MPPSC SES Civil cheat sheet

Divisibility: a number is divisible by 3 if the sum of its digits is divisible by 3; by 9 if the digit sum is divisible by 9; by 11 if the alternating digit sum is divisible by 11.

Percentage change formula: successive changes of a% and b% yield net change = a + b + ab/100 percent.

Time–speed–distance: distance = speed × time; for a train of length L crossing a platform of length P at speed v, time = (L + P)/v when units are consistent.

Work: if A can do a job in x days and B in y days, together they take xy/(x + y) days. If A is twice as efficient as B, A takes half the time of B.

Simple interest SI = P × R × T / 100; compound interest CI = P[(1 + R/100)^T − 1]. For two years, CI − SI = P(R/100)^2.

Average of n numbers = sum/n; if each number is increased by k, the average increases by k; if each is multiplied by k, the average is multiplied by k.

Ratio and proportion: if a:b = c:d then ad = bc. In a mixture of milk and water in ratio m:n, adding x litres of water changes the ratio to m : (n + x) when the total volume basis is consistent.

Logical reasoning: in a syllogism, a conclusion is valid only if it follows from all possible Venn diagrams of the premises; 'some A are B' does not imply 'some B are not A' unless stated.

Number series: check differences, ratios, squares/cubes, and alternating patterns. For alphabet series, convert letters to positions A=1 … Z=26 and look for constant or increasing gaps.

Limit definition of derivative: f'(x) = lim(h→0) [f(x+h) − f(x)]/h. Standard derivatives: d/dx(x^n) = nx^(n−1); d/dx(e^x) = e^x; d/dx(ln x) = 1/x; d/dx(sin x) = cos x.

Integration by parts: ∫u dv = uv − ∫v du. Choose u by LIATE order (Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential).

Definite integral property: ∫_a^b f(x) dx = −∫_b^a f(x) dx; ∫_a^b f(x) dx = ∫_a^c f(x) dx + ∫_c^b f(x) dx.

Matrix: a square matrix A is invertible iff det(A) ≠ 0. For 2×2 A = [[a,b],[c,d]], det = ad − bc and A⁻¹ = (1/det)[[d,−b],[−c,a]].

Eigenvalues: for a 2×2 matrix, λ² − (trace)λ + det = 0. Sum of eigenvalues = trace; product = determinant.

Probability: P(A∪B) = P(A) + P(B) − P(A∩B). For independent events, P(A∩B) = P(A)P(B). Bayes' theorem: P(A|B) = P(B|A)P(A)/P(B).

Mean, median, mode: for a grouped frequency distribution, median = L + [(N/2 − cf)/f] × h, where L is lower class boundary, cf cumulative frequency before median class, f frequency of median class, h class width.

Physics: Newton's second law F = ma; work W = F·d cosθ; kinetic energy KE = ½mv²; potential energy PE = mgh; power P = W/t.

Chemistry: pH = −log[H⁺]; for a strong acid HCl of 0.01 M, pH = 2. Equivalent weight = molecular weight / n-factor. Hardness of water is expressed as mg/L of CaCO₃ equivalent.

Flexure formula: M/I = σ/y = E/R. For a rectangular section of width b and depth d, section modulus Z = bd²/6 and I = bd³/12.

Shear stress in a beam: τ = VQ/(Ib), where Q is the first moment of area about the neutral axis. For a rectangular section, maximum shear stress = 1.5 × average shear stress.

Euler buckling load for a column: P_cr = π²EI/(KL)², where KL is the effective length. Effective length factors: both ends pinned K=1, fixed–fixed K=0.5, fixed–pinned K=0.7, fixed–free K=2.

Slope and deflection: for a simply supported beam with central point load W, maximum deflection = WL³/(48EI) at midspan. For a cantilever with end load W, maximum deflection = WL³/(3EI) at free end.

RCC design (limit state): design strength of concrete in bending = 0.36 f_ck b x_u, where x_u is the depth of the neutral axis; limiting x_u/d ratio is 0.53 for Fe415 and 0.48 for Fe500.

Steel design: for a tension member, design strength due to yielding of gross section T_dg = A_g f_y / γ_m0, with γ_m0 = 1.10. For rupture of net section T_dn = 0.9 A_n f_u / γ_m1, with γ_m1 = 1.25.

Concrete: nominal mix M20 = 1:1.5:3 (cement:sand:aggregate) by volume; M25 = 1:1:2. Water–cement ratio for normal strength concrete typically 0.4–0.6; lower w/c increases strength and durability.

Construction management: critical path method (CPM) identifies the longest path through the network; total float = LS − ES = LF − EF. An activity on the critical path has zero total float.

Estimating: for a building, plinth area estimate = plinth area × plinth area rate. For earthwork in excavation, volume by mid-section formula = L × (A1 + A2)/2 when cross-sections vary linearly.

Soil phase relations: void ratio e = V_v/V_s; porosity n = V_v/V_t = e/(1+e); degree of saturation S = V_w/V_v. Bulk unit weight γ = Gγ_w(1+w)/(1+e).

Atterberg limits: liquid limit (LL), plastic limit (PL), shrinkage limit (SL). Plasticity index PI = LL − PL. A soil with PI > 30 is highly plastic.

Effective stress: σ' = σ − u, where u is pore water pressure. For a soil with water table at depth z_w, effective stress at depth z is σ' = γ z − γ_w (z − z_w) for z > z_w.

Compaction: standard Proctor test uses a 2.5 kg rammer with 310 mm drop; modified Proctor uses 4.5 kg rammer with 450 mm drop. Maximum dry density increases with compactive effort.

Consolidation: coefficient of consolidation c_v = T_v H²/t, where T_v is time factor (T_v = 0.197 for 50% consolidation, 0.848 for 90%).

Shear strength: Mohr–Coulomb criterion τ = c + σ' tan φ. For a triaxial test, the failure plane is at 45° + φ/2 to the major principal plane.

Bearing capacity: Terzaghi's equation for a strip footing q_u = cN_c + γD_f N_q + 0.5γBN_γ. For a square footing, q_u = 1.3cN_c + γD_f N_q + 0.4γBN_γ.

Pile foundation: ultimate load capacity Q_u = Q_p + Q_s, where Q_p is end bearing = q_p A_p and Q_s is skin friction = Σ f_s A_s. For cohesive soil, skin friction f_s = α c_u.

Slope stability: factor of safety F = resisting moment / disturbing moment. For an infinite slope with seepage parallel to slope, F = (γ' tan φ)/(γ_sat tan β) when c = 0.

Continuity equation: Q = A₁V₁ = A₂V₂. Bernoulli's equation for steady incompressible flow: P/γ + z + V²/(2g) = constant along a streamline.

Flow through orifices: discharge Q = C_d A √(2gH), where C_d is coefficient of discharge (≈0.6 for sharp-edged orifice). For a rectangular notch, Q = (2/3) C_d b √(2g) H^(3/2).

Open channel flow: Manning's equation V = (1/n) R^(2/3) S^(1/2), where R is hydraulic radius = A/P and S is bed slope. For a rectangular channel, critical depth y_c = (q²/g)^(1/3).

Hydrology: rational method peak discharge Q = C i A / 3.6, where C is runoff coefficient, i is rainfall intensity (mm/h), A is area (km²), Q in m³/s. Unit hydrograph: volume of direct runoff = 1 cm over catchment area.

Dams: gravity dam stability requires no tension at heel and factor of safety against overturning > 1.5, against sliding > 1.0 (usually 1.5). Uplift pressure reduces effective weight.

Spillways: ogee spillway discharge Q = C L H^(3/2), with C ≈ 2.2 in SI units for a broad-crested weir. Energy dissipation uses hydraulic jump; sequent depth ratio y₂/y₁ = ½(√(1 + 8F₁²) − 1).

Irrigation: duty (D) in hectares per cumec, delta (Δ) in metres. Relation: Δ = 8.64 B / D, where B is base period in days. Consumptive use = evapotranspiration + metabolic water.

Pumps and turbines: specific speed of a centrifugal pump N_s = N√Q / H^(3/4). For a turbine, N_s = N√P / H^(5/4). Efficiency η = output/input.

Water demand: per capita demand = total annual demand / (population × 365). Design period for water supply is typically 30 years; for sewers, 20–30 years.

Water treatment: coagulation–flocculation (alum dose), sedimentation, filtration (rapid sand filter rate 100–150 L/m²/min), disinfection by chlorination. Breakpoint chlorination ensures free residual chlorine.

Wastewater: BOD₅ = (D₁ − D₂) × dilution factor, where D₁ and D₂ are initial and final dissolved oxygen. BOD exertion follows first-order kinetics: BOD_t = BOD_u (1 − e^(−kt)).

Sewer design: self-cleansing velocity ≥ 0.6 m/s; maximum velocity ≤ 3 m/s. Manning's formula used for sewer flow. Minimum diameter for public sewer is 150 mm.

Air pollution: primary pollutants (CO, SO₂, NOₓ, particulates) vs secondary (ozone, PAN). AQI categories: 0–50 good, 51–100 moderate, 101–200 poor, 201–300 very poor, 301–500 severe (India).

Noise: sound pressure level L_p = 20 log₁₀(P/P₀) dB, with P₀ = 20 μPa. Sound intensity level L_I = 10 log₁₀(I/I₀) dB, I₀ = 10⁻¹² W/m².

Solid waste: per capita waste generation in Indian cities ≈ 0.3–0.6 kg/day. Landfill leachate contains high BOD and heavy metals; sanitary landfill requires clay liner and leachate collection.

Environmental legislation (India): Water (Prevention and Control of Pollution) Act 1974; Air (Prevention and Control of Pollution) Act 1981; Environment (Protection) Act 1986; EIA Notification 2006.

Highway geometric design: superelevation e = V²/(127R) − f, where V in km/h, R in m, f lateral friction coefficient (0.15 for rural highways). Maximum superelevation 7% for plain terrain.

Stopping sight distance SSD = 0.278 V t + V²/(254(f ± g)), where t is reaction time (2.5 s), g grade. For level road, SSD = 0.278 V t + V²/(254f).

Pavement design: flexible pavement uses CBR method; thickness depends on CBR value. Rigid pavement uses Westergaard's equations for wheel load stress. ESWL (equivalent single wheel load) concept for dual wheels.

Traffic engineering: PCU (passenger car unit) values: car 1.0, bus/truck 3.0, motorcycle 0.5, cycle 0.4, bullock cart 6.0. Traffic volume = q = N/T, where N is number of vehicles in time T.

Railway engineering: broad gauge (BG) 1.676 m, metre gauge (MG) 1.000 m, narrow gauge (NG) 0.762 m. Sleeper density = number of sleepers per rail length (e.g., M+7).

Airport engineering: runway length correction for elevation, temperature, and gradient. Basic runway length increases by 7% per 300 m elevation rise and 1% per 1°C temperature rise above standard.

Bridges: IRC Class AA loading for national highways; Class A for other roads. Impact factor for RCC bridges decreases with span length. Scour depth = 2 × maximum scour depth for design.

Traffic signs: mandatory (red circle), cautionary (triangle), informatory (blue rectangle). In India, motor vehicle act 1988 governs traffic rules; National Highways Authority of India (NHAI) manages NHs.

Chain surveying: ranging = fixing intermediate points on a survey line. Offsets are perpendicular (or oblique) distances from the baseline to the object. Limiting length of offset depends on scale (e.g., 15 m for 1:1000).

Compass surveying: whole circle bearing (WCB) measured clockwise from north (0°–360°). Reduced bearing (RB) in quadrants. Magnetic declination = true bearing − magnetic bearing. Local attraction corrected by fore and back bearings.

Levelling: height of instrument (HI) = reduced level (RL) of benchmark + backsight (BS). RL of point = HI − foresight (FS) or HI − intermediate sight (IS). Rise and fall method: rise = previous staff reading − current staff reading.

Contouring: contour interval depends on scale and terrain; for flat ground, interval is small. Contours are closer where slope is steep. A contour line never crosses another contour except at an overhanging cliff.

Theodolite: horizontal angle measurement by repetition and reiteration. Face left and face right readings average out instrumental errors. Vertical angle used for tacheometry.

Tacheometry: stadia method, D = k s + C, where k = f/i (multiplying constant, usually 100), s = staff intercept, C = f + d (additive constant). For an anallatic lens, C = 0.

Curves: simple circular curve with radius R, tangent length T = R tan(Δ/2), length of curve L = πRΔ/180, where Δ is deflection angle in degrees. Degree of curve D = 1719/R (for 30 m chord).

Total station: combines electronic theodolite and EDM; measures horizontal and vertical angles and slope distance; computes coordinates. Accuracy typically ±(2 mm + 2 ppm).

Electromagnetic spectrum: visible (0.4–0.7 μm), near-infrared (0.7–1.3 μm), shortwave infrared (1.3–3 μm), thermal infrared (3–14 μm), microwave (1 mm–1 m). Atmospheric windows are wavelength bands with high transmission.

Spatial resolution = smallest object that can be resolved; Landsat TM has 30 m (visible/NIR), 120 m (thermal); IRS LISS-IV has 5.8 m. Temporal resolution = revisit period.

Spectral signatures: vegetation has high NIR reflectance and low red (chlorophyll absorption); water has low reflectance in NIR; soil has increasing reflectance with wavelength.

Remote sensing platforms: sun-synchronous polar orbit (e.g., Landsat, IRS) for consistent illumination; geostationary orbit (e.g., INSAT) for continuous monitoring.

GIS: raster vs vector data models. Overlay operations: union, intersection, identity. Buffer analysis creates polygons at a specified distance. Topology defines spatial relationships (adjacency, connectivity).

GPS: 24 operational satellites in 6 orbital planes; trilateration with at least 4 satellites for 3D position. Sources of error: ionospheric delay, tropospheric delay, multipath, clock error. DGPS improves accuracy to metre level.

Photogrammetry: scale of vertical photograph = f/H, where f is focal length and H is flying height above ground. Relief displacement d = r h/H, where r is radial distance from principal point, h is object height.

Digital image processing: radiometric correction (atmospheric, sensor), geometric correction (registration, orthorectification), image enhancement (contrast stretch, histogram equalisation), classification (supervised, unsupervised).

Types of estimates: approximate (plinth area, cubic content, unit rate), detailed (item-wise with measurements), revised, supplementary. Contingency typically 3–5% of estimated cost; work charged establishment 1–2%.

Earthwork volume: mid-section formula V = L × (A₁ + A₂)/2; trapezoidal formula V = L × [(A₁ + Aₙ)/2 + A₂ + … + Aₙ₋₁]; prismoidal formula V = L/6 × (A₁ + 4A_m + A₂) for three sections.

Rate analysis: task work or out-turn per day per worker; labour constants. For cement concrete 1:2:4, dry volume = 1.52 × wet volume; cement bags = dry volume of cement / 0.035.

Bar bending: standard hook length = 9d for 45° bend; 90° bend = 2d; 135° bend = 3d. Development length L_d = φ σ_s / (4 τ_bd).

CPM/PERT: CPM is deterministic (single time estimate), PERT probabilistic (optimistic, most likely, pessimistic). Expected time t_e = (t_o + 4t_m + t_p)/6; variance = ((t_p − t_o)/6)².

Network float: total float = LS − ES; free float = ES of successor − EF of activity. Independent float = max(0, ES_successor − LF_predecessor − duration).

Project cost control: S-curve plots cumulative cost vs time. Earned value management: cost variance CV = EV − AC; schedule variance SV = EV − PV; CPI = EV/AC; SPI = EV/PV.

Construction equipment: output of excavator = bucket capacity × cycles per hour × efficiency; bulldozer output depends on blade capacity and cycle time. Equipment cost = ownership cost + operating cost.

Madhya Pradesh: capital Bhopal; largest city Indore; formed on 1 November 1956; area 308,252 km² (second largest state by area). It borders Uttar Pradesh, Chhattisgarh, Maharashtra, Gujarat, and Rajasthan.

Major rivers: Narmada (lifeline of MP, origin Amarkantak), Tapti, Chambal, Betwa, Sone. Major dams: Sardar Sarovar (Narmada), Gandhi Sagar, Indira Sagar (largest reservoir in India by volume).

National parks in MP: Kanha, Bandhavgarh, Pench, Satpura, Panna, Madhav (Shivpuri). Kanha is known for barasingha (swamp deer); Bandhavgarh for tigers. Pachmarhi is a hill station and biosphere reserve.

UNESCO World Heritage Sites in MP: Khajuraho temples, Sanchi stupa, Bhimbetka rock shelters, and the historic ensemble of Gwalior (added 2021).

MP economy: agriculture (soybean, wheat, gram), mineral-rich (coal, manganese, bauxite, limestone). Major industries: automobile (Pithampur), cement, textiles, and IT in Indore.

Language: Hindi is the official language; regional dialects include Malvi, Nimadi, Bundeli, Bagheli. The MP Public Service Commission (MPPSC) conducts the State Engineering Service (SES) exam.

Reasoning: number series, coding–decoding, blood relations, direction sense, syllogism, seating arrangement. For blood relations, draw a family tree; for directions, use a compass sketch.

MPPSC SES exam pattern: written exam (technical and general studies) followed by interview. Negative marking may apply; candidates should check the latest official notification for exact scheme.