BUET Undergraduate Admission Main Written Examination flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Projectile range formula

For a projectile launched at speed u and angle θ on level ground, the horizontal range is R = u² sin 2θ / g, maximum at θ = 45°.

Work-energy theorem

The net work done by all forces on a body equals its change in kinetic energy: W_net = ΔK = ½mv² − ½mu².

Moment of inertia of rod

A uniform rod of mass M and length L has moment of inertia ML²/12 about its center and ML²/3 about an end.

Doppler effect formula

Observed frequency f' = f(v ± v_o)/(v ∓ v_s); choose signs so relative approach raises frequency and recession lowers it.

Total internal reflection condition

Light must travel from a denser to a rarer medium (n₁ > n₂) and the incidence angle must exceed the critical angle θ_c = sin⁻¹(n₂/n₁).

Photoelectric equation

Maximum kinetic energy of emitted electrons is K_max = hf − φ, where φ is the work function; stopping potential satisfies eV_s = K_max.

Radioactive half-life

The number of nuclei remaining after time t is N = N₀(1/2)^(t/T); decay constant λ = ln2/T and activity A = λN.

Ideal gas molar volume

At standard temperature and pressure, one mole of an ideal gas occupies 22.4 liters and contains 6.022×10²³ molecules.

pH definition

pH = −log[H⁺]; at 25 °C, pH + pOH = 14, and for a strong monoprotic acid of concentration C, pH = −log C.

Le Chatelier's principle

When a system at equilibrium is disturbed, it shifts to counteract the change: increasing pressure favors fewer gas moles, heating favors the endothermic direction.

First law of thermodynamics

The change in internal energy equals heat added plus work done on the system: ΔU = q + w; for gases at constant pressure, ΔH = ΔU + ΔnRT.

Electrochemical cell EMF

Standard cell potential is E°cell = E°cathode − E°anode; oxidation occurs at the anode and reduction at the cathode.

Markovnikov's rule

In addition of HX to an alkene, the hydrogen atom attaches to the carbon already bearing more hydrogen atoms, giving the more stable carbocation intermediate.

SN1 versus SN2

SN1 is a two-step reaction through a carbocation, rate depends only on substrate; SN2 is one-step, favored by strong nucleophile and polar aprotic solvent.

Aromatic substitution preference

Benzene undergoes electrophilic substitution rather than addition because substitution preserves the aromatic ring and its resonance stabilization energy.

Quadratic roots relation

For ax² + bx + c = 0, the roots α and β satisfy α + β = −b/a and αβ = c/a; the discriminant b² − 4ac determines whether roots are real or complex.

Binomial general term

In the expansion of (a + b)^n, the term containing a^(n−k)b^k is T_(k+1) = C(n,k) a^(n−k) b^k.

Product rule

The derivative of a product uv is (uv)' = u'v + uv'; for a quotient, (u/v)' = (u'v − uv')/v².

Integration by parts

∫u dv = uv − ∫v du; choose u according to LIATE order (logarithmic, inverse trig, algebraic, trig, exponential) to simplify the integral.

Standard trigonometric limits

As x approaches zero, lim (sin x)/x = 1 and lim (1 − cos x)/x² = 1/2; these are used to evaluate related limits.

Perpendicular line slopes

Two nonvertical lines are perpendicular if and only if the product of their slopes is −1, that is m₁m₂ = −1.

Circle center and radius

The circle x² + y² + 2gx + 2fy + c = 0 has center (−g, −f) and radius √(g² + f² − c), provided the quantity under the root is positive.

Addition rule of probability

For any two events, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); if independent, P(A ∩ B) = P(A)P(B).

Subject-verb agreement rule

A singular subject takes a singular verb; indefinite pronouns such as each, everyone, and neither are singular and require singular verbs.

Present perfect tense use

The present perfect (has/have + past participle) describes a past action with present relevance; simple past is used with definite past time markers like yesterday.

Passive voice formation

The passive is formed with the object as subject, a form of be, and the past participle, optionally followed by 'by' plus the agent; only transitive verbs can be passivized.

Second conditional structure

The second conditional uses 'if' + past simple in the condition and 'would' + base verb in the result, expressing unreal or improbable present situations.

Prepositions of time

Use 'in' with months, years, and seasons; 'on' with days and dates; 'at' with clock times and specific points such as noon.

Relative pronoun choice

Use 'who' for people, 'which' for things, and 'whose' for possession; defining relative clauses are not set off by commas.

বাংলা বর্ণমালার সংখ্যা

বাংলা বর্ণমালায় স্বরবর্ণ ১১টি ও ব্যঞ্জনবর্ণ ৩৯টি, মোট ৫০টি বর্ণ রয়েছে।

সন্ধি কত প্রকার

সন্ধি প্রধানত তিন প্রকার: স্বরসন্ধি, ব্যঞ্জনসন্ধি ও বিসর্গসন্ধি; যেমন বিদ্যা + আলয় = বিদ্যালয়।

সমাসের প্রকারভেদ

সমাস প্রধানত ছয় প্রকার: দ্বন্দ্ব, কর্মধারয়, তৎপুরুষ, বহুব্রীহি, দ্বিগু ও অব্যয়ীভাব।