BUET Undergraduate Admission Main Written Examination cheat sheet
BUET Undergraduate Admission Main Written Examination · Keep the key ideas within reach.
Physics
Projectile range R = u² sin 2θ / g is maximum at θ = 45°; complementary angles give equal range.
Newton's second law: F_net = ma; friction f ≤ μN, with equality at impending motion.
Work-energy theorem: W_net = ΔK; conservative force implies mechanical energy conservation.
Moment of inertia of a uniform rod about its center is ML²/12; about an end it is ML²/3.
Simple pendulum period T = 2π√(L/g), independent of mass and small amplitude.
Doppler effect: f' = f(v ± v_o)/(v ∓ v_s), signs chosen so approach increases observed frequency.
Snell's law n₁ sin θ₁ = n₂ sin θ₂; total internal reflection requires n₁ > n₂ and θ₁ > critical angle.
Photoelectric equation hf = φ + K_max; stopping potential V_s satisfies eV_s = K_max.
Half-life N = N₀(1/2)^(t/T); activity A = λN and λ = ln2 / T.
Chemistry
Ideal gas law PV = nRT; at STP one mole occupies 22.4 L and contains 6.022×10²³ particles.
pH = −log[H⁺]; for a strong acid pH = −log C, and pH + pOH = 14 at 25 °C.
Le Chatelier's principle: increasing pressure favors the side with fewer gas moles; raising temperature favors the endothermic direction.
First law of thermodynamics ΔU = q + w; enthalpy change ΔH = ΔU + ΔnRT for gases.
Oxidation is loss of electrons (anode); reduction is gain (cathode); E°cell = E°cathode − E°anode.
Markovnikov's rule: in HX addition to an alkene, H adds to the carbon with more hydrogens.
SN1 proceeds via carbocation (rate depends on substrate only); SN2 is concerted and favored by strong nucleophile and polar aprotic solvent.
Benzene undergoes electrophilic substitution, not addition, because aromaticity is preserved.
Mathematics
Quadratic ax² + bx + c = 0 has roots α, β with α + β = −b/a and αβ = c/a; discriminant D = b² − 4ac decides nature of roots.
Binomial theorem: (a + b)^n = Σ C(n,k) a^(n−k) b^k; general term T_(k+1) = C(n,k) a^(n−k) b^k.
Derivative rules: d/dx(x^n) = nx^(n−1), product rule (uv)' = u'v + uv', quotient rule (u/v)' = (u'v − uv')/v².
Integration by parts: ∫u dv = uv − ∫v du; choose u by LIATE order.
Definite integral property ∫₀^a f(x) dx = ∫₀^a f(a − x) dx simplifies symmetric integrands.
Limit: lim_{x→0} (sin x)/x = 1 and lim_{x→0} (1 − cos x)/x² = 1/2.
Straight line: slope m = (y₂ − y₁)/(x₂ − x₁); perpendicular slopes satisfy m₁m₂ = −1.
Circle x² + y² + 2gx + 2fy + c = 0 has center (−g, −f) and radius √(g² + f² − c).
Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); for independent events P(A ∩ B) = P(A)P(B).
English
Subject-verb agreement: singular subjects take singular verbs; 'each', 'everyone', 'neither' are singular.
Present perfect (has/have + past participle) links past action to present; simple past is used with definite past time markers.
Passive voice: object becomes subject + be + past participle + (by agent); only transitive verbs passivize.
Conditional type 2: If + past simple, would + base verb, for unreal present situations.
Prepositions of time: 'in' for months/years, 'on' for days/dates, 'at' for clock times.
Relative clauses: 'who' for people, 'which' for things, 'whose' for possession; defining clauses take no commas.
Common confusables: affect (verb) vs effect (noun); principal (main) vs principle (rule); complement vs compliment.
Bangla
বাংলা বর্ণমালায় স্বরবর্ণ ১১টি, ব্যঞ্জনবর্ণ ৩৯টি, মোট ৫০টি বর্ণ।
সন্ধি তিন প্রকার: স্বরসন্ধি, ব্যঞ্জনসন্ধি ও বিসর্গসন্ধি; যেমন বিদ্যা + আলয় = বিদ্যালয় (স্বরসন্ধি)।
সমাস প্রধানত ছয় প্রকার: দ্বন্দ্ব, কর্মধারয়, তৎপুরুষ, বহুব্রীহি, দ্বিগু ও অব্যয়ীভাব।
কারক ও বিভক্তি: কর্তৃকারকে শূন্য বিভক্তি, কর্মকারকে দ্বিতীয়া, করণকারকে তৃতীয়া।
বাক্য গঠনে কর্তা + কর্ম + ক্রিয়া ক্রম সাধারণ; প্রশ্নবোধক বাক্যে প্রশ্নসূচক শব্দ বাক্যের শুরুতে বসে।
সমার্থক শব্দ ও বিপরীত শব্দ জানা আবশ্যক; যেমন 'অগ্নি'র সমার্থক 'অনল', 'দিন'-এর বিপরীত 'রাত'।
ছন্দ: অক্ষরবৃত্ত, মাত্রাবৃত্ত ও স্বরবৃত্ত; মাত্রাবৃত্তে দীর্ঘ স্বর দুই মাত্রা, হ্রস্ব স্বর এক মাত্রা।