In Bangladesh Medical & DU Admission (HSC Botany - Cell & Vascular Bundles), classify Plant Vascular Bundles (Radial, Conjoint Collateral Open vs. Closed, Bicollateral, and Concentric: Hadrocentric vs. Leptocentric) with NCTB textbook examples.

1. Radial (Xylem and Phloem lie on separate alternating radii): all Roots (Dicot root has 2–4 xylem/phloem bundles; Monocot root has >6 polyarch bundles). 2. Conjoint Collateral OPEN (Cambium present between Xylem and Phloem): Dicot stems and Gymnosperm stems. 3. Conjoint Collateral CLOSED (No cambium): Monocot stems (scattered in ground tissue, e.g., Maize, Grass). 4. Bicollateral (Phloem on both outer and inner sides of Xylem with two strips of cambium): Cucurbita (gourd/pumpkin) stem. 5. Concentric Hadrocentric / Amphicribral (Xylem in center surrounded by Phloem): Pteris / Fern rhizome, Lycopodium. 6. Concentric Leptocentric / Amphivasal (Phloem in center surrounded by Xylem): Dracaena, Yucca.

In Bangladesh DGHS Medical Admission Test (MBBS/BDS Exam Structure), how are the 100 MCQ marks and 200 SSC/HSC GPA marks weighted, and what is the negative marking rule?

Total Merit Score = 300 marks: 200 marks from SSC & HSC GPA (SSC GPA × 15 = 75 marks + HSC GPA × 25 = 125 marks) PLUS 100 marks from the 1-hour (60-minute) 100-MCQ Written Test: Biology (30 marks), Chemistry (25 marks), Physics (20 marks), English (15 marks), and General Knowledge—Bangladesh History/Liberation War & International (10 marks). Each wrong MCQ deducts 0.25 marks (pass mark = 40/100).

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Semiconductors & Transistors), relate the Transistor Current Gain parameters Alpha (α) and Beta (β) in Common-Base vs. Common-Emitter configurations.

For any Bipolar Junction Transistor (NPN or PNP), Emitter current equals the sum of Base current and Collector current: I_E = I_B + I_C (where ~95–99% of emitter carriers reach the collector and I_B is very small in µA). Common-Base current amplification factor α = ΔI_C / ΔI_E (always slightly less than 1, typically 0.95–0.99). Common-Emitter current gain β = ΔI_C / ΔI_B (large, typically 20–500). Exact conversion formulas: β = α / (1 - α) and α = β / (1 + β) (with 1/α - 1/β = 1).

In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Dynamics: Projectiles & Coupled Pulleys), state the Trajectory Equation of a Projectile in Cartesian form y = x tan α - [gx² / (2u² cos²α)] and its shortcut using Horizontal Range R.

Standard Cartesian equation of projectile path (a parabola): y = x tan α - [gx² / (2u² cos²α)]. Factoring out x tan α and substituting R = (u² sin 2α)/g gives the high-speed admission formula: y = x tan α (1 - x/R) (or tan α = y/x + y/(R - x)), which immediately relates any point (x, y) on the trajectory to the launch angle α and total horizontal range R!

In Bangladesh Medical & Engineering Admission (HSC Quantitative Chemistry - Beer-Lambert Law & Redox Titration), state Beer-Lambert's Law of Spectrophotometry and calculate the equivalent weight of KMnO4, K2Cr2O7, H2C2O4, and Na2S2O3 in redox titrations.

Beer-Lambert Law: When monochromatic light passes through an absorbing solution, Absorbance A = log10(I0 / I) = ε · c · l (where ε is molar absorptivity in L·mol⁻¹·cm⁻¹, c is molar concentration in mol/L, and l is path length in cm). Redox Equivalent Weights (Molar Mass ÷ Electrons transferred per molecule): 1. KMnO4 (M = 158) in Acidic medium (MnO4⁻ + 8H⁺ + 5e⁻ -> Mn²⁺ + 4H2O, Δe = 5): Eq. Wt. = 158 / 5 = 31.6 (in neutral/weakly alkaline medium -> MnO2, Δe = 3, Eq. Wt. = 158/3; in strongly alkaline -> MnO4²⁻, Δe = 1). 2. K2Cr2O7 (M = 294.2) in Acidic medium (Cr2O7²⁻ + 14H⁺ + 6e⁻ -> 2Cr³⁺ + 7H2O, Δe = 6): Eq. Wt. = 294.2 / 6 = 49.03. 3. Oxalic Acid (C2O4²⁻ -> 2CO2 + 2e⁻, Δe = 2): Eq. Wt. = M / 2 = 126 / 2 = 63 (hydrated). 4. Sodium Thiosulfate Na2S2O3 (2S2O3²⁻ -> S4O6²⁻ + 2e⁻, Δe = 1 per molecule in iodometry): Eq. Wt. = M / 1.

In Bangladesh Medical & Engineering Admission (HSC Chemistry - Periodic Properties & Fajan's Rule), state Fajan's Rules of Polarization (covalent character in ionic bonds) and explain how polarization affects melting point, solubility in water, and thermal decomposition of carbonates.

Fajan's Rule: When a cation approaches an anion, the cation's positive charge attracts the anion's electron cloud while repelling its nucleus, distorting (polarizing) the anion and introducing COVALENT character into the ionic bond. Polarization increases with: 1. Small size of cation (Be²⁺ > Mg²⁺ > Ca²⁺ > Sr²⁺ > Ba²⁺), 2. Large size of anion (I⁻ > Br⁻ > Cl⁻ > F⁻), 3. High charge on cation or anion (Al³⁺ > Mg²⁺ > Na⁺), and 4. Pseudo-inert (d¹⁰) electronic configuration of cation (AgCl is more covalent and insoluble in water than NaCl; FeCl3 has a lower MP than FeCl2). Greater polarization -> MORE covalent character -> LOWER melting/boiling point, LOWER solubility in polar water, and LOWER thermal stability of metal carbonates (BeCO3 decomposes at the lowest temperature).

In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Matrices & Determinants), state the properties of Symmetric, Skew-Symmetric, Orthogonal, Idempotent, Involutory, and Nilpotent Matrices.

For a square matrix A: 1. Symmetric: A^T = A; 2. Skew-Symmetric: A^T = -A (all main diagonal entries are 0); 3. Orthogonal: A · A^T = A^T · A = I (so A⁻¹ = A^T and det(A) = ±1); 4. Idempotent: A² = A; 5. Involutory: A² = I (so A⁻¹ = A); 6. Nilpotent of index k: A^k = 0 (where k is the smallest positive integer). Also, for an n×n matrix A, det(adj A) = |A|^(n-1) and A · adj(A) = |A| · I.

In Bangladesh Medical & University Admission (English Grammar - Right Form of Verbs, Subjunctive & Conditional Sentences), state the grammar rules for 'As if / As though', 'Would that / I wish', and 'Lest'.

1. 'As if / As though': If the clause before 'as if/as though' is in the Present Indefinite tense, the clause after it takes the PAST INDEFINITE (with 'were' for all persons: 'He talks as if he KNEW everything / WERE a doctor'). If the clause before 'as if/as though' is in the Past Indefinite tense, the clause after it takes the PAST PERFECT ('He talked as if he HAD KNOWN everything'). 2. 'Lest' (meaning 'for fear that', inherently negative so never use 'not' after it): ALWAYS followed by 'Subject + SHOULD / MIGHT + Bare Infinitive (V1)' ('Walk fast lest you SHOULD miss the train'). 3. 'I wish / Would that / Fancy / It is high time + Subject': followed by the Past Indefinite (or 'were').

In Bangladesh Medical & DU Admission (HSC Biology - Genetics & Blood Groups), explain Erythroblastosis Fetalis (Hemolytic Disease of the Newborn) due to Rh Factor incompatibility and how it is prevented.

When an Rh-negative mother (dd) carries an Rh-positive fetus (Dd, inherited from an Rh+ father), the first pregnancy is usually unaffected because fetal RBCs cross the placenta mainly during placental separation at delivery, sensitizing the mother to produce anti-Rh (anti-D) IgG antibodies. In a subsequent pregnancy with another Rh+ fetus, maternal anti-D IgG antibodies cross the placenta and hemolyze fetal RBCs, causing fatal fetal anemia, jaundice, kernicterus, and hydrops fetalis (Erythroblastosis fetalis). It is prevented by administering anti-D immunoglobulin (RhoGAM) to the Rh- mother at 28 weeks gestation and within 72 hours after delivering an Rh+ baby.

In Bangladesh Medical & Engineering Admission (HSC Chemistry - Environmental Chemistry: Gas Laws & Water Quality Parameters), define DO, BOD, COD, and TDS in water pollution, and state their WHO acceptable standards.

1. DO (Dissolved Oxygen, measured by Winkler's iodometric titration method): oxygen gas dissolved in water essential for aquatic life—minimum 4.0–6.0 mg/L (ppm) required for fish survival (pure surface water has 7–8 ppm). 2. BOD (Biochemical Oxygen Demand): amount of dissolved O2 (in mg/L) consumed by aerobic microorganisms over 5 days at 20°C in the dark to decompose biodegradable organic waste (WHO safe drinking water BOD ≤ 1–3 ppm; >10 ppm indicates severe organic pollution). 3. COD (Chemical Oxygen Demand): total oxygen required to chemically oxidize BOTH biodegradable and non-biodegradable organic pollutants using acidic K2Cr2O7 (therefore, for any water sample, COD value is ALWAYS greater than BOD!). 4. TDS (Total Dissolved Solids): safe limit ≤ 500 ppm; WHO drinking water pH range: 6.5–8.5; Arsenic (As) acceptable limit in Bangladesh: ≤ 0.05 mg/L (50 ppb; WHO limit ≤ 0.01 mg/L).

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Special Theory of Relativity), write the Lorentz Transformation formulas for Length Contraction, Time Dilation, Relativistic Mass, and Relativistic Kinetic Energy.

Let the Lorentz factor γ = 1 / √(1 - v²/c²) ≥ 1: 1. Length Contraction (only along the direction of motion): L = L₀√(1 - v²/c²) = L₀ / γ (moving rod appears shorter: L t₀). 3. Relativistic Mass: m = m₀ / √(1 - v²/c²) = γm₀. 4. Total Relativistic Energy: E = mc² = E₀ + K, so Rest Mass Energy E₀ = m₀c², Relativistic Kinetic Energy K = (m - m₀)c² = (γ - 1)m₀c², and Energy-Momentum relation: E² = (pc)² + (m₀c²)² (for a massless photon with m₀ = 0, E = pc). Note shortcut: if a meter stick shrinks to half its rest length (L = L₀/2) or a particle's mass doubles (m = 2m₀), its speed is v = (√3 / 2)c ≈ 0.866c!

In Bangladesh Medical Admission (HSC Zoology - Hydra, Grasshopper & Rui Fish Labeo rohita), state the types of Nematocysts in Hydra, the mouthparts of Poekilocerus pictus, and the 'Venus Heart' circulation of Labeo rohita.

Hydra Nematocysts (4 types): 1. Stenotele / Penetrant (largest—injects toxic fluid 'hypnotoxin' composed of proteins and phenols to paralyze prey), 2. Volvent / Desmoneme (coils tightly around bristles of prey), 3. Streptoline Glutinant (long spiny sticky thread), and 4. Stereoline Glutinant (small spineless sticky thread for locomotion). Grasshopper mouthparts (Mandibulate / chewing type): Labrum (upper lip), a pair of toothed Mandibles, a pair of Maxillae, Labium (lower lip), and Hypopharynx (tongue). Labeo rohita (Rui fish) Heart: two-chambered (Sinus venosus -> Atrium -> Ventricle -> Bulbous arteriosus, no conus arteriosus)—called a 'Venus Heart' because ONLY deoxygenated (CO2-rich) blood passes through it in a single-circuit circulation straight to the 4 pairs of holobranch gills for oxygenation.

In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Integral Calculus Shortcuts), state the fast admission shortcuts for ∫ e^x [f(x) + f'(x)] dx and Wallis's Formula for ∫₀^(π/2) sin^n(x) dx and Area bounded by a Parabola y² = 4ax and its Latus Rectum or a line y = mx.

1. Cancellation integral: ∫ e^x [f(x) + f'(x)] dx = e^x · f(x) + c. 2. ∫ [f'(x) / f(x)] dx = ln|f(x)| + c. 3. ∫₀^(π/2) [sin^n(x) / (sin^n(x) + cos^n(x))] dx = π / 4 for ANY real n! 4. Area bounded by the parabola y² = 4ax and its latus rectum (x = a) is (8/3)a². 5. Area bounded between the parabola y² = 4ax and the straight line y = mx is (8a²) / (3m³); area between two parabolas y² = 4ax and x² = 4by is (16ab) / 3.

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Vector Calculus: Gradient, Divergence & Curl), define the Del operator (∇) and give the physical criteria for a Solenoidal vector field vs. an Irrotational (Conservative) vector field.

Del operator: ∇ = î(∂/∂x) + ĵ(∂/∂y) + k̂(∂/∂z). 1. Gradient of a scalar field φ (∇φ): is a VECTOR pointing in the direction of maximum rate of increase of φ. 2. Divergence of a vector field V (∇ · V = ∂Vx/∂x + ∂Vy/∂y + ∂Vz/∂z): is a SCALAR measuring net outward flux per unit volume; if ∇ · V = 0 everywhere, the vector field V is SOLENOIDAL (incompressible, e.g., magnetic field ∇ · B = 0). 3. Curl of a vector field V (∇ × V): is a VECTOR measuring rotation/vorticity; if ∇ × V = 0 everywhere, the vector field V is IRROTATIONAL (Conservative, e.g., electrostatic field ∇ × E = 0).

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Elasticity, Surface Tension & Viscosity), relate Surface Tension (T) to Surface Energy (E), state Jurin's Capillary Rise formula, and state Stokes' Law of Terminal Velocity.

Work done in increasing liquid surface area by ΔA is ΔW = T · ΔA, so Surface Tension T (in N/m) is numerically equal to Surface Energy E per unit area (in J/m²). Excess pressure inside a liquid drop of radius r: ΔP = 2T / r; inside a soap bubble (two air-liquid surfaces): ΔP = 4T / r. Capillary rise/depression formula: h = (2T cos θ) / (rρg) (for pure water in clean glass, contact angle θ = 0°; for mercury in glass, θ ≈ 139°–140° obtuse, so cos θ is negative and mercury is depressed). Stokes' Law for viscous drag on a sphere of radius r moving at speed v through a fluid of viscosity η: F = 6πηrv, yielding Terminal Velocity v_t = [2r²(ρ_s - ρ_f)g] / (9η).

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Rotational Mechanics & Moment of Inertia), state the Parallel-Axis and Perpendicular-Axis Theorems, and list the Moments of Inertia (I) and Radii of Gyration (K) for a Thin Rod, Circular Ring, Circular Disc, and Solid Sphere.

Perpendicular-Axis Theorem (for a planar lamina in the xy-plane): I_z = I_x + I_y. Parallel-Axis Theorem: I = I_G + Mh² (where I_G is moment of inertia about an axis through the center of mass and h is perpendicular distance between the two parallel axes); Radius of gyration K = √(I / M). Standard Moments of Inertia: 1. Thin uniform rod of length L about perpendicular axis through center: I = (1/12)ML² [about one end: I = (1/3)ML²]. 2. Thin circular ring / hollow cylinder of radius R about central axis: I = MR². 3. Uniform circular disc / solid cylinder about central axis: I = ½ MR² [about a diameter: I = ¼ MR²]. 4. Solid sphere of radius R about any diameter: I = (2/5)MR² [Hollow thin spherical shell: I = (2/3)MR²].

In Bangladesh Medical Admission (HSC Botany - Plant Families: Malvaceae vs. Poaceae), compare the floral characteristics and placentation of Family Poaceae (Gramineae, Monocot) and Family Malvaceae (Dicot).

Poaceae (Rice Oryza sativa, Wheat, Bamboo, Sugarcane): Spikelet inflorescence, perianth represented by 2 lodicules, 3 or 6 versatile stamens, feathery stigma, Basal placentation, and Caryopsis fruit. Malvaceae (China rose Hibiscus rosa-sinensis, Cotton, Lady's finger/Okra, Jute): young parts mucilaginous, free lateral stipules, Epicalyx present, twisted aestivation of 5 petals, numerous Monadelphous stamens (filaments fused into a staminal tube around the style), reniform (kidney-shaped) one-celled anthers with large spiny pollen grains, and Axile placentation (5 carpels).

In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Straight Lines & Circles), write the formulas for the perpendicular distance from a point to a line, distance between two parallel lines, and length of tangent from P(x1, y1) to the circle x² + y² + 2gx + 2fy + c = 0.

Perpendicular distance from (x1, y1) to ax + by + c = 0: d = |ax1 + by1 + c| / √(a² + b²). Distance between parallel lines ax + by + c1 = 0 and ax + by + c2 = 0: d = |c1 - c2| / √(a² + b²). For circle S ≡ x² + y² + 2gx + 2fy + c = 0: Center = (-g, -f), Radius r = √(g² + f² - c), x-intercept length = 2√(g² - c), y-intercept length = 2√(f² - c), and length of tangent from external point P(x1, y1) is √(S1) = √(x1² + y1² + 2gx1 + 2fy1 + c).

In Bangladesh Medical Admission (General Knowledge & Public Health Institutions of Bangladesh), match the premier medical, agricultural, and scientific research institutes of Bangladesh and their locations/achievements.

1. icddr,b (International Centre for Diarrhoeal Disease Research, Bangladesh, located at Mohakhali, Dhaka; originally established in 1960 as SEATO Cholera Research Laboratory): pioneered Oral Rehydration Solution (ORS), saving over 70 million lives globally. 2. IEDCR (Institute of Epidemiology, Disease Control and Research, Mohakhali, Dhaka): national infectious disease surveillance & outbreak response. 3. BSMMU (Bangabandhu Sheikh Mujib Medical University, Shahbag, Dhaka—established 1998 converting IPGMR of 1965, first medical university of Bangladesh). 4. BRRI (Bangladesh Rice Research Institute, Gazipur, 1970) & BARI (Bangladesh Agricultural Research Institute, Gazipur) & BINA (Mymensingh; Dr. Maqsudul Alam decoded the genome sequence of Tosha & Deshi Jute in 2010 and Macrophomina phaseolina fungus in 2012).

In Bangladesh Medical & BUET Admission (HSC Chemistry - Solubility Product K_sp & Ionic Product K_ip), state the relationship between K_ip and K_sp for unsaturated, saturated, and supersaturated solutions, and express K_sp for AB, AB2, A2B3, and Al(OH)3 in terms of molar solubility S.

If K_ip K_sp: solution is supersaturated and PRECIPITATION occurs until K_ip = K_sp! K_sp expressions in terms of molar solubility S (mol/L): 1:1 salt AB (e.g., AgCl, BaSO4): K_sp = S²; 1:2 or 2:1 salt AB2 / A2B (e.g., CaF2, PbCl2, Ag2CrO4): K_sp = 4S³; 1:3 salt AB3 [e.g., Al(OH)3, Fe(OH)3]: K_sp = 27S⁴; 2:3 salt A2B3 [e.g., Ca3(PO4)2]: K_sp = 108S⁵.

In Bangladesh Medical Admission (HSC Zoology - Human Physiology: Blood, Coagulation & Cranial Nerves), list the 13 Blood Clotting Factors (especially Factors I–IV and VIII–X) and the 12 Pairs of Human Cranial Nerves with their sensory/motor modalities.

4 Primary Clotting Factors ('FPTC'): Factor I = Fibrinogen; Factor II = Prothrombin; Factor III = Thromboplastin (Tissue Factor); Factor IV = Calcium ions (Ca²⁺, the only non-protein inorganic factor!). Factor VIII = Antihemophilic Factor A (Classic Hemophilia A); Factor IX = Christmas Factor / Plasma Thromboplastin Component (Hemophilia B); Factor XII = Hageman Factor; Factor XIII = Fibrin-stabilizing Factor. 12 Pairs of Cranial Nerves ('OOOTTAFVGVAH' / 'Some Say Marry Money But My Brother Says Big Brains Matter More'): Purely Sensory (1, 2, 8): I Olfactory (smell), II Optic (vision), VIII Vestibulocochlear/Auditory (hearing & balance). Purely Motor (3, 4, 6, 11, 12): III Oculomotor, IV Trochlear (smallest, supplies superior oblique), VI Abducens (supplies lateral rectus), XI Accessory, XII Hypoglossal (tongue muscles). Mixed Sensory & Motor (5, 7, 9, 10): V Trigeminal (largest, 3 branches), VII Facial, IX Glossopharyngeal, X Vagus (longest/wandering nerve).

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Simple Harmonic Motion & Lissajous Figures), write the differential equation, velocity, acceleration, kinetic energy, and potential energy of a particle in SHM of amplitude A and angular frequency ω.

Differential equation of SHM: d²x/dt² + ω²x = 0 (where ω = 2π/T = 2πf = √(k/m)). At displacement x from equilibrium: Velocity v = ω√(A² - x²) (maximum at mean position x = 0: v_max = ωA; zero at extreme position x = ±A); Acceleration a = -ω²x (zero at mean position; maximum at extreme position: a_max = ω²A). Kinetic Energy E_k = ½ k(A² - x²); Potential Energy E_p = ½ kx²; Total Mechanical Energy E = E_k + E_p = ½ kA² = 2π²mf²A² (constant everywhere).Note: If the time period of displacement is T, the time period of Kinetic and Potential Energy variation is T/2 (frequency is 2f)!

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Gravitation & Escape Velocity), derive the relationship between Escape Velocity (v_e) and Orbital Velocity (v_o) of a satellite orbiting close to the Earth's surface, and state the height and period of a Geostationary (Parking) Orbit.

Escape Velocity from Earth's surface: v_e = √(2GM / R) = √(2gR) ≈ 11.2 km/s (independent of the mass or angle of projection of the projectile!). Orbital Velocity of a satellite close to Earth's surface (r ≈ R): v_o = √(GM / R) = √(gR) ≈ 7.9 km/s. Therefore, v_e = √2 · v_o (if a satellite's orbital speed is increased by √2 times—or by 41.4%—or its kinetic energy is doubled, it escapes into infinity!). A Geostationary Satellite (such as Bangabandhu-1 launched on May 11, 2018 at 119.1° E) orbits in the equatorial plane from West to East with period T = 24 hours at an altitude h ≈ 35,800 km (~36,000 km) above Earth's surface.

In Bangladesh Medical Admission (HSC Botany - Photosynthesis & Respiration), compare the C3 (Calvin) Cycle and C4 (Hatch & Slack) Pathway across optimum temperature, first stable product, Kranz anatomy, and CO2 compensation point.

C3 Pathway (Rice, Wheat, Mango, Jute, 85% of plants): no Kranz anatomy (chloroplasts of one type), primary CO2 acceptor is 5C RuBP (via RuBisCO), first stable product is 3C 3-Phosphoglyceric acid (3-PGA), optimum temperature 10°C–25°C, high photorespiration, CO2 compensation point is high (50–100 ppm). C4 Pathway (Maize, Sugarcane, Sorghum, Amaranthus, Muthaghas): Kranz anatomy present (dimorphic chloroplasts: granal in mesophyll, agranal in bundle sheath), primary CO2 acceptor in mesophyll is 3C Phosphoenolpyruvate (PEP via PEP carboxylase), first stable product is 4C Oxaloacetic acid (OAA), optimum temperature 30°C–45°C, negligible photorespiration, low CO2 compensation point (0–10 ppm).

In Bangladesh Medical & Engineering Admission (HSC Organic Chemistry - Named Reactions), summarize the Wurtz, Friedel-Crafts, Reimer-Tiemann, Kolbe's Schmitt, Sandmeyer, Hoffmann Bromamide Degradation, Diazotization, and Clemmensen vs. Wolff-Kishner Reduction reactions.

1. Wurtz Reaction: 2 R-X + 2 Na (in dry ether) -> R-R (symmetrical alkane with double carbon chain). 2. Reimer-Tiemann Reaction: Phenol + CHCl3 + aq. NaOH at 60–70°C (followed by HCl) -> Salicylaldehyde (2-hydroxybenzaldehyde). 3. Kolbe-Schmitt Reaction: Sodium phenoxide + CO2 at 125°C under 4–7 atm pressure (followed by HCl) -> Salicylic acid (2-hydroxybenzoic acid—reacting Salicylic acid with acetic anhydride yields Aspirin / acetylsalicylic acid, while reacting with methanol yields Oil of Wintergreen / methyl salicylate). 4. Hoffmann Bromamide Degradation: Acid amide (R-CONH2) + Br2 + 4 KOH -> Primary Amine with ONE LESS carbon atom (R-NH2) + K2CO3 + 2 KBr. 5. Diazotization: Aniline (C6H5NH2) + NaNO2 + HCl at 0°C–5°C -> Benzene diazonium chloride (C6H5N2⁺Cl⁻). 6. Clemmensen Reduction (Zn-Hg amalgam + conc. HCl) & Wolff-Kishner Reduction (Hydrazine NH2NH2 + KOH in ethylene glycol): both reduce the carbonyl group (>C=O) of aldehydes and ketones directly to a methylene group (-CH2-) / alkane!

In Bangladesh Medical & Engineering Admission (HSC Organic Chemistry - Isomerism, Cis-Trans & Optical Activity), state the conditions for Geometrical (cis-trans) Isomerism and Optical Isomerism (Enantiomers, Diastereomers, Meso compounds, Racemic mixture), and calculate the number of optical isomers for a molecule with n chiral carbons.

Geometrical Isomerism occurs due to restricted rotation around a C=C double bond or cyclic ring when each doubly-bonded carbon is attached to two different groups [abC=Cab; cis has identical groups on the same side (higher dipole moment μ > 0, higher boiling point, lower melting point); trans has identical groups on opposite sides (symmetrical, μ ≈ 0, higher melting point due to compact crystal packing)]. Optical Isomerism requires a Chiral (Asymmetric) Carbon attached to 4 different groups (aCabcd) and absence of a plane/center of symmetry—rotating plane-polarized light measured by a Polarimeter. For a molecule with n dissimilar chiral centers, number of optically active stereoisomers = 2^n. A Racemic Mixture (dl- or (±)-mixture, e.g., lactic acid) contains 50% d-enantiomer and 50% l-enantiomer and is optically inactive due to EXTERNAL compensation; a Meso compound (e.g., meso-tartaric acid) has chiral carbons but is optically inactive due to INTERNAL compensation (plane of symmetry within the molecule).

In BUET/CKRUET/DU Engineering Admission (HSC Physics - Physical Optics, Interference & Diffraction), state the path difference and phase difference conditions for Constructive and Destructive Interference in Young's Double-Slit Experiment, plus Brewster's Law of Polarization.

Phase difference δ = (2π / λ) × Path difference Δx. Constructive Interference (Bright fringe): Path difference Δx = nλ = (2n)(λ/2), Phase difference δ = 2nπ (where n = 0, 1, 2...). Destructive Interference (Dark fringe): Path difference Δx = (2n + 1)(λ/2), Phase difference δ = (2n + 1)π. In Young's Double-Slit Experiment (slit separation d, screen distance D): fringe width of a single bright or dark fringe β = λD / (2d), and distance between two successive bright (or two successive dark) fringes Δy = λD / d. Note that for a Single-Slit Fraunhofner Diffraction pattern of slit width 'a', the conditions are reversed: minima occur at a sin θ = nλ. Brewster's Law (Polarization by Reflection): when unpolarized light is incident at the polarizing angle θ_p such that the reflected and refracted rays are mutually perpendicular (θ_p + r = 90°), the reflected light is 100% plane-polarized and μ = tan θ_p.

In Bangladesh Medical Admission (HSC Zoology - Animal Kingdom Classification), match the 9 major Animal Phyla to their symmetry, body cavity (Coelom), and unique excretory/locomotory organs.

1. Porifera (Sponges—Scypha): cellular grade, asymmetrical, ostia, spongocoel, osculum, choanocytes (collar cells), spicules/spongin. 2. Cnidaria (Hydra, Jellyfish Aurelia, Coral): radial symmetry, diploblastic, nematocysts (cnidocytes), gastrovascular cavity (coelenteron). 3. Platyhelminthes (Taenia solium, Fasciola hepatica): bilateral, triploblastic, acoelomate, flame cells for excretion. 4. Nematoda (Ascaris lumbricoides, Loa loa, Wuchereria): pseudocoelomate, unsegmented cylindrical tube-within-a-tube. 5. Annelida (Earthworm Metaphire posthuma, Leech): true coelomate, metameric segmentation, nephridia, setae or parapodia, closed circulation with haemoglobin dissolved in plasma. 6. Arthropoda (largest phylum): jointed appendages, chitinous exoskeleton, haemocoel (open circulation), Malpighian tubules / green glands. 7. Mollusca (2nd largest—Pila, Octopus): muscular foot, visceral mass, mantle, radula (rasping tongue). 8. Echinodermata (Starfish Asterias): pentamerous radial symmetry in adults (bilateral larvae), exclusively marine, water vascular system with tube feet. 9. Chordata: notochord, dorsal hollow nerve cord, pharyngeal gill slits, post-anal tail.

In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Polynomial Equations & Inverse Trigonometry), state the relation between roots and coefficients of a cubic equation ax³ + bx² + cx + d = 0, and the formula for tan⁻¹x + tan⁻¹y.

For cubic ax³ + bx² + cx + d = 0 with roots α, β, γ: 1. Sum of roots: α + β + γ = -b/a; 2. Sum of pairwise products: αβ + βγ + γα = +c/a; 3. Product of roots: αβγ = -d/a. For Inverse Tangents (when xy < 1): tan⁻¹x + tan⁻¹y = tan⁻¹[(x + y) / (1 - xy)], and tan⁻¹x - tan⁻¹y = tan⁻¹[(x - y) / (1 + xy)]. Also, sin⁻¹x + cos⁻¹x = π/2, tan⁻¹x + cot⁻¹x = π/2, and 2tan⁻¹x = sin⁻¹[2x / (1 + x²)] = cos⁻¹[(1 - x²) / (1 + x²)] = tan⁻¹[2x / (1 - x²)].

In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Differential Calculus & L'Hôpital's Rule), state the standard limits lim_(x→0) (sin x)/x, lim_(x→0) (e^x - 1)/x, and lim_(x→0) (1 + x)^(1/x), plus L'Hôpital's Rule and Maclaurin's Series.

Standard Limits: lim_(x→0) (sin x)/x = 1 (x in radians!); lim_(x→0) (tan x)/x = 1; lim_(x→0) (1 - cos x)/x² = ½; lim_(x→0) (e^x - 1)/x = 1; lim_(x→0) [ln(1 + x)]/x = 1; lim_(x→0) (1 + ax)^(b/x) = e^(ab). L'Hôpital's Rule: if lim_(x→a) f(x)/g(x) takes the indeterminate form 0/0 or ∞/∞, differentiate numerator and denominator separately: lim_(x→a) f(x)/g(x) = lim_(x→a) f'(x)/g'(x).

In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Statics: Lami's Theorem & Resultant of Coplanar Forces), state the Parallelogram Law of Forces and Lami's Theorem for three concurrent coplanar forces in equilibrium.

Parallelogram Law: If two forces P and Q act simultaneously at a point at an angle α, their resultant R has magnitude R = √(P² + Q² + 2PQ cos α) and makes angle θ with force P given by tan θ = (Q sin α) / (P + Q cos α) (when P = Q, R = 2P cos(α/2) bisecting the angle α). Lami's Theorem: If three coplanar, concurrent forces P, Q, and R acting at a point are in equilibrium, each force is directly proportional to the sine of the angle between the other two forces: P / sin α = Q / sin β = R / sin γ.

In Bangladesh Medical & DU Admission (HSC Chemistry - Qualitative Chemistry: Flame Test & Ion Identification), match the characteristic Flame Test colors and Nessler's / Potassium Pyroantimonate / Ammonium Oxalate reagents for cations.

Flame Test Colors (using conc. HCl and Pt/nichrome wire): Sodium (Na⁺): Golden Yellow (appears black through blue cobalt glass); Potassium (K⁺): Violet / Lilac (appears crimson/pinkish-red through cobalt glass); Calcium (Ca²⁺): Brick Red (appears light green through cobalt glass); Copper (Cu²⁺): Bluish-Green; Barium (Ba²⁺): Apple / Yellowish Green; Strontium (Sr²⁺): Crimson Red. Wet Confirmations: NH4⁺ + Alkaline Nessler's Reagent (K2[HgI4] + KOH/NaOH) -> Reddish-brown precipitate of Amino-mercuric iodide (NH2-Hg-O-Hg-I); Na⁺ + Potassium Pyroantimonate (K2H2Sb2O7) -> White microcrystalline precipitate of Na2H2Sb2O7; Ca²⁺ + Ammonium Oxalate [(NH4)2C2O4] -> White precipitate of Calcium oxalate (CaC2O4, insoluble in acetic acid, soluble in dilute HCl).

Bangladesh Medical (DGHS) & Engineering (BUET/CKRUET/DU) Admission: HSC Biology, Chemistry, Physics, Higher Mathematics & General Knowledge

Covers Bangladesh DGHS Medical & Dental Admission Test (MBBS/BDS) and BUET/CKRUET/Dhaka University 'Ka' Unit Engineering Admission (NCTB HSC Syllabus): HSC Botany & Zoology, HSC Chemistry (Qualitative, Quantitative, Organic, Electrochemistry), HSC Physics, and HSC Higher Mathematics (Calculus, Conics, Vectors, Matrices, Mechanics).

Level: advanced
Languages: en → en
Cards: 32
Markdown: Bangladesh Medical (DGHS) & Engineering (BUET/CKRUET/DU) Admission: HSC Biology, Chemistry, Physics, Higher Mathematics & General Knowledge (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	In Bangladesh Medical & DU Admission (HSC Botany - Cell & Vascular Bundles), classify Plant Vascular Bundles (Radial, Conjoint Collateral Open vs. Closed, Bicollateral, and Concentric: Hadrocentric vs. Leptocentric) with NCTB textbook examples.	1. Radial (Xylem and Phloem lie on separate alternating radii): all Roots (Dicot root has 2–4 xylem/phloem bundles; Monocot root has >6 polyarch bundles). 2. Conjoint Collateral OPEN (Cambium present between Xylem and Phloem): Dicot stems and Gymnosperm stems. 3. Conjoint Collateral CLOSED (No cambium): Monocot stems (scattered in ground tissue, e.g., Maize, Grass). 4. Bicollateral (Phloem on both outer and inner sides of Xylem with two strips of cambium): Cucurbita (gourd/pumpkin) stem. 5. Concentric Hadrocentric / Amphicribral (Xylem in center surrounded by Phloem): Pteris / Fern rhizome, Lycopodium. 6. Concentric Leptocentric / Amphivasal (Phloem in center surrounded by Xylem): Dracaena, Yucca.
2	In Bangladesh DGHS Medical Admission Test (MBBS/BDS Exam Structure), how are the 100 MCQ marks and 200 SSC/HSC GPA marks weighted, and what is the negative marking rule?	Total Merit Score = 300 marks: 200 marks from SSC & HSC GPA (SSC GPA × 15 = 75 marks + HSC GPA × 25 = 125 marks) PLUS 100 marks from the 1-hour (60-minute) 100-MCQ Written Test: Biology (30 marks), Chemistry (25 marks), Physics (20 marks), English (15 marks), and General Knowledge—Bangladesh History/Liberation War & International (10 marks). Each wrong MCQ deducts 0.25 marks (pass mark = 40/100).
3	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Semiconductors & Transistors), relate the Transistor Current Gain parameters Alpha (α) and Beta (β) in Common-Base vs. Common-Emitter configurations.	For any Bipolar Junction Transistor (NPN or PNP), Emitter current equals the sum of Base current and Collector current: I_E = I_B + I_C (where ~95–99% of emitter carriers reach the collector and I_B is very small in µA). Common-Base current amplification factor α = ΔI_C / ΔI_E (always slightly less than 1, typically 0.95–0.99). Common-Emitter current gain β = ΔI_C / ΔI_B (large, typically 20–500). Exact conversion formulas: β = α / (1 - α) and α = β / (1 + β) (with 1/α - 1/β = 1).
4	In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Dynamics: Projectiles & Coupled Pulleys), state the Trajectory Equation of a Projectile in Cartesian form y = x tan α - [gx² / (2u² cos²α)] and its shortcut using Horizontal Range R.	Standard Cartesian equation of projectile path (a parabola): y = x tan α - [gx² / (2u² cos²α)]. Factoring out x tan α and substituting R = (u² sin 2α)/g gives the high-speed admission formula: y = x tan α (1 - x/R) (or tan α = y/x + y/(R - x)), which immediately relates any point (x, y) on the trajectory to the launch angle α and total horizontal range R!
5	In Bangladesh Medical & Engineering Admission (HSC Quantitative Chemistry - Beer-Lambert Law & Redox Titration), state Beer-Lambert's Law of Spectrophotometry and calculate the equivalent weight of KMnO4, K2Cr2O7, H2C2O4, and Na2S2O3 in redox titrations.	Beer-Lambert Law: When monochromatic light passes through an absorbing solution, Absorbance A = log10(I0 / I) = ε · c · l (where ε is molar absorptivity in L·mol⁻¹·cm⁻¹, c is molar concentration in mol/L, and l is path length in cm). Redox Equivalent Weights (Molar Mass ÷ Electrons transferred per molecule): 1. KMnO4 (M = 158) in Acidic medium (MnO4⁻ + 8H⁺ + 5e⁻ -> Mn²⁺ + 4H2O, Δe = 5): Eq. Wt. = 158 / 5 = 31.6 (in neutral/weakly alkaline medium -> MnO2, Δe = 3, Eq. Wt. = 158/3; in strongly alkaline -> MnO4²⁻, Δe = 1). 2. K2Cr2O7 (M = 294.2) in Acidic medium (Cr2O7²⁻ + 14H⁺ + 6e⁻ -> 2Cr³⁺ + 7H2O, Δe = 6): Eq. Wt. = 294.2 / 6 = 49.03. 3. Oxalic Acid (C2O4²⁻ -> 2CO2 + 2e⁻, Δe = 2): Eq. Wt. = M / 2 = 126 / 2 = 63 (hydrated). 4. Sodium Thiosulfate Na2S2O3 (2S2O3²⁻ -> S4O6²⁻ + 2e⁻, Δe = 1 per molecule in iodometry): Eq. Wt. = M / 1.
6	In Bangladesh Medical & Engineering Admission (HSC Chemistry - Periodic Properties & Fajan's Rule), state Fajan's Rules of Polarization (covalent character in ionic bonds) and explain how polarization affects melting point, solubility in water, and thermal decomposition of carbonates.	Fajan's Rule: When a cation approaches an anion, the cation's positive charge attracts the anion's electron cloud while repelling its nucleus, distorting (polarizing) the anion and introducing COVALENT character into the ionic bond. Polarization increases with: 1. Small size of cation (Be²⁺ > Mg²⁺ > Ca²⁺ > Sr²⁺ > Ba²⁺), 2. Large size of anion (I⁻ > Br⁻ > Cl⁻ > F⁻), 3. High charge on cation or anion (Al³⁺ > Mg²⁺ > Na⁺), and 4. Pseudo-inert (d¹⁰) electronic configuration of cation (AgCl is more covalent and insoluble in water than NaCl; FeCl3 has a lower MP than FeCl2). Greater polarization -> MORE covalent character -> LOWER melting/boiling point, LOWER solubility in polar water, and LOWER thermal stability of metal carbonates (BeCO3 decomposes at the lowest temperature).
7	In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Matrices & Determinants), state the properties of Symmetric, Skew-Symmetric, Orthogonal, Idempotent, Involutory, and Nilpotent Matrices.	For a square matrix A: 1. Symmetric: A^T = A; 2. Skew-Symmetric: A^T = -A (all main diagonal entries are 0); 3. Orthogonal: A · A^T = A^T · A = I (so A⁻¹ = A^T and det(A) = ±1); 4. Idempotent: A² = A; 5. Involutory: A² = I (so A⁻¹ = A); 6. Nilpotent of index k: A^k = 0 (where k is the smallest positive integer). Also, for an n×n matrix A, det(adj A) = \|A\|^(n-1) and A · adj(A) = \|A\| · I.
8	In Bangladesh Medical & University Admission (English Grammar - Right Form of Verbs, Subjunctive & Conditional Sentences), state the grammar rules for 'As if / As though', 'Would that / I wish', and 'Lest'.	1. 'As if / As though': If the clause before 'as if/as though' is in the Present Indefinite tense, the clause after it takes the PAST INDEFINITE (with 'were' for all persons: 'He talks as if he KNEW everything / WERE a doctor'). If the clause before 'as if/as though' is in the Past Indefinite tense, the clause after it takes the PAST PERFECT ('He talked as if he HAD KNOWN everything'). 2. 'Lest' (meaning 'for fear that', inherently negative so never use 'not' after it): ALWAYS followed by 'Subject + SHOULD / MIGHT + Bare Infinitive (V1)' ('Walk fast lest you SHOULD miss the train'). 3. 'I wish / Would that / Fancy / It is high time + Subject': followed by the Past Indefinite (or 'were').
9	In Bangladesh Medical & DU Admission (HSC Biology - Genetics & Blood Groups), explain Erythroblastosis Fetalis (Hemolytic Disease of the Newborn) due to Rh Factor incompatibility and how it is prevented.	When an Rh-negative mother (dd) carries an Rh-positive fetus (Dd, inherited from an Rh+ father), the first pregnancy is usually unaffected because fetal RBCs cross the placenta mainly during placental separation at delivery, sensitizing the mother to produce anti-Rh (anti-D) IgG antibodies. In a subsequent pregnancy with another Rh+ fetus, maternal anti-D IgG antibodies cross the placenta and hemolyze fetal RBCs, causing fatal fetal anemia, jaundice, kernicterus, and hydrops fetalis (Erythroblastosis fetalis). It is prevented by administering anti-D immunoglobulin (RhoGAM) to the Rh- mother at 28 weeks gestation and within 72 hours after delivering an Rh+ baby.
10	In Bangladesh Medical & Engineering Admission (HSC Chemistry - Environmental Chemistry: Gas Laws & Water Quality Parameters), define DO, BOD, COD, and TDS in water pollution, and state their WHO acceptable standards.	1. DO (Dissolved Oxygen, measured by Winkler's iodometric titration method): oxygen gas dissolved in water essential for aquatic life—minimum 4.0–6.0 mg/L (ppm) required for fish survival (pure surface water has 7–8 ppm). 2. BOD (Biochemical Oxygen Demand): amount of dissolved O2 (in mg/L) consumed by aerobic microorganisms over 5 days at 20°C in the dark to decompose biodegradable organic waste (WHO safe drinking water BOD ≤ 1–3 ppm; >10 ppm indicates severe organic pollution). 3. COD (Chemical Oxygen Demand): total oxygen required to chemically oxidize BOTH biodegradable and non-biodegradable organic pollutants using acidic K2Cr2O7 (therefore, for any water sample, COD value is ALWAYS greater than BOD!). 4. TDS (Total Dissolved Solids): safe limit ≤ 500 ppm; WHO drinking water pH range: 6.5–8.5; Arsenic (As) acceptable limit in Bangladesh: ≤ 0.05 mg/L (50 ppb; WHO limit ≤ 0.01 mg/L).
11	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Special Theory of Relativity), write the Lorentz Transformation formulas for Length Contraction, Time Dilation, Relativistic Mass, and Relativistic Kinetic Energy.	Let the Lorentz factor γ = 1 / √(1 - v²/c²) ≥ 1: 1. Length Contraction (only along the direction of motion): L = L₀√(1 - v²/c²) = L₀ / γ (moving rod appears shorter: L < L₀). 2. Time Dilation: t = t₀ / √(1 - v²/c²) = γt₀ (moving clock runs slower: t > t₀). 3. Relativistic Mass: m = m₀ / √(1 - v²/c²) = γm₀. 4. Total Relativistic Energy: E = mc² = E₀ + K, so Rest Mass Energy E₀ = m₀c², Relativistic Kinetic Energy K = (m - m₀)c² = (γ - 1)m₀c², and Energy-Momentum relation: E² = (pc)² + (m₀c²)² (for a massless photon with m₀ = 0, E = pc). Note shortcut: if a meter stick shrinks to half its rest length (L = L₀/2) or a particle's mass doubles (m = 2m₀), its speed is v = (√3 / 2)c ≈ 0.866c!
12	In Bangladesh Medical Admission (HSC Zoology - Hydra, Grasshopper & Rui Fish Labeo rohita), state the types of Nematocysts in Hydra, the mouthparts of Poekilocerus pictus, and the 'Venus Heart' circulation of Labeo rohita.	Hydra Nematocysts (4 types): 1. Stenotele / Penetrant (largest—injects toxic fluid 'hypnotoxin' composed of proteins and phenols to paralyze prey), 2. Volvent / Desmoneme (coils tightly around bristles of prey), 3. Streptoline Glutinant (long spiny sticky thread), and 4. Stereoline Glutinant (small spineless sticky thread for locomotion). Grasshopper mouthparts (Mandibulate / chewing type): Labrum (upper lip), a pair of toothed Mandibles, a pair of Maxillae, Labium (lower lip), and Hypopharynx (tongue). Labeo rohita (Rui fish) Heart: two-chambered (Sinus venosus -> Atrium -> Ventricle -> Bulbous arteriosus, no conus arteriosus)—called a 'Venus Heart' because ONLY deoxygenated (CO2-rich) blood passes through it in a single-circuit circulation straight to the 4 pairs of holobranch gills for oxygenation.
13	In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Integral Calculus Shortcuts), state the fast admission shortcuts for ∫ e^x [f(x) + f'(x)] dx and Wallis's Formula for ∫₀^(π/2) sin^n(x) dx and Area bounded by a Parabola y² = 4ax and its Latus Rectum or a line y = mx.	1. Cancellation integral: ∫ e^x [f(x) + f'(x)] dx = e^x · f(x) + c. 2. ∫ [f'(x) / f(x)] dx = ln\|f(x)\| + c. 3. ∫₀^(π/2) [sin^n(x) / (sin^n(x) + cos^n(x))] dx = π / 4 for ANY real n! 4. Area bounded by the parabola y² = 4ax and its latus rectum (x = a) is (8/3)a². 5. Area bounded between the parabola y² = 4ax and the straight line y = mx is (8a²) / (3m³); area between two parabolas y² = 4ax and x² = 4by is (16ab) / 3.
14	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Vector Calculus: Gradient, Divergence & Curl), define the Del operator (∇) and give the physical criteria for a Solenoidal vector field vs. an Irrotational (Conservative) vector field.	Del operator: ∇ = î(∂/∂x) + ĵ(∂/∂y) + k̂(∂/∂z). 1. Gradient of a scalar field φ (∇φ): is a VECTOR pointing in the direction of maximum rate of increase of φ. 2. Divergence of a vector field V (∇ · V = ∂Vx/∂x + ∂Vy/∂y + ∂Vz/∂z): is a SCALAR measuring net outward flux per unit volume; if ∇ · V = 0 everywhere, the vector field V is SOLENOIDAL (incompressible, e.g., magnetic field ∇ · B = 0). 3. Curl of a vector field V (∇ × V): is a VECTOR measuring rotation/vorticity; if ∇ × V = 0 everywhere, the vector field V is IRROTATIONAL (Conservative, e.g., electrostatic field ∇ × E = 0).
15	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Elasticity, Surface Tension & Viscosity), relate Surface Tension (T) to Surface Energy (E), state Jurin's Capillary Rise formula, and state Stokes' Law of Terminal Velocity.	Work done in increasing liquid surface area by ΔA is ΔW = T · ΔA, so Surface Tension T (in N/m) is numerically equal to Surface Energy E per unit area (in J/m²). Excess pressure inside a liquid drop of radius r: ΔP = 2T / r; inside a soap bubble (two air-liquid surfaces): ΔP = 4T / r. Capillary rise/depression formula: h = (2T cos θ) / (rρg) (for pure water in clean glass, contact angle θ = 0°; for mercury in glass, θ ≈ 139°–140° obtuse, so cos θ is negative and mercury is depressed). Stokes' Law for viscous drag on a sphere of radius r moving at speed v through a fluid of viscosity η: F = 6πηrv, yielding Terminal Velocity v_t = [2r²(ρ_s - ρ_f)g] / (9η).
16	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Rotational Mechanics & Moment of Inertia), state the Parallel-Axis and Perpendicular-Axis Theorems, and list the Moments of Inertia (I) and Radii of Gyration (K) for a Thin Rod, Circular Ring, Circular Disc, and Solid Sphere.	Perpendicular-Axis Theorem (for a planar lamina in the xy-plane): I_z = I_x + I_y. Parallel-Axis Theorem: I = I_G + Mh² (where I_G is moment of inertia about an axis through the center of mass and h is perpendicular distance between the two parallel axes); Radius of gyration K = √(I / M). Standard Moments of Inertia: 1. Thin uniform rod of length L about perpendicular axis through center: I = (1/12)ML² [about one end: I = (1/3)ML²]. 2. Thin circular ring / hollow cylinder of radius R about central axis: I = MR². 3. Uniform circular disc / solid cylinder about central axis: I = ½ MR² [about a diameter: I = ¼ MR²]. 4. Solid sphere of radius R about any diameter: I = (2/5)MR² [Hollow thin spherical shell: I = (2/3)MR²].
17	In Bangladesh Medical Admission (HSC Botany - Plant Families: Malvaceae vs. Poaceae), compare the floral characteristics and placentation of Family Poaceae (Gramineae, Monocot) and Family Malvaceae (Dicot).	Poaceae (Rice Oryza sativa, Wheat, Bamboo, Sugarcane): Spikelet inflorescence, perianth represented by 2 lodicules, 3 or 6 versatile stamens, feathery stigma, Basal placentation, and Caryopsis fruit. Malvaceae (China rose Hibiscus rosa-sinensis, Cotton, Lady's finger/Okra, Jute): young parts mucilaginous, free lateral stipules, Epicalyx present, twisted aestivation of 5 petals, numerous Monadelphous stamens (filaments fused into a staminal tube around the style), reniform (kidney-shaped) one-celled anthers with large spiny pollen grains, and Axile placentation (5 carpels).
18	In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Straight Lines & Circles), write the formulas for the perpendicular distance from a point to a line, distance between two parallel lines, and length of tangent from P(x1, y1) to the circle x² + y² + 2gx + 2fy + c = 0.	Perpendicular distance from (x1, y1) to ax + by + c = 0: d = \|ax1 + by1 + c\| / √(a² + b²). Distance between parallel lines ax + by + c1 = 0 and ax + by + c2 = 0: d = \|c1 - c2\| / √(a² + b²). For circle S ≡ x² + y² + 2gx + 2fy + c = 0: Center = (-g, -f), Radius r = √(g² + f² - c), x-intercept length = 2√(g² - c), y-intercept length = 2√(f² - c), and length of tangent from external point P(x1, y1) is √(S1) = √(x1² + y1² + 2gx1 + 2fy1 + c).
19	In Bangladesh Medical Admission (General Knowledge & Public Health Institutions of Bangladesh), match the premier medical, agricultural, and scientific research institutes of Bangladesh and their locations/achievements.	1. icddr,b (International Centre for Diarrhoeal Disease Research, Bangladesh, located at Mohakhali, Dhaka; originally established in 1960 as SEATO Cholera Research Laboratory): pioneered Oral Rehydration Solution (ORS), saving over 70 million lives globally. 2. IEDCR (Institute of Epidemiology, Disease Control and Research, Mohakhali, Dhaka): national infectious disease surveillance & outbreak response. 3. BSMMU (Bangabandhu Sheikh Mujib Medical University, Shahbag, Dhaka—established 1998 converting IPGMR of 1965, first medical university of Bangladesh). 4. BRRI (Bangladesh Rice Research Institute, Gazipur, 1970) & BARI (Bangladesh Agricultural Research Institute, Gazipur) & BINA (Mymensingh; Dr. Maqsudul Alam decoded the genome sequence of Tosha & Deshi Jute in 2010 and Macrophomina phaseolina fungus in 2012).
20	In Bangladesh Medical & BUET Admission (HSC Chemistry - Solubility Product K_sp & Ionic Product K_ip), state the relationship between K_ip and K_sp for unsaturated, saturated, and supersaturated solutions, and express K_sp for AB, AB2, A2B3, and Al(OH)3 in terms of molar solubility S.	If K_ip < K_sp: solution is unsaturated (more solute can dissolve). If K_ip = K_sp: solution is saturated at equilibrium. If K_ip > K_sp: solution is supersaturated and PRECIPITATION occurs until K_ip = K_sp! K_sp expressions in terms of molar solubility S (mol/L): 1:1 salt AB (e.g., AgCl, BaSO4): K_sp = S²; 1:2 or 2:1 salt AB2 / A2B (e.g., CaF2, PbCl2, Ag2CrO4): K_sp = 4S³; 1:3 salt AB3 [e.g., Al(OH)3, Fe(OH)3]: K_sp = 27S⁴; 2:3 salt A2B3 [e.g., Ca3(PO4)2]: K_sp = 108S⁵.
21	In Bangladesh Medical Admission (HSC Zoology - Human Physiology: Blood, Coagulation & Cranial Nerves), list the 13 Blood Clotting Factors (especially Factors I–IV and VIII–X) and the 12 Pairs of Human Cranial Nerves with their sensory/motor modalities.	4 Primary Clotting Factors ('FPTC'): Factor I = Fibrinogen; Factor II = Prothrombin; Factor III = Thromboplastin (Tissue Factor); Factor IV = Calcium ions (Ca²⁺, the only non-protein inorganic factor!). Factor VIII = Antihemophilic Factor A (Classic Hemophilia A); Factor IX = Christmas Factor / Plasma Thromboplastin Component (Hemophilia B); Factor XII = Hageman Factor; Factor XIII = Fibrin-stabilizing Factor. 12 Pairs of Cranial Nerves ('OOOTTAFVGVAH' / 'Some Say Marry Money But My Brother Says Big Brains Matter More'): Purely Sensory (1, 2, 8): I Olfactory (smell), II Optic (vision), VIII Vestibulocochlear/Auditory (hearing & balance). Purely Motor (3, 4, 6, 11, 12): III Oculomotor, IV Trochlear (smallest, supplies superior oblique), VI Abducens (supplies lateral rectus), XI Accessory, XII Hypoglossal (tongue muscles). Mixed Sensory & Motor (5, 7, 9, 10): V Trigeminal (largest, 3 branches), VII Facial, IX Glossopharyngeal, X Vagus (longest/wandering nerve).
22	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Simple Harmonic Motion & Lissajous Figures), write the differential equation, velocity, acceleration, kinetic energy, and potential energy of a particle in SHM of amplitude A and angular frequency ω.	Differential equation of SHM: d²x/dt² + ω²x = 0 (where ω = 2π/T = 2πf = √(k/m)). At displacement x from equilibrium: Velocity v = ω√(A² - x²) (maximum at mean position x = 0: v_max = ωA; zero at extreme position x = ±A); Acceleration a = -ω²x (zero at mean position; maximum at extreme position: a_max = ω²A). Kinetic Energy E_k = ½ k(A² - x²); Potential Energy E_p = ½ kx²; Total Mechanical Energy E = E_k + E_p = ½ kA² = 2π²mf²A² (constant everywhere).Note: If the time period of displacement is T, the time period of Kinetic and Potential Energy variation is T/2 (frequency is 2f)!
23	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Gravitation & Escape Velocity), derive the relationship between Escape Velocity (v_e) and Orbital Velocity (v_o) of a satellite orbiting close to the Earth's surface, and state the height and period of a Geostationary (Parking) Orbit.	Escape Velocity from Earth's surface: v_e = √(2GM / R) = √(2gR) ≈ 11.2 km/s (independent of the mass or angle of projection of the projectile!). Orbital Velocity of a satellite close to Earth's surface (r ≈ R): v_o = √(GM / R) = √(gR) ≈ 7.9 km/s. Therefore, v_e = √2 · v_o (if a satellite's orbital speed is increased by √2 times—or by 41.4%—or its kinetic energy is doubled, it escapes into infinity!). A Geostationary Satellite (such as Bangabandhu-1 launched on May 11, 2018 at 119.1° E) orbits in the equatorial plane from West to East with period T = 24 hours at an altitude h ≈ 35,800 km (~36,000 km) above Earth's surface.
24	In Bangladesh Medical Admission (HSC Botany - Photosynthesis & Respiration), compare the C3 (Calvin) Cycle and C4 (Hatch & Slack) Pathway across optimum temperature, first stable product, Kranz anatomy, and CO2 compensation point.	C3 Pathway (Rice, Wheat, Mango, Jute, 85% of plants): no Kranz anatomy (chloroplasts of one type), primary CO2 acceptor is 5C RuBP (via RuBisCO), first stable product is 3C 3-Phosphoglyceric acid (3-PGA), optimum temperature 10°C–25°C, high photorespiration, CO2 compensation point is high (50–100 ppm). C4 Pathway (Maize, Sugarcane, Sorghum, Amaranthus, Muthaghas): Kranz anatomy present (dimorphic chloroplasts: granal in mesophyll, agranal in bundle sheath), primary CO2 acceptor in mesophyll is 3C Phosphoenolpyruvate (PEP via PEP carboxylase), first stable product is 4C Oxaloacetic acid (OAA), optimum temperature 30°C–45°C, negligible photorespiration, low CO2 compensation point (0–10 ppm).
25	In Bangladesh Medical & Engineering Admission (HSC Organic Chemistry - Named Reactions), summarize the Wurtz, Friedel-Crafts, Reimer-Tiemann, Kolbe's Schmitt, Sandmeyer, Hoffmann Bromamide Degradation, Diazotization, and Clemmensen vs. Wolff-Kishner Reduction reactions.	1. Wurtz Reaction: 2 R-X + 2 Na (in dry ether) -> R-R (symmetrical alkane with double carbon chain). 2. Reimer-Tiemann Reaction: Phenol + CHCl3 + aq. NaOH at 60–70°C (followed by HCl) -> Salicylaldehyde (2-hydroxybenzaldehyde). 3. Kolbe-Schmitt Reaction: Sodium phenoxide + CO2 at 125°C under 4–7 atm pressure (followed by HCl) -> Salicylic acid (2-hydroxybenzoic acid—reacting Salicylic acid with acetic anhydride yields Aspirin / acetylsalicylic acid, while reacting with methanol yields Oil of Wintergreen / methyl salicylate). 4. Hoffmann Bromamide Degradation: Acid amide (R-CONH2) + Br2 + 4 KOH -> Primary Amine with ONE LESS carbon atom (R-NH2) + K2CO3 + 2 KBr. 5. Diazotization: Aniline (C6H5NH2) + NaNO2 + HCl at 0°C–5°C -> Benzene diazonium chloride (C6H5N2⁺Cl⁻). 6. Clemmensen Reduction (Zn-Hg amalgam + conc. HCl) & Wolff-Kishner Reduction (Hydrazine NH2NH2 + KOH in ethylene glycol): both reduce the carbonyl group (>C=O) of aldehydes and ketones directly to a methylene group (-CH2-) / alkane!
26	In Bangladesh Medical & Engineering Admission (HSC Organic Chemistry - Isomerism, Cis-Trans & Optical Activity), state the conditions for Geometrical (cis-trans) Isomerism and Optical Isomerism (Enantiomers, Diastereomers, Meso compounds, Racemic mixture), and calculate the number of optical isomers for a molecule with n chiral carbons.	Geometrical Isomerism occurs due to restricted rotation around a C=C double bond or cyclic ring when each doubly-bonded carbon is attached to two different groups [abC=Cab; cis has identical groups on the same side (higher dipole moment μ > 0, higher boiling point, lower melting point); trans has identical groups on opposite sides (symmetrical, μ ≈ 0, higher melting point due to compact crystal packing)]. Optical Isomerism requires a Chiral (Asymmetric) Carbon attached to 4 different groups (aCabcd) and absence of a plane/center of symmetry—rotating plane-polarized light measured by a Polarimeter. For a molecule with n dissimilar chiral centers, number of optically active stereoisomers = 2^n. A Racemic Mixture (dl- or (±)-mixture, e.g., lactic acid) contains 50% d-enantiomer and 50% l-enantiomer and is optically inactive due to EXTERNAL compensation; a Meso compound (e.g., meso-tartaric acid) has chiral carbons but is optically inactive due to INTERNAL compensation (plane of symmetry within the molecule).
27	In BUET/CKRUET/DU Engineering Admission (HSC Physics - Physical Optics, Interference & Diffraction), state the path difference and phase difference conditions for Constructive and Destructive Interference in Young's Double-Slit Experiment, plus Brewster's Law of Polarization.	Phase difference δ = (2π / λ) × Path difference Δx. Constructive Interference (Bright fringe): Path difference Δx = nλ = (2n)(λ/2), Phase difference δ = 2nπ (where n = 0, 1, 2...). Destructive Interference (Dark fringe): Path difference Δx = (2n + 1)(λ/2), Phase difference δ = (2n + 1)π. In Young's Double-Slit Experiment (slit separation d, screen distance D): fringe width of a single bright or dark fringe β = λD / (2d), and distance between two successive bright (or two successive dark) fringes Δy = λD / d. Note that for a Single-Slit Fraunhofner Diffraction pattern of slit width 'a', the conditions are reversed: minima occur at a sin θ = nλ. Brewster's Law (Polarization by Reflection): when unpolarized light is incident at the polarizing angle θ_p such that the reflected and refracted rays are mutually perpendicular (θ_p + r = 90°), the reflected light is 100% plane-polarized and μ = tan θ_p.
28	In Bangladesh Medical Admission (HSC Zoology - Animal Kingdom Classification), match the 9 major Animal Phyla to their symmetry, body cavity (Coelom), and unique excretory/locomotory organs.	1. Porifera (Sponges—Scypha): cellular grade, asymmetrical, ostia, spongocoel, osculum, choanocytes (collar cells), spicules/spongin. 2. Cnidaria (Hydra, Jellyfish Aurelia, Coral): radial symmetry, diploblastic, nematocysts (cnidocytes), gastrovascular cavity (coelenteron). 3. Platyhelminthes (Taenia solium, Fasciola hepatica): bilateral, triploblastic, acoelomate, flame cells for excretion. 4. Nematoda (Ascaris lumbricoides, Loa loa, Wuchereria): pseudocoelomate, unsegmented cylindrical tube-within-a-tube. 5. Annelida (Earthworm Metaphire posthuma, Leech): true coelomate, metameric segmentation, nephridia, setae or parapodia, closed circulation with haemoglobin dissolved in plasma. 6. Arthropoda (largest phylum): jointed appendages, chitinous exoskeleton, haemocoel (open circulation), Malpighian tubules / green glands. 7. Mollusca (2nd largest—Pila, Octopus): muscular foot, visceral mass, mantle, radula (rasping tongue). 8. Echinodermata (Starfish Asterias): pentamerous radial symmetry in adults (bilateral larvae), exclusively marine, water vascular system with tube feet. 9. Chordata: notochord, dorsal hollow nerve cord, pharyngeal gill slits, post-anal tail.
29	In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Polynomial Equations & Inverse Trigonometry), state the relation between roots and coefficients of a cubic equation ax³ + bx² + cx + d = 0, and the formula for tan⁻¹x + tan⁻¹y.	For cubic ax³ + bx² + cx + d = 0 with roots α, β, γ: 1. Sum of roots: α + β + γ = -b/a; 2. Sum of pairwise products: αβ + βγ + γα = +c/a; 3. Product of roots: αβγ = -d/a. For Inverse Tangents (when xy < 1): tan⁻¹x + tan⁻¹y = tan⁻¹[(x + y) / (1 - xy)], and tan⁻¹x - tan⁻¹y = tan⁻¹[(x - y) / (1 + xy)]. Also, sin⁻¹x + cos⁻¹x = π/2, tan⁻¹x + cot⁻¹x = π/2, and 2tan⁻¹x = sin⁻¹[2x / (1 + x²)] = cos⁻¹[(1 - x²) / (1 + x²)] = tan⁻¹[2x / (1 - x²)].
30	In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Differential Calculus & L'Hôpital's Rule), state the standard limits lim_(x→0) (sin x)/x, lim_(x→0) (e^x - 1)/x, and lim_(x→0) (1 + x)^(1/x), plus L'Hôpital's Rule and Maclaurin's Series.	Standard Limits: lim_(x→0) (sin x)/x = 1 (x in radians!); lim_(x→0) (tan x)/x = 1; lim_(x→0) (1 - cos x)/x² = ½; lim_(x→0) (e^x - 1)/x = 1; lim_(x→0) [ln(1 + x)]/x = 1; lim_(x→0) (1 + ax)^(b/x) = e^(ab). L'Hôpital's Rule: if lim_(x→a) f(x)/g(x) takes the indeterminate form 0/0 or ∞/∞, differentiate numerator and denominator separately: lim_(x→a) f(x)/g(x) = lim_(x→a) f'(x)/g'(x).
31	In BUET/CKRUET/DU Engineering Admission (HSC Higher Mathematics - Statics: Lami's Theorem & Resultant of Coplanar Forces), state the Parallelogram Law of Forces and Lami's Theorem for three concurrent coplanar forces in equilibrium.	Parallelogram Law: If two forces P and Q act simultaneously at a point at an angle α, their resultant R has magnitude R = √(P² + Q² + 2PQ cos α) and makes angle θ with force P given by tan θ = (Q sin α) / (P + Q cos α) (when P = Q, R = 2P cos(α/2) bisecting the angle α). Lami's Theorem: If three coplanar, concurrent forces P, Q, and R acting at a point are in equilibrium, each force is directly proportional to the sine of the angle between the other two forces: P / sin α = Q / sin β = R / sin γ.
32	In Bangladesh Medical & DU Admission (HSC Chemistry - Qualitative Chemistry: Flame Test & Ion Identification), match the characteristic Flame Test colors and Nessler's / Potassium Pyroantimonate / Ammonium Oxalate reagents for cations.	Flame Test Colors (using conc. HCl and Pt/nichrome wire): Sodium (Na⁺): Golden Yellow (appears black through blue cobalt glass); Potassium (K⁺): Violet / Lilac (appears crimson/pinkish-red through cobalt glass); Calcium (Ca²⁺): Brick Red (appears light green through cobalt glass); Copper (Cu²⁺): Bluish-Green; Barium (Ba²⁺): Apple / Yellowish Green; Strontium (Sr²⁺): Crimson Red. Wet Confirmations: NH4⁺ + Alkaline Nessler's Reagent (K2[HgI4] + KOH/NaOH) -> Reddish-brown precipitate of Amino-mercuric iodide (NH2-Hg-O-Hg-I); Na⁺ + Potassium Pyroantimonate (K2H2Sb2O7) -> White microcrystalline precipitate of Na2H2Sb2O7; Ca²⁺ + Ammonium Oxalate [(NH4)2C2O4] -> White precipitate of Calcium oxalate (CaC2O4, insoluble in acetic acid, soluble in dilute HCl).