MECEE-BL Medical Education Common Entrance Examination — Bachelor Level (Nepal)

A projectile is launched from ground level with an initial velocity of 30 m/s at an elevation angle of 30° to the horizontal. Assuming g = 10 m/s² and negligible air resistance, what is the maximum vertical height reached by the projectile?

• A22.5 m
• B45 m
• C5.6 m
• D11.25 m

A curved roadway with a radius of curvature of 200 m is banked for an optimum design speed of 72 km/h without relying on friction. Taking g = 10 m/s², what is the required banking angle θ of the road?

• Atan⁻¹(0.4)
• Btan⁻¹(0.2)
• Ctan⁻¹(0.1)
• Dtan⁻¹(0.5)

A vehicle traveling along a horizontal straight road at 20 m/s brakes to a complete halt. If the coefficient of kinetic friction between the tyres and the road surface is μ = 0.5 and g = 10 m/s², what is the minimum stopping distance?

• A20 m
• B80 m
• C40 m
• D10 m

A solid uniform sphere and a solid cylinder having identical mass M and outer radius R roll down the same inclined plane from rest without slipping. What is the ratio of the linear acceleration of the sphere to that of the cylinder (a_sphere / a_cylinder)?

• A14 / 15
• B15 / 14
• C5 / 4
• D7 / 6

At what depth d below the surface of the Earth will the acceleration due to gravity become one-fourth (g/4) of its value at the surface? (Let R be the radius of the Earth, assumed spherical of uniform density).

• AR / 4
• BR / 2
• CR / 8
• D3R / 4

A particle executes simple harmonic motion (SHM) with amplitude A about an equilibrium position. At what displacement x from the mean position is its kinetic energy exactly equal to its potential energy?

• AA / 2
• BA / √2
• CA / (2√2)
• D(A√3) / 2

What is the excess pressure inside a hollow spherical soap bubble of radius r = 2 mm floating in air, given that the surface tension of the soap solution is T = 0.03 N/m?

• A30 Pa
• B60 Pa
• C120 Pa
• D15 Pa

Two spherical water droplets with radii in the ratio 1 : 3 fall through calm air at terminal velocity, governed by Stokes' law. What is the ratio of their terminal velocities (v₁ : v₂)?

• A1 : 3
• B1 : 27
• C1 : 9
• D3 : 1

A pendulum clock keeps accurate time at 15°C. The pendulum rod has a linear thermal expansion coefficient α = 2.0 × 10⁻⁵ K⁻¹. If the ambient temperature increases to 35°C, how much time does the clock lose in a full 24-hour day?

• A8.64 s
• B17.28 s
• C34.56 s
• D4.32 s

A sample of a monoatomic ideal gas (γ = 5/3) initially at an absolute temperature of 300 K and volume V₁ is compressed adiabatically to one-eighth of its initial volume (V₂ = V₁ / 8). What is the final temperature T₂ of the gas?

• A600 K
• B900 K
• C1200 K
• D2400 K

A Carnot heat engine operates between a heat source at 600 K and a cold sink at 400 K. In each cycle the engine absorbs 900 J of heat from the source. What is the net mechanical work output per cycle?

• A150 J
• B300 J
• C600 J
• D450 J

A train blowing a whistle of frequency 640 Hz travels at 20 m/s toward a stationary observer on a platform. If the speed of sound in still air is 340 m/s, what frequency is heard by the observer?

• A604 Hz
• B640 Hz
• C680 Hz
• D720 Hz

An organ pipe open at both ends has a fundamental resonant frequency of 300 Hz. If one end of this identical pipe is now closed, what will be the fundamental frequency of the resulting closed pipe?

• A75 Hz
• B150 Hz
• C300 Hz
• D600 Hz

A ray of monochromatic light passes through an equilateral glass prism (apex angle A = 60°) at minimum deviation. If the refractive index of the glass is μ = √2, what is the angle of minimum deviation δ_m?

• A15°
• B45°
• C30°
• D60°

A biconvex glass lens (refractive index μ_g = 1.5) has a focal length of 20 cm in air. When this lens is completely immersed in water (μ_w = 4/3), what is its new focal length?

• A40 cm
• B60 cm
• C80 cm
• D100 cm

In a Young's double-slit experiment, the distance between the two slits is d = 0.5 mm and the distance from the slits to the viewing screen is D = 1.0 m. If light of wavelength λ = 500 nm is used, what is the fringe width β?

• A0.5 mm
• B1.0 mm
• C2.0 mm
• D2.5 mm

A parallel-plate capacitor with air between its plates has a capacitance of 10 μF. It is charged to a potential difference of 100 V and then disconnected from the charging battery. A dielectric slab of dielectric constant K = 5 is then inserted to completely fill the space between the plates. What is the new potential difference across the plates?

• A50 V
• B100 V
• C500 V
• D20 V

In a potentiometer experiment, a cell is balanced against a wire length of 60 cm on open circuit. When the cell is shunted with an external resistor R = 5 Ω, the balancing length shifts to 50 cm. What is the internal resistance r of the cell?

• A0.5 Ω
• B1.0 Ω
• C1.5 Ω
• D2.0 Ω

Two electric light bulbs rated 40 W, 220 V and 60 W, 220 V are connected in series across a 220 V mains supply. Which bulb will glow brighter and why?

• AThe 60 W bulb, because its manufacturer power rating is higher
• BBoth bulbs will glow with equal brightness because the series current is identical
• CThe 40 W bulb, because its higher filament resistance dissipates greater power in series
• DNeither bulb will glow because the supply voltage is insufficient

A flat circular coil of radius R = 5 cm with N = 100 tightly wound turns carries a steady current of I = 1 A. What is the magnetic flux density B at the center of the coil? (Take μ₀ = 4π × 10⁻⁷ T·m/A.)

• A8π × 10⁻⁴ T
• B2π × 10⁻⁴ T
• C4π × 10⁻⁵ T
• D4π × 10⁻⁴ T

A straight conducting metal rod of length L = 0.5 m rotates with one end pivoted at an angular speed of ω = 40 rad/s in a uniform magnetic field B = 0.2 T oriented perpendicular to the plane of rotation. What is the induced electromotive force (EMF) developed between the ends of the rod?

• A0.5 V
• B1.0 V
• C2.0 V
• D4.0 V

A series LCR circuit has an inductance L = 0.2 H, a capacitance C = 5 μF and a resistance R = 10 Ω connected across an AC voltage source. What are the resonant angular frequency ω₀ and the quality factor (Q-factor) of the circuit?

• Aω₀ = 500 rad/s, Q = 10
• Bω₀ = 1000 rad/s, Q = 20
• Cω₀ = 1000 rad/s, Q = 200
• Dω₀ = 2000 rad/s, Q = 40

Monochromatic ultraviolet light of frequency 1.0 × 10¹⁵ Hz shines on a metallic photosurface with a work function of φ = 2.14 eV. Taking Planck's constant h = 6.63 × 10⁻³⁴ J·s and 1 eV = 1.60 × 10⁻¹⁹ J, what is the maximum kinetic energy of the emitted photoelectrons?

• A1.00 eV
• B2.00 eV
• C3.14 eV
• D4.14 eV

A radioactive medical isotope has a half-life of 15 hours. If an initial diagnostic sample contains 80 mg of this pure radioactive substance, what mass of the isotope remains undecayed after 45 hours?

• A5 mg
• B20 mg
• C10 mg
• D40 mg

In a bipolar junction transistor (BJT) circuit, the collector current increases by 1.96 mA when the emitter current increases by 2.00 mA. What are the common-base current gain (α) and common-emitter current gain (β) of the transistor?

• Aα = 0.96, β = 24
• Bα = 0.99, β = 99
• Cα = 0.98, β = 50
• Dα = 0.98, β = 49

What volume of dry carbon dioxide gas measured at standard temperature and pressure (STP, 0°C and 1 atm, molar volume = 22.4 L) is evolved when 10.0 g of pure calcium carbonate (CaCO₃, molar mass = 100.0 g/mol) is completely decomposed by thermal heating?

• A1.12 L
• B2.24 L
• C4.48 L
• D22.4 L

An electron (mass m = 9.11 × 10⁻³¹ kg, charge e = 1.60 × 10⁻¹⁹ C) is accelerated from rest through a potential difference of V = 400 V. What is its de Broglie wavelength λ?

• A0.123 nm (1.23 Å)
• B0.00307 nm (0.0307 Å)
• C0.0614 nm (0.614 Å)
• D1.23 nm (12.3 Å)

According to the Valence Shell Electron Pair Repulsion (VSEPR) theory and hybridization concepts, what are the central atom hybridization and actual molecular geometry of xenon tetrafluoride (XeF₄)?

• Asp³d, see-saw
• Bsp³d², square planar
• Csp³d², tetrahedral
• Dsp³d³, pentagonal planar

For the Haber synthesis reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g) carried out at 298 K, the standard enthalpy change is ΔH° = -92.40 kJ. Taking R = 8.314 J·K⁻¹·mol⁻¹, what is the standard internal energy change ΔU° for this reaction?

• A-97.36 kJ
• B-87.44 kJ
• C-92.40 kJ
• D+87.44 kJ

For which of the following reversible gaseous equilibrium reactions does the equilibrium constant K_p equal K_c at all temperatures?

• AN₂(g) + 3H₂(g) ⇌ 2NH₃(g)
• BPCl₅(g) ⇌ PCl₃(g) + Cl₂(g)
• C2SO₂(g) + O₂(g) ⇌ 2SO₃(g)
• DH₂(g) + I₂(g) ⇌ 2HI(g)

What is the pH of an acidic buffer solution prepared by mixing 50 mL of 0.20 M acetic acid (CH₃COOH, pK_a = 4.74) with 50 mL of 0.10 M sodium acetate (CH₃COONa)?

• A4.14
• B4.74
• C4.44
• D5.04

The solubility product constant K_sp of lead(II) chloride (PbCl₂) in water at 25°C is 3.2 × 10⁻⁵. What is the molar solubility S of PbCl₂ in pure water?

• A1.0 × 10⁻² M
• B2.0 × 10⁻² M
• C4.0 × 10⁻³ M
• D8.0 × 10⁻³ M

Consider a standard electrochemical Daniell cell: Zn(s) | Zn²⁺(0.01 M) || Cu²⁺(1.0 M) | Cu(s). Given that the standard cell potential is E°_cell = 1.10 V and 2.303 RT / F = 0.0591 V at 298 K, what is the EMF (E_cell) of this operational cell?

• A1.04 V
• B1.10 V
• C1.16 V
• D1.22 V

A first-order chemical decomposition reaction has a rate constant k = 6.93 × 10⁻³ s⁻¹. What is the time required for exactly 75% of the starting reactant to react completely?

• A50 s
• B100 s
• C200 s
• D400 s

What is the theoretical depression in freezing point (ΔT_f) for a 0.10 m aqueous solution of barium chloride (BaCl₂), assuming complete electrolytic dissociation? (Cryoscopic constant of water K_f = 1.86 K·kg·mol⁻¹).

• A0.186 °C
• B0.372 °C
• C0.558 °C
• D0.744 °C

Why is the electron gain enthalpy of chlorine (Δ_egH = -349 kJ/mol) more negative (releases more energy) than that of fluorine (Δ_egH = -328 kJ/mol), despite fluorine having a higher electronegativity?

• AChlorine has lower nuclear charge than fluorine
• BFluorine's extremely small 2p orbital has high electron-electron repulsion that resists a…
• CFluorine has completely empty 2d orbitals that repel electrons
• DChlorine has a smaller covalent atomic radius than fluorine

Which chemical compounds are responsible for the temporary hardness of natural water, and how can this temporary hardness be eliminated simply?

• ACalcium and magnesium chlorides; eliminated by boiling the water
• BCalcium and magnesium sulfates; eliminated by simple filtration
• CSodium and potassium carbonates; eliminated by adding soap
• DCalcium and magnesium bicarbonates; eliminated by boiling the water

Among the oxoacids of phosphorus—hypophosphorous acid (H₃PO₂), phosphorous acid (H₃PO₃), and orthophosphoric acid (H₃PO₄)—which is the strongest reducing agent and what is its basicity?

• AH₃PO₃, basicity = 2 (dibasic)
• BH₃PO₄, basicity = 3 (tribasic)
• CH₃PO₂, basicity = 1 (monobasic)
• DH₃PO₂, basicity = 2 (dibasic)

How does the bleaching mechanism of moist sulfur dioxide (SO₂) differ fundamentally from the bleaching action of chlorine (Cl₂) water?

• ASO₂ bleaches by oxidation and is permanent; Cl₂ bleaches by reduction and is temporary
• BBoth gases bleach solely by nascent oxygen and produce permanent results
• CSO₂ bleaches through thermal dehydration; Cl₂ bleaches by precipitation
• DSO₂ bleaches by reduction and is temporary; Cl₂ bleaches by oxidation and is permanent

In the metallurgy of iron using a blast furnace, limestone (CaCO₃) is added with iron ore and coke. What chemical role does it play, and what is the chemical formula of the resulting slag?

• AActs as an oxidizing agent; forms iron silicate slag (FeSiO₃)
• BActs as a basic flux; forms calcium silicate slag (CaSiO₃)
• CActs as a reducing agent; forms calcium aluminate slag (CaAl₂O₄)
• DActs as an acidic flux; forms sulfur dioxide gas (SO₂)

What are the spin-only magnetic moments (in Bohr Magnetons, BM) of the hexacyanoferrate(III) complex [Fe(CN)₆]³⁻ and the hexaaquairon(III) complex [Fe(H₂O)₆]³⁺? (Atomic number of Fe = 26).

• A[Fe(CN)₆]³⁻ has 5.92 BM, while [Fe(H₂O)₆]³⁺ has 1.73 BM
• BBoth complexes have 1.73 BM
• CBoth complexes have 0 BM (diamagnetic)
• D[Fe(CN)₆]³⁻ has 1.73 BM, while [Fe(H₂O)₆]³⁺ has 5.92 BM

Which of the following organic compounds possesses a chiral molecular structure and optical activity despite not containing any asymmetric sp³ carbon atom?

• A2-Chlorobutane
• BLactic acid (2-hydroxypropanoic acid)
• CPenta-2,3-diene (an allene derivative with orthogonal terminal π-systems)
• D2-Methylbut-2-ene

An alkene with molecular formula C₆H₁₂ yields acetone (propan-2-one) and propanal in equimolar amounts upon reductive ozonolysis with O₃ followed by Zn / H₂O. What is the systematic IUPAC name of the alkene?

• A3-Methylpent-2-ene
• BHex-2-ene
• C2,3-Dimethylbut-2-ene
• D2-Methylpent-2-ene

Which of the following alkyl halides undergoes nucleophilic substitution via the bimolecular S_N2 mechanism at the fastest rate when reacted with sodium iodide in dry acetone?

• ACH₃CH₂I (Ethyl iodide)
• BCH₃I (Methyl iodide)
• C(CH₃)₂CHI (Isopropyl iodide)
• D(CH₃)₃CI (tert-Butyl iodide)

When treated with Lucas reagent (a solution of anhydrous ZnCl₂ in concentrated HCl) at room temperature, an unknown alcohol produces immediate turbidity/cloudiness. What class of alcohol is it?

• ASecondary (2°) alcohol
• BPrimary (1°) alcohol
• CMethanol
• DTertiary (3°) alcohol

Benzaldehyde (C₆H₅CHO), which has no α-hydrogen, is heated with 50% aqueous sodium hydroxide. Which pair of products is formed by the Cannizzaro reaction?

• ABenzoin only
• BBenzyl alcohol and toluene
• CBenzyl alcohol and sodium benzoate
• DSodium benzoate and benzene

What is the correct arrangement of the following substituted benzoic acids in order of increasing acid strength (weakest acid to strongest acid)?

• ABenzoic acid < p-Methoxybenzoic acid < p-Chlorobenzoic acid < p-Nitrobenzoic acid
• Bp-Nitrobenzoic acid < p-Chlorobenzoic acid < Benzoic acid < p-Methoxybenzoic acid
• Cp-Chlorobenzoic acid < p-Methoxybenzoic acid < Benzoic acid < p-Nitrobenzoic acid
• Dp-Methoxybenzoic acid < Benzoic acid < p-Chlorobenzoic acid < p-Nitrobenzoic acid

An unknown organic amine reacts with Hinsberg's reagent (benzenesulfonyl chloride) to form a sulfonamide precipitate that completely dissolves upon addition of aqueous sodium hydroxide (NaOH). What type of amine is it?

• ASecondary (2°) amine
• BPrimary (1°) amine
• CTertiary (3°) amine
• DQuaternary ammonium salt