Bihar Combined Entrance Competitive Examination (BCECE)

Which of the following physical quantities has the same dimensional formula as that of Planck's constant (h)?

• ALinear momentum
• BAngular momentum
• CTorque
• DForce

A projectile is thrown with an initial velocity of 20 m/s at an angle of 30 degrees with the horizontal. Taking g = 10 m/s^2, what is the maximum height attained by the projectile?

• A5.0 meters
• B10.0 meters
• C15.0 meters
• D20.0 meters

A force F = (3i + 4j) N acts on a particle and displaces it from position r1 = (i + j) m to position r2 = (3i + 5j) m. What is the work done by the force on the particle?

• A10 Joules
• B14 Joules
• C22 Joules
• D25 Joules

A bullet of mass 10 g is fired horizontally from a gun of mass 4 kg with a muzzle velocity of 400 m/s. What is the recoil velocity of the gun?

• A-1.0 m/s
• B-2.0 m/s
• C-4.0 m/s
• D-10.0 m/s

A block of mass 5 kg is placed on a rough inclined plane making an angle of 30 degrees with the horizontal. If the coefficient of static friction is 0.6, what is the frictional force acting on the block? (Take g = 10 m/s^2)

• A25 N
• B26 N
• C30 N
• D43 N

A solid cylinder and a hollow sphere, having the same mass and radius, are rotating about their respective standard axes of symmetry. What is the ratio of their moments of inertia (I_cylinder / I_sphere)?

• A3:4
• B4:5
• C5:4
• D3:5

If the radius of the Earth shrinks by 1% while its mass remains constant, how will the acceleration due to gravity (g) at the surface of the Earth change?

• ADecrease by 1%
• BIncrease by 1%
• CDecrease by 2%
• DIncrease by 2%

According to Kepler's Third Law of planetary motion, the square of the period of revolution (T) of a planet is directly proportional to the cube of the semi-major axis of its orbit (R). If the distance of a planet from the Sun becomes 4 times its present value, what will its new orbital period become?

• A2 times the original period
• B4 times the original period
• C8 times the original period
• D16 times the original period

A solid sphere of mass M and radius R rolls down an inclined plane of inclination theta without slipping. What is the linear acceleration of the sphere down the incline?

• Ag * sin(theta)
• B(5/7) * g * sin(theta)
• C(2/3) * g * sin(theta)
• D(3/5) * g * sin(theta)

A particle of mass m moving with speed v collides head-on elastically with another particle of mass 2m at rest. What is the fraction of kinetic energy lost by the colliding particle of mass m?

• A1/9
• B4/9
• C8/9
• D1/3

In a thermodynamic system, 200 Joules of heat is supplied to the system, and the system performs 50 Joules of work. What is the change in the internal energy of the system?

• A150 Joules
• B250 Joules
• C200 Joules
• D100 Joules

Which of the following processes of heat transfer does not require any material medium?

• AConduction
• BConvection
• CRadiation
• DAdvection

A Carnot engine operates between temperatures of 600 K and 300 K. What is the efficiency of this engine?

• A25%
• B50%
• C66.7%
• D75%

An ideal gas expands adiabatically. During this process, what is the relation between the work done by the gas (W) and the change in its internal energy (dU)?

• AW = dU
• BW = -dU
• CW = 0
• DdU = 0

If the absolute temperature of an ideal gas is quadrupled, how does the root-mean-square (rms) speed of its molecules change?

• AIt remains unchanged
• BIt is doubled
• CIt is halved
• DIt becomes four times the initial speed

One mole of a monoatomic ideal gas undergoes a cyclic process. If the heat absorbed in path A is 50 J, path B is 30 J, and the work done during path C is -40 J, what is the net work done during the complete cycle?

• A40 J
• B80 J
• C120 J
• D0 J

Two equal positive point charges, each of magnitude q, are placed at a distance r apart. If a third equal positive charge q is placed at the midpoint of the line joining the two charges, what is the net electrostatic force acting on this third charge?

• AZero
• Bq^2 / (4 * pi * epsilon_0 * r^2)
• C4 * q^2 / (pi * epsilon_0 * r^2)
• Dq^2 / (pi * epsilon_0 * r^2)

The resistance of a copper wire is 10 Ohms at 0 degrees Celsius. If the temperature coefficient of resistance of copper is 0.004 per degree Celsius, what will be its resistance at 50 degrees Celsius?

• A10.2 Ohms
• B11.0 Ohms
• C12.0 Ohms
• D14.0 Ohms

Three capacitors of capacitances 3 microfarads, 6 microfarads, and 9 microfarads are connected in series. What is the equivalent capacitance of this combination?

• A1.63 microfarads
• B18.0 microfarads
• C1.80 microfarads
• D4.50 microfarads

A solenoid of length 0.5 meters has 500 turns and carries a current of 2 Amperes. What is the magnetic field inside the solenoid near its center? (Take mu_0 = 4 * pi * 10^-7 T*m/A)

• A1.26 * 10^-3 Tesla
• B2.51 * 10^-3 Tesla
• C6.28 * 10^-4 Tesla
• D5.02 * 10^-3 Tesla

A circular loop of wire of radius 10 cm is placed in a uniform magnetic field of 0.5 Tesla, perpendicular to the plane of the loop. If the magnetic field is reduced to zero in 0.1 seconds, what is the average induced electromotive force (emf) in the loop?

• A0.157 Volts
• B1.57 Volts
• C0.314 Volts
• D3.14 Volts

A series LCR circuit contains a resistor of 100 Ohms, an inductor of L = 0.5 Henry, and a capacitor of C = 8 microfarads. What is the resonant frequency (in radians per second) of the circuit?

• A250 rad/s
• B500 rad/s
• C1000 rad/s
• D2000 rad/s

A proton is moving along the positive x-axis with a speed of 3 * 10^5 m/s. It enters a region where a uniform electric field of E = 6 * 10^4 V/m is along the positive y-axis. What must be the magnitude and direction of the magnetic field (B) so that the proton continues to move along the x-axis undeflected?

• A0.2 Tesla, along the positive z-axis
• B0.2 Tesla, along the negative z-axis
• C5.0 Tesla, along the positive z-axis
• D5.0 Tesla, along the negative z-axis

Two coaxial circular coils, one of small radius r and another of large radius R (where R >> r), are placed with their centers coinciding. What is the mutual inductance (M) of this system of coils as a function of their radii?

• AM is proportional to r / R
• BM is proportional to r^2 / R
• CM is proportional to r / R^2
• DM is proportional to r^2 * R

A ray of light passes through an equilateral glass prism such that the angle of incidence is equal to the angle of emergence, and each of these angles is equal to 3/4 of the angle of the prism. What is the angle of deviation?

• A30 degrees
• B45 degrees
• C60 degrees
• D15 degrees

An astronomical telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. What is the magnifying power of this telescope when adjusted for normal vision (focused at infinity)?

• A30
• B75
• C155
• D145

In a Young's Double Slit Experiment, the slit separation is 0.2 mm and the screen is placed 1.2 meters away. If light of wavelength 500 nm is used, what is the width of the interference fringes?

• A1.5 mm
• B3.0 mm
• C4.5 mm
• D6.0 mm

A biconvex lens of glass (refractive index = 1.5) has radii of curvature of 20 cm and 30 cm for its two surfaces. What is the focal length of this lens in air?

• A12 cm
• B24 cm
• C36 cm
• D48 cm

A ray of unpolarized light is incident on the surface of a glass plate of refractive index sqrt(3). At what angle of incidence will the reflected ray be completely polarized?

• A30 degrees
• B45 degrees
• C60 degrees
• D90 degrees

What is the de Broglie wavelength associated with an electron accelerated through a potential difference of 100 Volts? (Take h = 6.63 * 10^-34 J*s, m = 9.1 * 10^-31 kg, e = 1.6 * 10^-19 C)

• A1.227 Angstroms
• B0.123 Angstroms
• C12.27 Angstroms
• D122.7 Angstroms

In a hydrogen atom, an electron transitions from the orbit n = 3 to the orbit n = 2. What is the wavelength of the emitted photon? (Rydberg constant, R = 1.097 * 10^7 m^-1)

• A656.3 nm
• B486.1 nm
• C434.0 nm
• D364.6 nm

The half-life of a radioactive substance is 10 days. What fraction of the initial active nuclei will remain undecayed after 30 days?

• A1/3
• B1/4
• C1/8
• D1/16

The work function of a metal surface is 2.0 eV. If light of wavelength 300 nm is incident on the metal, what is the stopping potential required to cut off the photoelectric current? (Take h*c = 1240 eV*nm)

• A1.13 Volts
• B2.13 Volts
• C4.13 Volts
• D0.13 Volts

A certain helium nucleus (Alpha particle) has a mass defect of 0.0303 amu. What is the binding energy per nucleon of this nucleus? (Take 1 amu = 931.5 MeV)

• A28.2 MeV
• B7.07 MeV
• C14.1 MeV
• D3.54 MeV

Which of the following concentration terms is independent of temperature?

• AMolarity
• BMolality
• CNormality
• DFormalty

A mixture of 4 g of Helium and 16 g of Oxygen is kept in a vessel. What is the mole fraction of Helium in this mixture?

• A0.20
• B0.33
• C0.50
• D0.67

An organic compound contains 40.0% Carbon, 6.7% Hydrogen, and 53.3% Oxygen by mass. What is the empirical formula of the compound?

• ACHO
• BCH2O
• CCHO2
• DC2H4O

For a first-order reaction, the rate constant (k) is 6.93 * 10^-3 s^-1. What is the half-life (t_1/2) of this reaction?

• A10 seconds
• B100 seconds
• C1000 seconds
• D50 seconds

What is the pH of a buffer solution prepared by mixing equal volumes of 0.2 M acetic acid and 0.2 M sodium acetate? (Given: pKa of acetic acid = 4.76)

• A3.76
• B4.76
• C5.76
• D7.00

The solubility product (Ksp) of sparingly soluble salt AB2 is 4.0 * 10^-12. What is its molar solubility in water?

• A1.0 * 10^-4 M
• B2.0 * 10^-6 M
• C1.0 * 10^-6 M
• D2.0 * 10^-4 M

What is the cell potential (E_cell) at 298 K for the following cell: Zn(s) | Zn^2+(0.1 M) || Cu^2+(1.0 M) | Cu(s)? (Given: Standard cell potential E°_cell = 1.10 V; 2.303RT/F = 0.059 V at 298 K)

• A1.070 V
• B1.100 V
• C1.130 V
• D1.159 V

An aqueous solution of a non-volatile solute freezes at -0.372 degrees Celsius. If Kf for water is 1.86 K kg/mol, what is the molality of the solution?

• A0.10 mol/kg
• B0.20 mol/kg
• C0.50 mol/kg
• D1.00 mol/kg

A metal crystallizes in a face-centered cubic (fcc) lattice. If the edge length of the unit cell is 'a', what is the closest distance between two metal atoms in the lattice?

• Aa
• Ba / sqrt(2)
• Csqrt(3) * a / 2
• Dsqrt(2) * a

The enthalpy of vaporization of water is 40.66 kJ/mol. What is the entropy change (dS) for the vaporization of 1 mole of water at its boiling point (100 degrees Celsius)?

• A109 J/(K*mol)
• B406.6 J/(K*mol)
• C273 J/(K*mol)
• D10.9 J/(K*mol)

At 298 K, the molar conductivities at infinite dilution for NaCl, HCl, and CH3COONa are 126.4, 426.16, and 91.0 S cm^2/mol, respectively. What is the molar conductivity at infinite dilution for CH3COOH?

• A390.76 S cm^2/mol
• B590.76 S cm^2/mol
• C290.76 S cm^2/mol
• D426.16 S cm^2/mol

According to Freundlich adsorption isotherm, the variation of physical adsorption with pressure is expressed as x/m = k * P^(1/n). What are the possible values of 1/n under normal conditions?

• AExactly 0
• BExactly 1
• CBetween 0 and 1
• DGreater than 1

Which of the following elements has the highest first ionization enthalpy?

• ABoron
• BCarbon
• CNitrogen
• DOxygen

According to VSEPR theory, what is the shape of a CIF3 molecule?

• ATrigonal planar
• BTrigonal bipyramidal
• CT-shaped
• DTrigonal pyramidal