BTEB Diploma in Engineering Semester Final Examinations cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R for DC circuits.

Three-phase power: P = √3 · V_L · I_L · cos φ, where φ is the phase angle between phase voltage and current.

Transformer EMF equation: E = 4.44 · f · N · Φ_max.

Synchronous speed of an induction motor: N_s = 120f / P, with f in Hz and P the number of poles.

Bending stress in a beam: σ = M·y / I; maximum stress occurs at the greatest distance y from the neutral axis.

Euler buckling load for a pin-ended column: P_cr = π²EI / L².

Concrete mix nominal grades: M15 = 1:2:4, M20 = 1:1.5:3, M25 = 1:1:2 (cement:sand:coarse aggregate by volume).

Slump test measures workability of fresh concrete; a typical structural slump range is 25–100 mm depending on element type.

In a computer, cache memory sits between CPU and main memory; hit ratio and access time determine effective access time.

Equations of motion: v = u + at, s = ut + ½at², v² = u² + 2as for constant acceleration.

Newton's second law: F = ma; weight W = mg with g ≈ 9.81 m/s².

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh.

Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a; discriminant b² − 4ac decides the nature of roots.

Derivative rules: d/dx(xⁿ) = n·xⁿ⁻¹; d/dx(sin x) = cos x; d/dx(eˣ) = eˣ; d/dx(ln x) = 1/x.

Integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1; ∫(1/x) dx = ln|x| + C.

Molarity M = moles of solute / litres of solution; normality = molarity × n-factor.

pH = −log₁₀[H⁺]; a pH of 7 at 25 °C indicates a neutral aqueous solution.

Binomial expansion: (a + b)ⁿ = Σ C(n,k)·aⁿ⁻ᵏ·bᵏ for k = 0 to n.

First-angle projection: the object lies between observer and plane; the view from the front is placed above the top view in the layout.

Third-angle projection: the plane lies between observer and object; the top view is placed above the front view.

Standard sheet sizes ISO A-series: A0 = 841 × 1189 mm; each lower number halves the longer side (A1 = 594 × 841 mm).

Line conventions: continuous thick for visible outlines, dashed for hidden edges, chain thin for centre lines, and continuous thin for dimension lines.

Dimensioning rule: each dimension is given once, placed on the view that shows the feature true shape, with arrowheads touching extension lines.

Scale: representative fraction RF = drawing length / actual length; a 1:50 scale means 1 mm on paper equals 50 mm actual.

Isometric projection uses three axes at 120° with equal foreshortening; isometric drawing is often made full size along the axes.

A regular hexagon inscribed in a circle has side length equal to the circle radius.

Bench vice, hacksaw, file, scriber, centre punch, and try square are standard fitting-shop hand tools; a hacksaw blade has 14–32 teeth per inch depending on material.

Filing cross-section shapes: flat, half-round, triangular, square, and round files are chosen by the contour being finished.

Drill speed rule: rpm = (1000 × cutting speed in m/min) / (π × drill diameter in mm).

In arc welding, electrode angle is about 70–80° to the workpiece in the direction of travel; polarity selection depends on electrode type.

Carpentry joints: mortise-and-tenon resists tension and compression; dovetail resists pulling apart; halving joint resists sliding.

Sheet-metal allowance for a bend: bend allowance = (π/180) × bend angle × (inside radius + K × thickness), with K the neutral-axis factor.

Electrical wiring colour practice (IEC): brown = line, blue = neutral, green-yellow = protective earth.

Safety rule: lockout/tagout is applied before servicing any machine; a machine guard is never removed while the machine is running.

English tense: present perfect uses have/has + past participle and links a past action to the present; simple past uses the past form for a finished time.

Active to passive: object becomes subject, verb becomes be + past participle, and the original subject moves to a by-phrase (only if relevant).

Reported speech: present tense in the reporting clause shifts the reported verb one step back in time (present → past, will → would).

Subject–verb agreement: a singular subject takes a singular verb; compound subjects joined by 'and' take a plural verb unless they form one idea.

Bangla alphabet has 11 vowels (স্বরবর্ণ) and 39 consonants (ব্যঞ্জনবর্ণ) in the standard classification.

Bangla sandhi (সন্ধি) combines two sounds; স্বরসন্ধি joins vowels, ব্যঞ্জনসন্ধি joins consonants, and বিসর্গসন্ধি involves the visarga.

In Bangla grammar, কারক denotes the relation of a noun to a verb; বিভক্তি is the case ending that marks it (e.g., -কে, -তে, -এর).

Essay structure: introduction stating the thesis, body paragraphs each with one claim and evidence, and a conclusion that restates the position.

Functions of management: planning, organising, staffing, directing, and controlling (POSDC).

Break-even quantity = fixed cost / (selling price per unit − variable cost per unit).

Contribution margin ratio = (selling price − variable cost) / selling price; it shows the share of each sale covering fixed cost.

Maslow's hierarchy of needs, from bottom: physiological, safety, social, esteem, self-actualisation.

SWOT analysis classifies internal strengths and weaknesses and external opportunities and threats; it is a planning tool, not a decision rule.

Project network: critical path is the longest path through the activity network; its duration equals the minimum project completion time.

Industrial attachment report usually contains introduction, company profile, work performed, observations, and conclusion with recommendations.

Entrepreneurship terms: fixed capital funds plant and machinery; working capital funds day-to-day operations such as raw material and wages.

Depreciation by straight-line method = (original cost − salvage value) / useful life in years.