and Second Derivative Test for Maxima/Minima? | Every differentiable function is continuous, but a continuous function need not be differentiable (e.g., f(x) = \|x\| at x = 0). LMVT: If f is continuous on [a, b] and differentiable on (a, b), there exists c in (a, b) such that f'(c) = [f(b) - f(a)] / (b - a) (Rolle's Theorem is the special case where f(a) = f(b) => f'(c) = 0). Second Derivative Test: If f'(c) = 0 and f''(c) < 0, then c is a point of Local Maximum; if f'(c) = 0 and f''(c) > 0, then c is a point of Local Minimum; if f''(c) = 0, the test fails (use First Derivative Test). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Python Immutable types: int, float, bool, str, tuple (cannot be modified in-place); Mutable types: list, dict, set.; B) Einstein's Photoelectric Equation: K_max = e*V_0 = h*nu - phi_0 = h*(nu - nu_0) (stopping potential V_0 depends on frequency nu, NOT intensity).; C) Lucas Test (conc. HCl + anhyd. ZnCl2 for 1°, 2°, 3° alcohols): 3° alcohol gives immediate turbidity, 2° in ~5 mins, 1° no turbidity at room temp. Tollens' Test (ammoniacal AgNO3 -> Silver Mirror):…; D) Every differentiable function is continuous, but a continuous function need not be differentiable (e.g., f(x) = \|x\| at x = 0). LMVT: If f is continuous on [a, b] and differentiable on (a, b), there exists c in (a, b) such that f'(c) = [f(b) - f(a)] / (b - a) (Rolle's Theorem is the special case where f(a) = f(b) => f'(c) = 0). Second Derivative Test: If f'(c) = 0 and f''(c) < 0, then c is a point of Local Maximum; if f'(c) = 0 and f''(c) > 0, then c is a point of Local Minimum; if f''(c) = 0, the test fails (use First Derivative Test). ✓ |
| 5 | In Semiconductor Electronics, compare Intrinsic vs Extrinsic (n-type and p-type) Semiconductors and Forward-Biased vs Reverse-Biased p-n Junction Diodes. | Intrinsic semiconductor (pure Si/Ge): n_e = n_h = n_i. Extrinsic: n-type (doped with pentavalent Group 15 donor impurities like P, As, Sb -> n_e >> n_h) vs p-type (doped with trivalent Group 13 acceptor impurities like B, Al, In, Ga -> n_h >> n_e), satisfying n_e * n_h = n_i^2. Forward Bias (p to +ve, n to -ve): Depletion layer width and barrier potential DECREASE, allowing large majority-carrier current (mA). Reverse Bias: Depletion layer widens, allowing only tiny minority saturation current (muA). Full-wave rectifier ripples at 2*f (100 Hz for 50 Hz AC input). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Intrinsic semiconductor (pure Si/Ge): n_e = n_h = n_i. Extrinsic: n-type (doped with pentavalent Group 15 donor impurities like P, As, Sb -> n_e >> n_h) vs p-type (doped with trivalent Group 13 acceptor impurities like B, Al, In, Ga -> n_h >> n_e), satisfying n_e * n_h = n_i^2. Forward Bias (p to +ve, n to -ve): Depletion layer width and barrier potential DECREASE, allowing large majority-carrier current (mA). Reverse Bias: Depletion layer widens, allowing only tiny minority saturation current (muA). Full-wave rectifier ripples at 2*f (100 Hz for 50 Hz AC input). ✓; B) Spectrochemical Series (increasing crystal field splitting Delta_0): I- < Br- < SCN- < Cl- < F- < OH- < H2O < NCS- < EDTA4- < NH3 < en < CN- < CO.; C) Griffith (1928): Transforming Principle using Streptococcus pneumoniae (R-strain & heat-killed S-strain in mice); Avery, MacLeod & McCarty (1944): Proved DNA is the transforming principle using…; D) Python Immutable types: int, float, bool, str, tuple (cannot be modified in-place); Mutable types: list, dict, set. |
| 6 | In Principles of Inheritance and Variation, state Mendel's Laws, compare Incomplete Dominance vs Codominance, and classify Mendelian vs Chromosomal Genetic Disorders. | Mendel's 3 Laws: Dominance, Segregation (universally valid without exceptions - purity of gametes), and Independent Assortment (applies to unlinked genes; T.H. Morgan studied Linkage & Recombination in Drosophila). Incomplete Dominance (Snapdragon Antirrhinum majus): Both phenotypic and genotypic F2 ratios are 1:2:1 (Red : Pink : White). Codominance: Human ABO blood group (IA and IB alleles are codominant over i, controlled by 3 alleles giving 6 genotypes and 4 phenotypes). Mendelian Disorders: Haemophilia & Colour Blindness (X-linked recessive), Sickle-Cell Anaemia (Autosomal recessive point mutation at 6th codon of beta-globin: GAG Glutamic acid -> GUG Valine), Phenylketonuria & Thalassemia (Autosomal recessive). Chromosomal Aneuploidy: Down's Syndrome (Trisomy of chromosome 21, 47 chromosomes), Klinefelter's Syndrome (47, XXY - gynecomastia, sterile male), Turner's Syndrome (45, XO - rudimentary ovaries, sterile female). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) For \|A\| = n: Total relations = 2^(n^2); Reflexive relations = 2^(n(n-1)); Symmetric relations = 2^(n(n+1)/2).; B) Mendel's 3 Laws: Dominance, Segregation (universally valid without exceptions - purity of gametes), and Independent Assortment (applies to unlinked genes; T.H. Morgan studied Linkage & Recombination in Drosophila). Incomplete Dominance (Snapdragon Antirrhinum majus): Both phenotypic and genotypic F2 ratios are 1:2:1 (Red : Pink : White). Codominance: Human ABO blood group (IA and IB alleles are codominant over i, controlled by 3 alleles giving 6 genotypes and 4 phenotypes). Mendelian Disorders: Haemophilia & Colour Blindness (X-linked recessive), Sickle-Cell Anaemia (Autosomal recessive point mutation at 6th codon of beta-globin: GAG Glutamic acid -> GUG Valine), Phenylketonuria & Thalassemia (Autosomal recessive). Chromosomal Aneuploidy: Down's Syndrome (Trisomy of chromosome 21, 47 chromosomes), Klinefelter's Syndrome (47, XXY - gynecomastia, sterile male), Turner's Syndrome (45, XO - rudimentary ovaries, sterile female). ✓; C) For a short dipole (r >> a): E_axial = (1 / 4*pi*epsilon_0) * (2p / r^3) (along p); E_equatorial = (1 / 4*pi*epsilon_0) * (p / r^3) (opposite to p), so \|E_axial\| = 2 * \|E_equatorial\|.; D) Units of k for n-th order: mol^(1-n) L^(n-1) s^-1. |
| 7 | What is the electric field on the axial line vs equatorial line of a short electric dipole (dipole moment p = q * 2a), and what are the torque and potential energy in a uniform field E? | For a short dipole (r >> a): E_axial = (1 / 4*pi*epsilon_0) * (2p / r^3) (along p); E_equatorial = (1 / 4*pi*epsilon_0) * (p / r^3) (opposite to p), so \|E_axial\| = 2 * \|E_equatorial\|. In a uniform field E: Torque tau = p x E (magnitude pE sin(theta)), and Potential Energy U = -p . E = -pE cos(theta) (stable equilibrium at theta = 0°, unstable at theta = 180°). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Lens Maker's Formula: 1/f = (n_21 - 1) * (1/R_1 - 1/R_2).; B) SN2 (Bimolecular): Single-step concerted mechanism with backside attack, pentacoordinate transition state, 100% Waldens Inversion of configuration, Rate = k[R-X][Nu-], favored by polar aprotic solvents,…; C) Exponential Growth (J-shaped, unlimited resources): dN/dt = rN; Verhulst-Pearl Logistic Growth (S-shaped/Sigmoid, carrying capacity K): dN/dt = rN * [(K - N) / K].; D) For a short dipole (r >> a): E_axial = (1 / 4*pi*epsilon_0) * (2p / r^3) (along p); E_equatorial = (1 / 4*pi*epsilon_0) * (p / r^3) (opposite to p), so \|E_axial\| = 2 * \|E_equatorial\|. In a uniform field E: Torque tau = p x E (magnitude pE sin(theta)), and Potential Energy U = -p . E = -pE cos(theta) (stable equilibrium at theta = 0°, unstable at theta = 180°). ✓ |
| 8 | In d- and f-Block Elements, what is Lanthanoid Contraction, what are its consequences, and why do Transition Metals show variable oxidation states, colored ions, and catalytic activity? | Lanthanoid Contraction is the steady decrease in atomic and ionic radii of lanthanoids (Ce to Lu, 4f series) with increasing atomic number due to poor shielding of 4f electrons. Consequences: 1) 4d and 5d transition elements of the same group (e.g., Zr and Hf) have almost identical atomic radii (160 pm vs 159 pm), making them difficult to separate; 2) Basic strength of hydroxides decreases from La(OH)3 to Lu(OH)3. Transition metals form colored ions due to d-d transitions of unpaired (n-1)d electrons (Zn2+, Cd2+, Hg2+ with d10 and Sc3+, Ti4+ with d0 are colorless and diamagnetic; magnetic moment mu = sqrt(n(n+2)) BM). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Lucas Test (conc. HCl + anhyd. ZnCl2 for 1°, 2°, 3° alcohols): 3° alcohol gives immediate turbidity, 2° in ~5 mins, 1° no turbidity at room temp. Tollens' Test (ammoniacal AgNO3 -> Silver Mirror):…; B) Lanthanoid Contraction is the steady decrease in atomic and ionic radii of lanthanoids (Ce to Lu, 4f series) with increasing atomic number due to poor shielding of 4f electrons. Consequences: 1) 4d and 5d transition elements of the same group (e.g., Zr and Hf) have almost identical atomic radii (160 pm vs 159 pm), making them difficult to separate; 2) Basic strength of hydroxides decreases from La(OH)3 to Lu(OH)3. Transition metals form colored ions due to d-d transitions of unpaired (n-1)d electrons (Zn2+, Cd2+, Hg2+ with d10 and Sc3+, Ti4+ with d0 are colorless and diamagnetic; magnetic moment mu = sqrt(n(n+2)) BM). ✓; C) For \|A\| = n: Total relations = 2^(n^2); Reflexive relations = 2^(n(n-1)); Symmetric relations = 2^(n(n+1)/2).; D) Current I = n*e*A*v_d, where drift velocity v_d = (e*E/m)*tau and mobility mu = v_d / E = e*tau/m. |
| 9 | Compare SN1 and SN2 Nucleophilic Substitution Mechanisms in Haloalkanes and explain why Aryl Halides (Chlorobenzene) are unreactive towards nucleophilic substitution. | SN2 (Bimolecular): Single-step concerted mechanism with backside attack, pentacoordinate transition state, 100% Waldens Inversion of configuration, Rate = k[R-X][Nu-], favored by polar aprotic solvents, reactivity order: Methyl > 1° > 2° > 3°. SN1 (Unimolecular): Two-step mechanism via planar sp2 Carbocation intermediate, gives Racemisation (retention + inversion), Rate = k[R-X], favored by polar protic solvents, reactivity order: Allylic/Benzylic > 3° > 2° > 1°. Aryl halides resist nucleophilic substitution due to: 1) Partial double-bond character of C-X bond from resonance, 2) sp2 hybridized carbon (shorter/stronger bond), and 3) Instability of phenyl cation. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Double Fertilization (unique to Angiosperms, discovered by Nawaschin): Out of 2 male gametes released by the pollen tube into the 7-celled, 8-nucleate embryo sac, 1 male gamete (n) fuses with the egg cell…; B) SN2 (Bimolecular): Single-step concerted mechanism with backside attack, pentacoordinate transition state, 100% Waldens Inversion of configuration, Rate = k[R-X][Nu-], favored by polar aprotic solvents, reactivity order: Methyl > 1° > 2° > 3°. SN1 (Unimolecular): Two-step mechanism via planar sp2 Carbocation intermediate, gives Racemisation (retention + inversion), Rate = k[R-X], favored by polar protic solvents, reactivity order: Allylic/Benzylic > 3° > 2° > 1°. Aryl halides resist nucleophilic substitution due to: 1) Partial double-bond character of C-X bond from resonance, 2) sp2 hybridized carbon (shorter/stronger bond), and 3) Instability of phenyl cation. ✓; C) Integration by Parts (ILATE rule: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential): int u*v dx = u * (int v dx) - int [du/dx * (int v dx)] dx.; D) Faraday-Lenz Law: Induced EMF e = -N * (dPhi_B / dt), where the negative sign (Lenz's Law) obeys Conservation of Energy. |
| 10 | What are the salient features of the Genetic Code (Marshall Nirenberg, Har Gobind Khorana, Severo Ochoa) and the structure/regulation of the Lac Operon (Jacob & Monod)? | Genetic Code (64 codons): 61 code for 20 amino acids + 3 Stop/Nonsense codons (UAA - Ochre, UAG - Amber, UGA - Opal). AUG has dual functions: codes for Methionine and acts as the Initiator Codon. The code is triplet, unambiguous, degenerate (multiple codons for one amino acid), comma-less, and nearly universal. Lac Operon in E. coli: Consists of regulatory gene 'i' (codes for constitutively expressed Repressor protein), Promoter (p), Operator (o), and 3 structural genes—z (beta-galactosidase), y (permease), and a (transacetylase). Lactose (allolactose) acts as the Inducer that binds and inactivates the repressor, switching ON transcription (negative inducible regulation). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Integration by Parts (ILATE rule: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential): int u*v dx = u * (int v dx) - int [du/dx * (int v dx)] dx.; B) Genetic Code (64 codons): 61 code for 20 amino acids + 3 Stop/Nonsense codons (UAA - Ochre, UAG - Amber, UGA - Opal). AUG has dual functions: codes for Methionine and acts as the Initiator Codon. The code is triplet, unambiguous, degenerate (multiple codons for one amino acid), comma-less, and nearly universal. Lac Operon in E. coli: Consists of regulatory gene 'i' (codes for constitutively expressed Repressor protein), Promoter (p), Operator (o), and 3 structural genes—z (beta-galactosidase), y (permease), and a (transacetylase). Lactose (allolactose) acts as the Inducer that binds and inactivates the repressor, switching ON transcription (negative inducible regulation). ✓; C) Current I = n*e*A*v_d, where drift velocity v_d = (e*E/m)*tau and mobility mu = v_d / E = e*tau/m.; D) Spectrochemical Series (increasing crystal field splitting Delta_0): I- < Br- < SCN- < Cl- < F- < OH- < H2O < NCS- < EDTA4- < NH3 < en < CN- < CO. |
| 11 | In Class 12 Mathematics (Relations, Functions & Matrices), how many Reflexive, Symmetric, and Equivalence Relations exist on a set A with n elements, and what are the properties of Determinants & Adjoint? | For \|A\| = n: Total relations = 2^(n^2); Reflexive relations = 2^(n(n-1)); Symmetric relations = 2^(n(n+1)/2). A function f: A -> B is Bijective (Invertible) iff it is both One-One (Injective) and Onto (Surjective). For an n x n square matrix A: \|kA\| = k^n * \|A\|; A * adj(A) = \|A\| * I_n; \|adj(A)\| = \|A\|^(n-1); \|adj(adj(A))\| = \|A\|^((n-1)^2); and (AB)^(-1) = B^(-1) * A^(-1). Any square matrix A can be uniquely expressed as the sum of a Symmetric matrix (1/2)(A + A^T) and a Skew-Symmetric matrix (1/2)(A - A^T). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Corner Point Theorem: The optimal value (maximum or minimum) of the objective function Z = ax + by over a bounded convex feasible region ALWAYS occurs at a corner point (vertex) of the feasible region.; B) For \|A\| = n: Total relations = 2^(n^2); Reflexive relations = 2^(n(n-1)); Symmetric relations = 2^(n(n+1)/2). A function f: A -> B is Bijective (Invertible) iff it is both One-One (Injective) and Onto (Surjective). For an n x n square matrix A: \|kA\| = k^n * \|A\|; A * adj(A) = \|A\| * I_n; \|adj(A)\| = \|A\|^(n-1); \|adj(adj(A))\| = \|A\|^((n-1)^2); and (AB)^(-1) = B^(-1) * A^(-1). Any square matrix A can be uniquely expressed as the sum of a Symmetric matrix (1/2)(A + A^T) and a Skew-Symmetric matrix (1/2)(A - A^T). ✓; C) Lens Maker's Formula: 1/f = (n_21 - 1) * (1/R_1 - 1/R_2).; D) Rosenmund Reduction: R-COCl + H2 (Pd-BaSO4) -> R-CHO; Stephen: R-CN + SnCl2/HCl -> R-CHO; Etard: Toluene + CrO2Cl2 -> Benzaldehyde; Clemmensen Reduction: >C=O + Zn-Hg / conc. |
| 12 | In Electrochemistry, state the Nernst Equation, Kohlrausch's Law of Independent Migration of Ions, and Faraday's Two Laws of Electrolysis. | Nernst Equation at 298 K: E_cell = E^0_cell - (0.0591 / n) * log10(Q), and Delta_G^0 = -n * F * E^0_cell = -2.303 * R * T * log10(K_c) (where F = 96,487 C/mol ≈ 96,500 C/mol). Kohlrausch's Law: Limiting molar conductivity Lambda_m^0 of an electrolyte is the sum of the limiting ionic conductivities of its cations and anions (used to find Lambda_m^0 of weak electrolytes like CH3COOH). Faraday's 1st Law: Mass deposited w = Z * I * t = (Molar Mass / (n * F)) * Q. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Finkelstein: R-X + NaI (in dry acetone) -> R-I + NaX; Swarts: R-Br + AgF -> R-F; Wurtz: 2 R-X + 2 Na (dry ether) -> R-R; Reimer-Tiemann Reaction: Phenol + CHCl3 + aq.; B) Nernst Equation at 298 K: E_cell = E^0_cell - (0.0591 / n) * log10(Q), and Delta_G^0 = -n * F * E^0_cell = -2.303 * R * T * log10(K_c) (where F = 96,487 C/mol ≈ 96,500 C/mol). Kohlrausch's Law: Limiting molar conductivity Lambda_m^0 of an electrolyte is the sum of the limiting ionic conductivities of its cations and anions (used to find Lambda_m^0 of weak electrolytes like CH3COOH). Faraday's 1st Law: Mass deposited w = Z * I * t = (Molar Mass / (n * F)) * Q. ✓; C) Restriction Endonucleases ('Molecular Scissors', e.g., EcoRI recognizes palindromic sequence 5'-GAATTC-3' and produces sticky ends).; D) For a short dipole (r >> a): E_axial = (1 / 4*pi*epsilon_0) * (2p / r^3) (along p); E_equatorial = (1 / 4*pi*epsilon_0) * (p / r^3) (opposite to p), so \|E_axial\| = 2 * \|E_equatorial\|. |
| 13 | In Ecology (Organisms, Populations & Ecosystems), state the Logistic vs Exponential Growth Equations, Lindeman's 10% Law, Ecological Pyramids, and Biodiversity Conservation (In-situ vs Ex-situ). | Exponential Growth (J-shaped, unlimited resources): dN/dt = rN; Verhulst-Pearl Logistic Growth (S-shaped/Sigmoid, carrying capacity K): dN/dt = rN * [(K - N) / K]. Lindeman's 10% Law (1942): Only 10% of energy is transferred to each successive trophic level; Pyramid of Energy is ALWAYS upright (never inverted), whereas Pyramid of Biomass in an aquatic/sea ecosystem (phytoplankton < zooplankton) is inverted. Species-Area Relationship (Alexander von Humboldt): log S = log C + Z * log A (Z = 0.1–0.2, or 0.6–1.2 for continents). In-situ conservation (on-site): Biosphere Reserves, National Parks, Wildlife Sanctuaries, Sacred Groves, Biodiversity Hotspots (36 globally, 4 in India: Western Ghats, Himalayas, Indo-Burma, Sundaland). Ex-situ (off-site): Botanical gardens, Zoological parks, Seed banks, Cryopreservation (-196°C in liquid N2). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Exponential Growth (J-shaped, unlimited resources): dN/dt = rN; Verhulst-Pearl Logistic Growth (S-shaped/Sigmoid, carrying capacity K): dN/dt = rN * [(K - N) / K]. Lindeman's 10% Law (1942): Only 10% of energy is transferred to each successive trophic level; Pyramid of Energy is ALWAYS upright (never inverted), whereas Pyramid of Biomass in an aquatic/sea ecosystem (phytoplankton < zooplankton) is inverted. Species-Area Relationship (Alexander von Humboldt): log S = log C + Z * log A (Z = 0.1–0.2, or 0.6–1.2 for continents). In-situ conservation (on-site): Biosphere Reserves, National Parks, Wildlife Sanctuaries, Sacred Groves, Biodiversity Hotspots (36 globally, 4 in India: Western Ghats, Himalayas, Indo-Burma, Sundaland). Ex-situ (off-site): Botanical gardens, Zoological parks, Seed banks, Cryopreservation (-196°C in liquid N2). ✓; B) Scalar Projection of vector a on vector b = (a .; C) Faraday-Lenz Law: Induced EMF e = -N * (dPhi_B / dt), where the negative sign (Lenz's Law) obeys Conservation of Energy.; D) Finkelstein: R-X + NaI (in dry acetone) -> R-I + NaX; Swarts: R-Br + AgF -> R-F; Wurtz: 2 R-X + 2 Na (dry ether) -> R-R; Reimer-Tiemann Reaction: Phenol + CHCl3 + aq. |
| 14 | In Dual Nature of Radiation, Atoms & Nuclei, state Einstein's Photoelectric Equation, de Broglie Wavelength, Bohr's Radius/Energy formulas, and Nuclear Mass Defect. | Einstein's Photoelectric Equation: K_max = e*V_0 = h*nu - phi_0 = h*(nu - nu_0) (stopping potential V_0 depends on frequency nu, NOT intensity). de Broglie Wavelength: lambda = h / p = h / sqrt(2*m*K) (for an electron accelerated through V volts: lambda ≈ 1.227 / sqrt(V) nm). Bohr's Hydrogen Atom: r_n = 0.529 * n^2 / Z Angstrom; E_n = -13.6 * Z^2 / n^2 eV. Nuclear Radius R = R_0 * A^(1/3) (guaranteeing constant nuclear density independent of A); Binding Energy = Delta_m * 931.5 MeV. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Einstein's Photoelectric Equation: K_max = e*V_0 = h*nu - phi_0 = h*(nu - nu_0) (stopping potential V_0 depends on frequency nu, NOT intensity). de Broglie Wavelength: lambda = h / p = h / sqrt(2*m*K) (for an electron accelerated through V volts: lambda ≈ 1.227 / sqrt(V) nm). Bohr's Hydrogen Atom: r_n = 0.529 * n^2 / Z Angstrom; E_n = -13.6 * Z^2 / n^2 eV. Nuclear Radius R = R_0 * A^(1/3) (guaranteeing constant nuclear density independent of A); Binding Energy = Delta_m * 931.5 MeV. ✓; B) Lanthanoid Contraction is the steady decrease in atomic and ionic radii of lanthanoids (Ce to Lu, 4f series) with increasing atomic number due to poor shielding of 4f electrons.; C) Mendel's 3 Laws: Dominance, Segregation (universally valid without exceptions - purity of gametes), and Independent Assortment (applies to unlinked genes; T.H.; D) Corner Point Theorem: The optimal value (maximum or minimum) of the objective function Z = ax + by over a bounded convex feasible region ALWAYS occurs at a corner point (vertex) of the feasible region. |
| 15 | In Linear Programming (LPP) and Probability (Class 12 Maths), state the Fundamental Theorem of Linear Programming, Conditional Probability, Independent Events, and Total Probability. | Corner Point Theorem: The optimal value (maximum or minimum) of the objective function Z = ax + by over a bounded convex feasible region ALWAYS occurs at a corner point (vertex) of the feasible region. Conditional Probability: P(E \| F) = P(E n F) / P(F); P(A u B) = P(A) + P(B) - P(A n B). Two events A and B are Independent iff P(A n B) = P(A) * P(B) (whereas Mutually Exclusive events have P(A n B) = 0). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Current I = n*e*A*v_d, where drift velocity v_d = (e*E/m)*tau and mobility mu = v_d / E = e*tau/m.; B) Units of k for n-th order: mol^(1-n) L^(n-1) s^-1.; C) Griffith (1928): Transforming Principle using Streptococcus pneumoniae (R-strain & heat-killed S-strain in mice); Avery, MacLeod & McCarty (1944): Proved DNA is the transforming principle using…; D) Corner Point Theorem: The optimal value (maximum or minimum) of the objective function Z = ax + by over a bounded convex feasible region ALWAYS occurs at a corner point (vertex) of the feasible region. Conditional Probability: P(E \| F) = P(E n F) / P(F); P(A u B) = P(A) + P(B) - P(A n B). Two events A and B are Independent iff P(A n B) = P(A) * P(B) (whereas Mutually Exclusive events have P(A n B) = 0). ✓ |
| 16 | In Differential Equations (Class 12 Maths), how do you determine Order and Degree, and how do you solve a First-Order Linear Differential Equation dy/dx + P(x)*y = Q(x)? | Order is the order of the highest order derivative present in the equation; Degree is the highest power of the highest order derivative ONLY when the differential equation is a polynomial equation in its derivatives (otherwise Degree is 'not defined', e.g., when sin(dy/dx) or e^(dy/dx) is present). For a First-Order Linear DE dy/dx + P(x)*y = Q(x): Integrating Factor (I.F.) = e^(int P(x) dx), and the general solution is y * (I.F.) = int [Q(x) * (I.F.)] dx + C. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) For a short dipole (r >> a): E_axial = (1 / 4*pi*epsilon_0) * (2p / r^3) (along p); E_equatorial = (1 / 4*pi*epsilon_0) * (p / r^3) (opposite to p), so \|E_axial\| = 2 * \|E_equatorial\|.; B) Order is the order of the highest order derivative present in the equation; Degree is the highest power of the highest order derivative ONLY when the differential equation is a polynomial equation in its derivatives (otherwise Degree is 'not defined', e.g., when sin(dy/dx) or e^(dy/dx) is present). For a First-Order Linear DE dy/dx + P(x)*y = Q(x): Integrating Factor (I.F.) = e^(int P(x) dx), and the general solution is y * (I.F.) = int [Q(x) * (I.F.)] dx + C. ✓; C) Raoult's Law: p_A = p_A^0 * x_A (Positive deviation: Ethanol + Acetone, Delta_H_mix > 0, minimum-boiling azeotrope; Negative deviation: Chloroform + Acetone or HNO3 + H2O, Delta_H_mix < 0, maximum-boiling…; D) Double Fertilization (unique to Angiosperms, discovered by Nawaschin): Out of 2 male gametes released by the pollen tube into the 7-celled, 8-nucleate embryo sac, 1 male gamete (n) fuses with the egg cell… |
| 17 | In Class 12 Integral Calculus, what are the Integration by Parts formula, the special integral int e^x [f(x) + f'(x)] dx, and King's Property of Definite Integrals? | Integration by Parts (ILATE rule: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential): int u*v dx = u * (int v dx) - int [du/dx * (int v dx)] dx. Special cancellation integral: int e^x * [f(x) + f'(x)] dx = e^x * f(x) + C. King's Property of Definite Integrals: int_a^b f(x) dx = int_a^b f(a + b - x) dx (and int_0^a f(x) dx = int_0^a f(a - x) dx). Also, int_-a^a f(x) dx = 0 if f(x) is an Odd function (f(-x) = -f(x)), and = 2 * int_0^a f(x) dx if f(x) is an Even function (f(-x) = f(x)). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Gauss's Law: Total electric flux through any closed surface S is Phi_E = oint E .; B) Intrinsic semiconductor (pure Si/Ge): n_e = n_h = n_i.; C) Reducing Sugars (free aldehyde/ketone group): All monosaccharides (Glucose, Fructose, Galactose) + Maltose and Lactose.; D) Integration by Parts (ILATE rule: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential): int u*v dx = u * (int v dx) - int [du/dx * (int v dx)] dx. Special cancellation integral: int e^x * [f(x) + f'(x)] dx = e^x * f(x) + C. King's Property of Definite Integrals: int_a^b f(x) dx = int_a^b f(a + b - x) dx (and int_0^a f(x) dx = int_0^a f(a - x) dx). Also, int_-a^a f(x) dx = 0 if f(x) is an Odd function (f(-x) = -f(x)), and = 2 * int_0^a f(x) dx if f(x) is an Even function (f(-x) = f(x)). ✓ |
| 18 | Summarize the key NCERT Organic Name Reactions of Aldehydes, Ketones, Carboxylic Acids, and Amines (Rosenmund, Stephen, Etard, Clemmensen, Wolff-Kishner, Aldol, Cannizzaro, HVZ, Hoffmann Bromamide, Gabriel Phthalimide, and Carbylamine). | Rosenmund Reduction: R-COCl + H2 (Pd-BaSO4) -> R-CHO; Stephen: R-CN + SnCl2/HCl -> R-CHO; Etard: Toluene + CrO2Cl2 -> Benzaldehyde; Clemmensen Reduction: >C=O + Zn-Hg / conc. HCl -> -CH2-; Wolff-Kishner: >C=O + NH2NH2 / KOH-ethylene glycol -> -CH2-; Aldol Condensation: Aldehydes/ketones having at least one alpha-Hydrogen with dil. NaOH -> beta-hydroxy aldehyde/ketone -> alpha,beta-unsaturated carbonyl; Cannizzaro Reaction: Aldehydes with NO alpha-Hydrogen (HCHO, C6H5CHO) + conc. NaOH -> disproportionation to alcohol + carboxylic acid salt; Hell-Volhard-Zelinsky (HVZ): R-CH2-COOH + X2 / Red P -> alpha-halo carboxylic acid; Hoffmann Bromamide Degradation: R-CONH2 + Br2 + 4 NaOH -> R-NH2 (1° amine with one less carbon); Gabriel Phthalimide Synthesis: Prepares pure aliphatic 1° amines (cannot prepare aniline); Carbylamine Test (Isocyanide test): Aliphatic/aromatic 1° amine + CHCl3 + 3 KOH -> foul-smelling R-NC. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Rosenmund Reduction: R-COCl + H2 (Pd-BaSO4) -> R-CHO; Stephen: R-CN + SnCl2/HCl -> R-CHO; Etard: Toluene + CrO2Cl2 -> Benzaldehyde; Clemmensen Reduction: >C=O + Zn-Hg / conc. HCl -> -CH2-; Wolff-Kishner: >C=O + NH2NH2 / KOH-ethylene glycol -> -CH2-; Aldol Condensation: Aldehydes/ketones having at least one alpha-Hydrogen with dil. NaOH -> beta-hydroxy aldehyde/ketone -> alpha,beta-unsaturated carbonyl; Cannizzaro Reaction: Aldehydes with NO alpha-Hydrogen (HCHO, C6H5CHO) + conc. NaOH -> disproportionation to alcohol + carboxylic acid salt; Hell-Volhard-Zelinsky (HVZ): R-CH2-COOH + X2 / Red P -> alpha-halo carboxylic acid; Hoffmann Bromamide Degradation: R-CONH2 + Br2 + 4 NaOH -> R-NH2 (1° amine with one less carbon); Gabriel Phthalimide Synthesis: Prepares pure aliphatic 1° amines (cannot prepare aniline); Carbylamine Test (Isocyanide test): Aliphatic/aromatic 1° amine + CHCl3 + 3 KOH -> foul-smelling R-NC. ✓; B) Griffith (1928): Transforming Principle using Streptococcus pneumoniae (R-strain & heat-killed S-strain in mice); Avery, MacLeod & McCarty (1944): Proved DNA is the transforming principle using…; C) Scalar Projection of vector a on vector b = (a .; D) Einstein's Photoelectric Equation: K_max = e*V_0 = h*nu - phi_0 = h*(nu - nu_0) (stopping potential V_0 depends on frequency nu, NOT intensity). |
| 19 | In Class 12 Physical Chemistry (Solutions), state Raoult's Law, the four Colligative Properties, and the van't Hoff Factor (i) for association vs dissociation. | Raoult's Law: p_A = p_A^0 * x_A (Positive deviation: Ethanol + Acetone, Delta_H_mix > 0, minimum-boiling azeotrope; Negative deviation: Chloroform + Acetone or HNO3 + H2O, Delta_H_mix < 0, maximum-boiling azeotrope). 4 Colligative Properties: 1) Relative Lowering of Vapor Pressure: (p^0 - p)/p^0 = i * x_2, 2) Elevation of Boiling Point: Delta_T_b = i * K_b * m, 3) Depression of Freezing Point: Delta_T_f = i * K_f * m, 4) Osmotic Pressure: Pi = i * C * R * T (best for molar mass of proteins/polymers). van't Hoff factor: i > 1 for dissociation (e.g., NaCl in water, i -> 2) and i < 1 for association (e.g., ethanoic acid dimerizes in benzene via H-bonding, i -> 0.5). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) SN2 (Bimolecular): Single-step concerted mechanism with backside attack, pentacoordinate transition state, 100% Waldens Inversion of configuration, Rate = k[R-X][Nu-], favored by polar aprotic solvents,…; B) Raoult's Law: p_A = p_A^0 * x_A (Positive deviation: Ethanol + Acetone, Delta_H_mix > 0, minimum-boiling azeotrope; Negative deviation: Chloroform + Acetone or HNO3 + H2O, Delta_H_mix < 0, maximum-boiling azeotrope). 4 Colligative Properties: 1) Relative Lowering of Vapor Pressure: (p^0 - p)/p^0 = i * x_2, 2) Elevation of Boiling Point: Delta_T_b = i * K_b * m, 3) Depression of Freezing Point: Delta_T_f = i * K_f * m, 4) Osmotic Pressure: Pi = i * C * R * T (best for molar mass of proteins/polymers). van't Hoff factor: i > 1 for dissociation (e.g., NaCl in water, i -> 2) and i < 1 for association (e.g., ethanoic acid dimerizes in benzene via H-bonding, i -> 0.5). ✓; C) Genetic Code (64 codons): 61 code for 20 amino acids + 3 Stop/Nonsense codons (UAA - Ochre, UAG - Amber, UGA - Opal).; D) Gauss's Law: Total electric flux through any closed surface S is Phi_E = oint E . |
| 20 | In Ray and Wave Optics, state the Lens Maker's Formula, Prism Formula, Magnifying Power of Compound Microscope/Telescope, and Young's Double-Slit Fringe Width. | Lens Maker's Formula: 1/f = (n_21 - 1) * (1/R_1 - 1/R_2). Prism Refractive Index at Minimum Deviation (D_m): n = sin((A + D_m)/2) / sin(A/2). Astronomical Telescope magnifying power (normal adjustment): m = f_0 / f_e, tube length L = f_0 + f_e (Objective has large f_0 and large aperture). Young's Double-Slit Experiment (YDSE): Fringe width beta = lambda * D / d, and intensity I = 4*I_0 * cos^2(phi/2). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Units of k for n-th order: mol^(1-n) L^(n-1) s^-1.; B) Double Fertilization (unique to Angiosperms, discovered by Nawaschin): Out of 2 male gametes released by the pollen tube into the 7-celled, 8-nucleate embryo sac, 1 male gamete (n) fuses with the egg cell…; C) Scalar Projection of vector a on vector b = (a .; D) Lens Maker's Formula: 1/f = (n_21 - 1) * (1/R_1 - 1/R_2). Prism Refractive Index at Minimum Deviation (D_m): n = sin((A + D_m)/2) / sin(A/2). Astronomical Telescope magnifying power (normal adjustment): m = f_0 / f_e, tube length L = f_0 + f_e (Objective has large f_0 and large aperture). Young's Double-Slit Experiment (YDSE): Fringe width beta = lambda * D / d, and intensity I = 4*I_0 * cos^2(phi/2). ✓ |
| 21 | In Moving Charges and Magnetism, compare the Biot-Savart Law and Ampere's Circuital Law, and give the force per unit length between two parallel current-carrying conductors. | Biot-Savart Law: dB = (mu_0 / 4*pi) * I (dl x r_hat) / r^2 (gives B at center of circular coil of N turns: B = mu_0*N*I / (2R)). Ampere's Circuital Law: oint B . dl = mu_0 * I_enclosed (gives B inside a long solenoid: B = mu_0*n*I). Force per unit length between two parallel wires separated by distance d: f = F/L = (mu_0 * I_1 * I_2) / (2*pi*d) (parallel currents ATTRACT, antiparallel currents REPEL; defines 1 Ampere). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Raoult's Law: p_A = p_A^0 * x_A (Positive deviation: Ethanol + Acetone, Delta_H_mix > 0, minimum-boiling azeotrope; Negative deviation: Chloroform + Acetone or HNO3 + H2O, Delta_H_mix < 0, maximum-boiling…; B) Lucas Test (conc. HCl + anhyd. ZnCl2 for 1°, 2°, 3° alcohols): 3° alcohol gives immediate turbidity, 2° in ~5 mins, 1° no turbidity at room temp. Tollens' Test (ammoniacal AgNO3 -> Silver Mirror):…; C) Biot-Savart Law: dB = (mu_0 / 4*pi) * I (dl x r_hat) / r^2 (gives B at center of circular coil of N turns: B = mu_0*N*I / (2R)). Ampere's Circuital Law: oint B . dl = mu_0 * I_enclosed (gives B inside a long solenoid: B = mu_0*n*I). Force per unit length between two parallel wires separated by distance d: f = F/L = (mu_0 * I_1 * I_2) / (2*pi*d) (parallel currents ATTRACT, antiparallel currents REPEL; defines 1 Ampere). ✓; D) Integration by Parts (ILATE rule: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential): int u*v dx = u * (int v dx) - int [du/dx * (int v dx)] dx. |
| 22 | In Coordination Compounds, compare Valence Bond Theory (VBT) and Crystal Field Theory (CFT) for Octahedral and Tetrahedral complexes using the Spectrochemical Series. | Spectrochemical Series (increasing crystal field splitting Delta_0): I- < Br- < SCN- < Cl- < F- < OH- < H2O < NCS- < EDTA4- < NH3 < en < CN- < CO. Strong-field ligands (CO, CN-, en, NH3) cause pairing when Delta_0 > P: e.g., [Fe(CN)6]^4- and [Co(NH3)6]^3+ are Inner Orbital d2sp3 (low-spin, diamagnetic t2g^6 eg^0) octahedral complexes, whereas weak-field [CoF6]^3- is Outer Orbital sp3d2 (high-spin, paramagnetic t2g^4 eg^2). [Ni(CN)4]^2- is dsp2 Square Planar (diamagnetic), whereas [NiCl4]^2- and [Ni(CO)4] are sp3 Tetrahedral (where Delta_t = (4/9)*Delta_0). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Spectrochemical Series (increasing crystal field splitting Delta_0): I- < Br- < SCN- < Cl- < F- < OH- < H2O < NCS- < EDTA4- < NH3 < en < CN- < CO. Strong-field ligands (CO, CN-, en, NH3) cause pairing when Delta_0 > P: e.g., [Fe(CN)6]^4- and [Co(NH3)6]^3+ are Inner Orbital d2sp3 (low-spin, diamagnetic t2g^6 eg^0) octahedral complexes, whereas weak-field [CoF6]^3- is Outer Orbital sp3d2 (high-spin, paramagnetic t2g^4 eg^2). [Ni(CN)4]^2- is dsp2 Square Planar (diamagnetic), whereas [NiCl4]^2- and [Ni(CO)4] are sp3 Tetrahedral (where Delta_t = (4/9)*Delta_0). ✓; B) Reducing Sugars (free aldehyde/ketone group): All monosaccharides (Glucose, Fructose, Galactose) + Maltose and Lactose.; C) Every differentiable function is continuous, but a continuous function need not be differentiable (e.g., f(x) = \|x\| at x = 0).; D) Biot-Savart Law: dB = (mu_0 / 4*pi) * I (dl x r_hat) / r^2 (gives B at center of circular coil of N turns: B = mu_0*N*I / (2R)). |
| 23 | What are the key Chemical Distinction Tests in Class 12 Organic Chemistry (Lucas Test, Tollens' Test, Fehling's Test, Iodoform Test, and Hinsberg's Test)? | Lucas Test (conc. HCl + anhyd. ZnCl2 for 1°, 2°, 3° alcohols): 3° alcohol gives immediate turbidity, 2° in ~5 mins, 1° no turbidity at room temp. Tollens' Test (ammoniacal AgNO3 -> Silver Mirror): Positive for both aliphatic and aromatic aldehydes (and formic acid), negative for ketones. Fehling's Test (reddish-brown Cu2O precipitate): Positive for aliphatic aldehydes, negative for aromatic aldehydes (benzaldehyde) and ketones. Iodoform Test (I2 + NaOH -> yellow ppt of CHI3): Positive for compounds containing CH3-C=O or CH3-CH(OH)- group (ethanol is the only 1° alcohol, ethanal is the only aldehyde giving positive iodoform test). Hinsberg's Reagent (Benzenesulphonyl chloride C6H5SO2Cl): Distinguishes 1° (soluble in alkali), 2° (insoluble in alkali), and 3° amines (does not react). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Genetic Code (64 codons): 61 code for 20 amino acids + 3 Stop/Nonsense codons (UAA - Ochre, UAG - Amber, UGA - Opal).; B) Lucas Test (conc. HCl + anhyd. ZnCl2 for 1°, 2°, 3° alcohols): 3° alcohol gives immediate turbidity, 2° in ~5 mins, 1° no turbidity at room temp. Tollens' Test (ammoniacal AgNO3 -> Silver Mirror): Positive for both aliphatic and aromatic aldehydes (and formic acid), negative for ketones. Fehling's Test (reddish-brown Cu2O precipitate): Positive for aliphatic aldehydes, negative for aromatic aldehydes (benzaldehyde) and ketones. Iodoform Test (I2 + NaOH -> yellow ppt of CHI3): Positive for compounds containing CH3-C=O or CH3-CH(OH)- group (ethanol is the only 1° alcohol, ethanal is the only aldehyde giving positive iodoform test). Hinsberg's Reagent (Benzenesulphonyl chloride C6H5SO2Cl): Distinguishes 1° (soluble in alkali), 2° (insoluble in alkali), and 3° amines (does not react). ✓; C) Corner Point Theorem: The optimal value (maximum or minimum) of the objective function Z = ax + by over a bounded convex feasible region ALWAYS occurs at a corner point (vertex) of the feasible region.; D) Intrinsic semiconductor (pure Si/Ge): n_e = n_h = n_i. |
| 24 | In Biomolecules (Class 12 Chemistry/Biology), distinguish Reducing vs Non-reducing Sugars, DNA vs RNA Nitrogenous Bases, Denaturation of Proteins, and Essential Amino Acids. | Reducing Sugars (free aldehyde/ketone group): All monosaccharides (Glucose, Fructose, Galactose) + Maltose and Lactose. Non-reducing Sugar: Sucrose (glycosidic linkage between C1 of alpha-D-glucose and C2 of beta-D-fructose; invert sugar on hydrolysis). Protein Denaturation (change in temp/pH, e.g., boiling egg or curdling milk): Destroys 2°, 3°, and 4° structures (hydrogen/disulfide bonds break) while 1° primary peptide sequence remains intact. Nucleic Acids: DNA has Deoxyribose + Adenine (A), Guanine (G), Cytosine (C), Thymine (T); RNA has Ribose + A, G, C, and Uracil (U in place of Thymine). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Restriction Endonucleases ('Molecular Scissors', e.g., EcoRI recognizes palindromic sequence 5'-GAATTC-3' and produces sticky ends).; B) Python Immutable types: int, float, bool, str, tuple (cannot be modified in-place); Mutable types: list, dict, set.; C) Reducing Sugars (free aldehyde/ketone group): All monosaccharides (Glucose, Fructose, Galactose) + Maltose and Lactose. Non-reducing Sugar: Sucrose (glycosidic linkage between C1 of alpha-D-glucose and C2 of beta-D-fructose; invert sugar on hydrolysis). Protein Denaturation (change in temp/pH, e.g., boiling egg or curdling milk): Destroys 2°, 3°, and 4° structures (hydrogen/disulfide bonds break) while 1° primary peptide sequence remains intact. Nucleic Acids: DNA has Deoxyribose + Adenine (A), Guanine (G), Cytosine (C), Thymine (T); RNA has Ribose + A, G, C, and Uracil (U in place of Thymine). ✓; D) Raoult's Law: p_A = p_A^0 * x_A (Positive deviation: Ethanol + Acetone, Delta_H_mix > 0, minimum-boiling azeotrope; Negative deviation: Chloroform + Acetone or HNO3 + H2O, Delta_H_mix < 0, maximum-boiling… |
| 25 | In Electromagnetic Induction & Alternating Current (AC), what are Faraday's Law, Lenz's Law, the Resonance condition in a Series LCR Circuit, and Transformer losses? | Faraday-Lenz Law: Induced EMF e = -N * (dPhi_B / dt), where the negative sign (Lenz's Law) obeys Conservation of Energy. In a Series LCR AC circuit, Impedance Z = sqrt(R^2 + (X_L - X_C)^2); Resonance occurs when X_L = X_C, giving resonant angular frequency omega_0 = 1 / sqrt(L*C), minimum impedance Z = R, and Power Factor cos(phi) = R/Z = 1. Transformer (works on Mutual Induction, AC only): V_s/V_p = N_s/N_p = I_p/I_s; energy losses are Flux Leakage, Resistance of Windings (Copper loss), Eddy Currents (minimized by laminated iron core), and Hysteresis (minimized by soft iron core). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Nernst Equation at 298 K: E_cell = E^0_cell - (0.0591 / n) * log10(Q), and Delta_G^0 = -n * F * E^0_cell = -2.303 * R * T * log10(K_c) (where F = 96,487 C/mol ≈ 96,500 C/mol).; B) Reducing Sugars (free aldehyde/ketone group): All monosaccharides (Glucose, Fructose, Galactose) + Maltose and Lactose.; C) Faraday-Lenz Law: Induced EMF e = -N * (dPhi_B / dt), where the negative sign (Lenz's Law) obeys Conservation of Energy. In a Series LCR AC circuit, Impedance Z = sqrt(R^2 + (X_L - X_C)^2); Resonance occurs when X_L = X_C, giving resonant angular frequency omega_0 = 1 / sqrt(L*C), minimum impedance Z = R, and Power Factor cos(phi) = R/Z = 1. Transformer (works on Mutual Induction, AC only): V_s/V_p = N_s/N_p = I_p/I_s; energy losses are Flux Leakage, Resistance of Windings (Copper loss), Eddy Currents (minimized by laminated iron core), and Hysteresis (minimized by soft iron core). ✓; D) Order is the order of the highest order derivative present in the equation; Degree is the highest power of the highest order derivative ONLY when the differential equation is a polynomial equation in its… |
| 26 | In Class 12 Biology (Reproduction in Flowering Plants & Humans), explain Double Fertilization in Angiosperms and hormonal control of Spermatogenesis & the Menstrual Cycle. | Double Fertilization (unique to Angiosperms, discovered by Nawaschin): Out of 2 male gametes released by the pollen tube into the 7-celled, 8-nucleate embryo sac, 1 male gamete (n) fuses with the egg cell (n) to form the diploid Zygote (2n - Syngamy), while the 2nd male gamete (n) fuses with the two polar nuclei (n + n) in the central cell to form the triploid Primary Endosperm Nucleus (3n - Triple Fusion). In humans, LH (Luteinizing Hormone) surge on Day 14 of the menstrual cycle triggers Ovulation and conversion of the Graafian follicle into the progesterone-secreting Corpus Luteum; in males, LH acts on Leydig cells (androgens) and FSH acts on Sertoli cells. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Exponential Growth (J-shaped, unlimited resources): dN/dt = rN; Verhulst-Pearl Logistic Growth (S-shaped/Sigmoid, carrying capacity K): dN/dt = rN * [(K - N) / K].; B) Gauss's Law: Total electric flux through any closed surface S is Phi_E = oint E .; C) Double Fertilization (unique to Angiosperms, discovered by Nawaschin): Out of 2 male gametes released by the pollen tube into the 7-celled, 8-nucleate embryo sac, 1 male gamete (n) fuses with the egg cell (n) to form the diploid Zygote (2n - Syngamy), while the 2nd male gamete (n) fuses with the two polar nuclei (n + n) in the central cell to form the triploid Primary Endosperm Nucleus (3n - Triple Fusion). In humans, LH (Luteinizing Hormone) surge on Day 14 of the menstrual cycle triggers Ovulation and conversion of the Graafian follicle into the progesterone-secreting Corpus Luteum; in males, LH acts on Leydig cells (androgens) and FSH acts on Sertoli cells. ✓; D) Nernst Equation at 298 K: E_cell = E^0_cell - (0.0591 / n) * log10(Q), and Delta_G^0 = -n * F * E^0_cell = -2.303 * R * T * log10(K_c) (where F = 96,487 C/mol ≈ 96,500 C/mol). |
| 27 | In Biotechnology (Principles & Applications), what are Restriction Endonucleases, pBR322 Cloning Vector markers, PCR steps, Bt Cotton (cry genes), and Recombinant Insulin? | Restriction Endonucleases ('Molecular Scissors', e.g., EcoRI recognizes palindromic sequence 5'-GAATTC-3' and produces sticky ends). pBR322 vector has ori, rop, and two antibiotic resistance selectable markers (amp^R and tet^R) for insertional inactivation. Polymerase Chain Reaction (PCR - Kary Mullis): 1) Denaturation (~94°C), 2) Primer Annealing (~54°C), 3) Extension (~72°C using thermostable Taq DNA Polymerase from Thermus aquaticus). Bt Cotton (Bacillus thuringiensis): Protoxin crystal protein encoded by cryIAc & cryIIAb (cotton bollworms) and cryIAb (corn borer) is activated by the alkaline pH of the insect midgut. Human Insulin (Eli Lilly, 1983): Pro-insulin has A-peptide, B-peptide, and C-peptide; mature functional insulin lacks the C-peptide (A and B chains linked by disulfide bridges). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Restriction Endonucleases ('Molecular Scissors', e.g., EcoRI recognizes palindromic sequence 5'-GAATTC-3' and produces sticky ends). pBR322 vector has ori, rop, and two antibiotic resistance selectable markers (amp^R and tet^R) for insertional inactivation. Polymerase Chain Reaction (PCR - Kary Mullis): 1) Denaturation (~94°C), 2) Primer Annealing (~54°C), 3) Extension (~72°C using thermostable Taq DNA Polymerase from Thermus aquaticus). Bt Cotton (Bacillus thuringiensis): Protoxin crystal protein encoded by cryIAc & cryIIAb (cotton bollworms) and cryIAb (corn borer) is activated by the alkaline pH of the insect midgut. Human Insulin (Eli Lilly, 1983): Pro-insulin has A-peptide, B-peptide, and C-peptide; mature functional insulin lacks the C-peptide (A and B chains linked by disulfide bridges). ✓; B) Order is the order of the highest order derivative present in the equation; Degree is the highest power of the highest order derivative ONLY when the differential equation is a polynomial equation in its…; C) Biot-Savart Law: dB = (mu_0 / 4*pi) * I (dl x r_hat) / r^2 (gives B at center of circular coil of N turns: B = mu_0*N*I / (2R)).; D) SN2 (Bimolecular): Single-step concerted mechanism with backside attack, pentacoordinate transition state, 100% Waldens Inversion of configuration, Rate = k[R-X][Nu-], favored by polar aprotic solvents,… |
| 28 | Summarize the key NCERT Class 12 Organic Name Reactions for Haloalkanes, Alcohols, Phenols, and Ethers (Finkelstein, Swarts, Sandmeyer, Reimer-Tiemann, Kolbe's, and Williamson Synthesis). | Finkelstein: R-X + NaI (in dry acetone) -> R-I + NaX; Swarts: R-Br + AgF -> R-F; Wurtz: 2 R-X + 2 Na (dry ether) -> R-R; Reimer-Tiemann Reaction: Phenol + CHCl3 + aq. NaOH (followed by H+) -> Salicylaldehyde (2-Hydroxybenzaldehyde, via dichlorocarbene :CCl2 electrophile); Kolbe's Reaction: Phenol + NaOH + CO2 (4–7 atm, 400 K, H+) -> Salicylic Acid (2-Hydroxybenzoic acid; acetylation of salicylic acid with acetic anhydride yields Aspirin); Williamson Ether Synthesis (SN2): R'-ONa + R-X -> R'-O-R (requires primary alkyl halide R-X; if 3° R-X is used, elimination gives an alkene). | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Mendel's 3 Laws: Dominance, Segregation (universally valid without exceptions - purity of gametes), and Independent Assortment (applies to unlinked genes; T.H.; B) Order is the order of the highest order derivative present in the equation; Degree is the highest power of the highest order derivative ONLY when the differential equation is a polynomial equation in its…; C) Finkelstein: R-X + NaI (in dry acetone) -> R-I + NaX; Swarts: R-Br + AgF -> R-F; Wurtz: 2 R-X + 2 Na (dry ether) -> R-R; Reimer-Tiemann Reaction: Phenol + CHCl3 + aq. NaOH (followed by H+) -> Salicylaldehyde (2-Hydroxybenzaldehyde, via dichlorocarbene :CCl2 electrophile); Kolbe's Reaction: Phenol + NaOH + CO2 (4–7 atm, 400 K, H+) -> Salicylic Acid (2-Hydroxybenzoic acid; acetylation of salicylic acid with acetic anhydride yields Aspirin); Williamson Ether Synthesis (SN2): R'-ONa + R-X -> R'-O-R (requires primary alkyl halide R-X; if 3° R-X is used, elimination gives an alkene). ✓; D) Lens Maker's Formula: 1/f = (n_21 - 1) * (1/R_1 - 1/R_2). |
| 29 | In Class 12 Computer Science (Python & SQL), what are the differences between Mutable and Immutable data types in Python, File Modes, and SQL GROUP BY vs WHERE? | Python Immutable types: int, float, bool, str, tuple (cannot be modified in-place); Mutable types: list, dict, set. File modes: 'r' (read), 'w' (write - overwrites), 'a' (append), 'rb'/'wb' (binary using `pickle.dump()` and `pickle.load()`), `csv.writer()` / `csv.reader()`. In SQL, `WHERE` filters individual rows BEFORE grouping (cannot contain aggregate functions like COUNT, SUM, AVG), whereas `HAVING` filters groups created by `GROUP BY` and can use aggregate functions. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Python Immutable types: int, float, bool, str, tuple (cannot be modified in-place); Mutable types: list, dict, set. File modes: 'r' (read), 'w' (write - overwrites), 'a' (append), 'rb'/'wb' (binary using `pickle.dump()` and `pickle.load()`), `csv.writer()` / `csv.reader()`. In SQL, `WHERE` filters individual rows BEFORE grouping (cannot contain aggregate functions like COUNT, SUM, AVG), whereas `HAVING` filters groups created by `GROUP BY` and can use aggregate functions. ✓; B) Biot-Savart Law: dB = (mu_0 / 4*pi) * I (dl x r_hat) / r^2 (gives B at center of circular coil of N turns: B = mu_0*N*I / (2R)).; C) Lanthanoid Contraction is the steady decrease in atomic and ionic radii of lanthanoids (Ce to Lu, 4f series) with increasing atomic number due to poor shielding of 4f electrons.; D) Genetic Code (64 codons): 61 code for 20 amino acids + 3 Stop/Nonsense codons (UAA - Ochre, UAG - Amber, UGA - Opal). |
| 30 | In Molecular Basis of Inheritance, trace the discovery of DNA as the Genetic Material (Griffith, Avery-MacLeod-McCarty, Hershey-Chase), Meselson-Stahl Experiment, and the Central Dogma. | Griffith (1928): Transforming Principle using Streptococcus pneumoniae (R-strain & heat-killed S-strain in mice); Avery, MacLeod & McCarty (1944): Proved DNA is the transforming principle using DNase/RNase/Protease; Hershey & Chase (1952 - unequivocal proof): Used bacteriophage labeled with radioactive 32P (DNA) and 35S (protein coat). Meselson & Stahl (1958): Proved Semi-Conservative DNA Replication in E. coli using heavy nitrogen isotope 15NH4Cl and 14NH4Cl density gradient centrifugation in CsCl. DNA Replication is continuous on the 3'->5' template (Leading strand) and discontinuous via Okazaki fragments on the 5'->3' template (Lagging strand, joined by DNA Ligase) because DNA Polymerase III synthesizes ONLY in the 5' -> 3' direction. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Every differentiable function is continuous, but a continuous function need not be differentiable (e.g., f(x) = \|x\| at x = 0).; B) Griffith (1928): Transforming Principle using Streptococcus pneumoniae (R-strain & heat-killed S-strain in mice); Avery, MacLeod & McCarty (1944): Proved DNA is the transforming principle using DNase/RNase/Protease; Hershey & Chase (1952 - unequivocal proof): Used bacteriophage labeled with radioactive 32P (DNA) and 35S (protein coat). Meselson & Stahl (1958): Proved Semi-Conservative DNA Replication in E. coli using heavy nitrogen isotope 15NH4Cl and 14NH4Cl density gradient centrifugation in CsCl. DNA Replication is continuous on the 3'->5' template (Leading strand) and discontinuous via Okazaki fragments on the 5'->3' template (Lagging strand, joined by DNA Ligase) because DNA Polymerase III synthesizes ONLY in the 5' -> 3' direction. ✓; C) Initial Capacitance C_0 = epsilon_0 * A / d.; D) Lanthanoid Contraction is the steady decrease in atomic and ionic radii of lanthanoids (Ce to Lu, 4f series) with increasing atomic number due to poor shielding of 4f electrons. |
| 31 | In Chemical Kinetics, compare Zero-Order and First-Order Reactions (Rate Law, Units of k, Integrated Rate Equation, and Half-Life t_1/2) and the Arrhenius Equation. | Units of k for n-th order: mol^(1-n) L^(n-1) s^-1. Zero Order: [R] = [R]_0 - k*t, units of k = mol L^-1 s^-1, and t_1/2 = [R]_0 / (2k) (proportional to initial concentration; e.g., enzyme catalysis or decomposition of NH3 on hot Pt). First Order: k = (2.303 / t) * log10([R]_0 / [R]), units of k = s^-1, and t_1/2 = 0.693 / k (INDEPENDENT of initial concentration [R]_0; e.g., all radioactive decay). Arrhenius Equation: k = A * e^(-E_a / RT), or log10(k2/k1) = (E_a / 2.303R) * [(T2 - T1)/(T1*T2)]. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Rosenmund Reduction: R-COCl + H2 (Pd-BaSO4) -> R-CHO; Stephen: R-CN + SnCl2/HCl -> R-CHO; Etard: Toluene + CrO2Cl2 -> Benzaldehyde; Clemmensen Reduction: >C=O + Zn-Hg / conc.; B) Exponential Growth (J-shaped, unlimited resources): dN/dt = rN; Verhulst-Pearl Logistic Growth (S-shaped/Sigmoid, carrying capacity K): dN/dt = rN * [(K - N) / K].; C) Initial Capacitance C_0 = epsilon_0 * A / d.; D) Units of k for n-th order: mol^(1-n) L^(n-1) s^-1. Zero Order: [R] = [R]_0 - k*t, units of k = mol L^-1 s^-1, and t_1/2 = [R]_0 / (2k) (proportional to initial concentration; e.g., enzyme catalysis or decomposition of NH3 on hot Pt). First Order: k = (2.303 / t) * log10([R]_0 / [R]), units of k = s^-1, and t_1/2 = 0.693 / k (INDEPENDENT of initial concentration [R]_0; e.g., all radioactive decay). Arrhenius Equation: k = A * e^(-E_a / RT), or log10(k2/k1) = (E_a / 2.303R) * [(T2 - T1)/(T1*T2)]. ✓ |
| 32 | In Vector Algebra and 3D Geometry (Class 12 Maths), what are the formulas for Projection of a Vector, Area of a Triangle/Parallelogram, and Shortest Distance between Two Skew Lines? | Scalar Projection of vector a on vector b = (a . b) / \|b\|. Area of Parallelogram with adjacent sides a and b = \|a x b\|; Area of Parallelogram with diagonals d1 and d2 = (1/2)*\|d1 x d2\|; Area of Triangle = (1/2)*\|a x b\|. Shortest Distance between two skew lines r = a1 + lambda*b1 and r = a2 + mu*b2 is d = \|(b1 x b2) . (a2 - a1)\| / \|b1 x b2\| (lines are coplanar/intersecting if d = 0). Distance between parallel lines r = a1 + lambda*b and r = a2 + mu*b is d = \|b x (a2 - a1)\| / \|b\|. | High-yield exam verification (CBSE Class 12 Board Exam (Science Stream NCERT)): distinguish the controlling statutory/doctrinal rule, timeframe, and exception from common test distractors. | A) Scalar Projection of vector a on vector b = (a . b) / \|b\|. Area of Parallelogram with adjacent sides a and b = \|a x b\|; Area of Parallelogram with diagonals d1 and d2 = (1/2)*\|d1 x d2\|; Area of Triangle = (1/2)*\|a x b\|. Shortest Distance between two skew lines r = a1 + lambda*b1 and r = a2 + mu*b2 is d = \|(b1 x b2) . (a2 - a1)\| / \|b1 x b2\| (lines are coplanar/intersecting if d = 0). Distance between parallel lines r = a1 + lambda*b and r = a2 + mu*b is d = \|b x (a2 - a1)\| / \|b\|. ✓; B) Initial Capacitance C_0 = epsilon_0 * A / d.; C) Nernst Equation at 298 K: E_cell = E^0_cell - (0.0591 / n) * log10(Q), and Delta_G^0 = -n * F * E^0_cell = -2.303 * R * T * log10(K_c) (where F = 96,487 C/mol ≈ 96,500 C/mol).; D) Mendel's 3 Laws: Dominance, Segregation (universally valid without exceptions - purity of gametes), and Independent Assortment (applies to unlinked genes; T.H. |

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