I85PREP
⌘ K
GUJCET study materials
GUJCET study resources

GUJCET practice questions

One question at a time. Build your GUJCET understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Physics

Two point charges, kept at a separation r in vacuum, repel each other with a force F. If the separation between them is doubled while the charges remain unchanged, the magnitude of the force becomes

  1. 2F
  2. 4F
  3. F/2
  4. F/4 Correct answer.

Explanation

Coulomb's law states that the electrostatic force between two point charges is inversely proportional to the square of the distance separating them. Doubling the separation therefore multiplies the force by 1/2² = 1/4, so the new force is F/4.

Question 2Physics

Three identical resistors, each of resistance 6 Ω, are connected in parallel. The equivalent resistance of the combination is

  1. 3 Ω
  2. 18 Ω
  3. 6 Ω
  4. 2 Ω Correct answer.

Explanation

For resistors in parallel, the reciprocals add: 1/R = 1/6 + 1/6 + 1/6 = 3/6 = 1/2, giving R = 2 Ω. Identical resistors in parallel always give an equivalent resistance smaller than one resistor, here one third of 6 Ω.

Question 3Physics

A convex lens has a focal length of 25 cm. The power of this lens is

  1. +4 D Correct answer.
  2. 0.25 D
  3. +25 D
  4. −4 D

Explanation

The power of a lens in dioptres is the reciprocal of its focal length expressed in metres: P = 1/f. Converting 25 cm to 0.25 m gives P = 1/0.25 = +4 D, and the positive sign is used because the lens is converging.

Question 4Physics

A proton and an alpha particle enter a uniform magnetic field perpendicular to the field lines, both with the same speed. If the proton moves in a circular path of radius r, the radius of the alpha particle's path is

  1. √2 r
  2. 2r Correct answer.
  3. r/2
  4. r

Explanation

A charged particle moving perpendicular to a magnetic field follows a circle of radius r = mv/(qB). An alpha particle has about four times the proton mass and twice the proton charge, so its radius is (4m·v)/(2e·B) = 2r when the speed and field are the same.

Question 5Physics

The self-inductance of a coil is 0.5 H. If the current through the coil changes uniformly from 2 A to 6 A in 0.2 s, the magnitude of the induced emf is

  1. 5 V
  2. 10 V Correct answer.
  3. 40 V
  4. 20 V

Explanation

Self-induced emf is given by ε = L|dI/dt|, where L is the self-inductance and dI/dt is the rate of change of current. Here dI = 4 A and dt = 0.2 s, so dI/dt = 20 A/s and ε = 0.5 × 20 = 10 V.

Question 6Physics

An alternating current has an rms value of 5 A. The peak value of this current is approximately

  1. 2.5 A
  2. 10 A
  3. 7.07 A Correct answer.
  4. 5 A

Explanation

For a sinusoidal alternating current, the rms value is the peak value divided by √2. Rearranging gives I₀ = √2 × I_rms = 1.414 × 5 ≈ 7.07 A, which is always larger than the rms value.

Question 7Physics

The threshold frequency of a metal surface is 5 × 10¹⁴ Hz. Light of frequency 8 × 10¹⁴ Hz is incident on the surface. Taking h = 6.63 × 10⁻³⁴ J s, the maximum kinetic energy of the emitted photoelectrons is about

  1. 2.0 × 10⁻¹⁹ J Correct answer.
  2. 5.3 × 10⁻¹⁹ J
  3. 3.3 × 10⁻¹⁹ J
  4. 8.0 × 10⁻¹⁹ J

Explanation

Einstein's photoelectric equation gives the maximum kinetic energy as K_max = h(f − f₀). The frequency difference is 3 × 10¹⁴ Hz, so K_max = 6.63 × 10⁻³⁴ × 3 × 10¹⁴ ≈ 2.0 × 10⁻¹⁹ J.

Question 8Physics

In a hydrogen atom an electron makes a transition from the n = 3 level to the n = 2 level. The energy of the emitted photon is closest to

  1. 3.40 eV
  2. 0.85 eV
  3. 1.89 eV Correct answer.
  4. 1.51 eV

Explanation

The photon energy equals the difference between the two level energies: E = 13.6(1/2² − 1/3²) eV = 13.6(1/4 − 1/9) = 13.6 × 5/36 ≈ 1.89 eV. This transition produces the Hα line of the Balmer series, which lies in the visible region.

Question 9Physics

A radioactive sample has a half-life of 20 minutes. The fraction of the original number of nuclei remaining after 1 hour is

  1. 1/3
  2. 1/2
  3. 1/8 Correct answer.
  4. 1/6

Explanation

One hour contains 60/20 = 3 half-lives. The surviving fraction after n half-lives is (1/2)ⁿ, so after three half-lives it is (1/2)³ = 1/8 of the original nuclei.

Question 10Physics

When a zener diode is used as a voltage regulator, it is operated in the

  1. forward bias region with zero current
  2. reverse bias region below the breakdown voltage
  3. forward bias region above the knee voltage
  4. reverse breakdown region Correct answer.

Explanation

A zener diode holds its terminal voltage nearly constant when reverse biased beyond the breakdown voltage, where the zener or avalanche mechanism produces a large current with little change in voltage. Voltage regulators deliberately use this reverse breakdown region.

Question 11Physics

The dimensional formula of Planck's constant is the same as that of which physical quantity?

  1. Power
  2. Energy
  3. Linear momentum
  4. Angular momentum Correct answer.

Explanation

Planck's constant has units of joule-second, which reduce to kg m² s⁻¹, or [ML²T⁻¹]. Angular momentum is the product of moment of inertia and angular velocity and has the same dimensional formula. Hence h and angular momentum are dimensionally identical.

Question 12Physics

A car starts from rest and moves along a straight road with a constant acceleration of 2.0 m/s². What distance does it cover in the first 5.0 s?

  1. 5.0 m
  2. 25 m Correct answer.
  3. 50 m
  4. 10 m

Explanation

For uniform acceleration starting from rest, use s = ut + ½at² with u = 0, a = 2.0 m/s² and t = 5.0 s. This gives s = ½ × 2.0 × 25 = 25 m. The velocity-time area under the line also confirms this value.

Question 13Physics

During an isothermal expansion of an ideal gas, 80 J of heat is absorbed by the gas. What is the work done by the gas?

  1. 80 J Correct answer.
  2. 40 J
  3. −80 J
  4. 0 J

Explanation

For an ideal gas at constant temperature, the internal energy does not change, so ΔU = 0. The first law then gives Q = ΔU + W, hence W = Q = 80 J. Expansion work done by the gas is positive, consistent with the absorbed heat.

Question 14Physics

A metal wire of resistance R is stretched uniformly until its length is doubled. What is its new resistance?

  1. 4R Correct answer.
  2. 2R
  3. R
  4. R/2

Explanation

Stretching keeps the volume constant, so doubling the length halves the cross-sectional area. Since R = ρl/A, the new resistance is ρ(2l)/(A/2) = 4R. Thus resistance varies as the square of the length when volume is fixed.

Question 15Physics

An electron with kinetic energy K moves perpendicular to a uniform magnetic field B. The radius of its circular path is proportional to which expression?

  1. 1/(B√K)
  2. K/B
  3. K²/B
  4. √K/B Correct answer.

Explanation

The magnetic force provides centripetal force, so evB = mv²/r and r = mv/(eB). Using K = ½mv² gives v = √(2K/m), so r = √(2mK)/(eB). Therefore r is proportional to √K/B.

Question 16Physics

In a series LCR circuit driven at resonance, the current in the circuit is

  1. equal to the current through the capacitor only
  2. minimum but nonzero
  3. zero
  4. maximum Correct answer.

Explanation

At resonance the inductive and capacitive reactances are equal and cancel, so the impedance is purely resistive and minimum. The current is therefore V/R, its maximum value for the given source voltage. The voltages across L and C are equal in magnitude but opposite in phase.

Question 17Physics

A ray of light travels from water of refractive index 1.33 towards air. The critical angle for the water-air boundary is closest to

  1. 41°
  2. 49° Correct answer.
  3. 90°
  4. 30°

Explanation

The critical angle satisfies sin C = 1/n for a denser-to-rarer boundary. With n = 1.33, sin C = 0.752, giving C ≈ 48.8°. This rounds to 49°.

Question 18Physics

In Young's double-slit experiment, the slit separation is doubled and the distance from the slits to the screen is halved. The fringe width becomes

  1. 4β
  2. β/4 Correct answer.
  3. β/2
  4. 2β

Explanation

Fringe width is β = λD/d. With D replaced by D/2 and d replaced by 2d, the new width is λ(D/2)/(2d) = λD/(4d) = β/4. Both changes reduce the fringe width.

Question 19Physics

A nucleus of mass number 240 undergoes fission into two fragments of mass number 120 each. If the binding energy per nucleon is 7.6 MeV for the parent and 8.5 MeV for each fragment, the energy released is

  1. 108 MeV
  2. 432 MeV
  3. 216 MeV Correct answer.
  4. 0.9 MeV

Explanation

The total binding energy before fission is 240 × 7.6 = 1824 MeV. After fission it is 240 × 8.5 = 2040 MeV, because the total nucleon number is conserved. The energy released is the increase in binding energy, 2040 − 1824 = 216 MeV.

Question 20Physics

When silicon is doped with boron, the resulting material has

  1. electrons as majority carriers
  2. holes as majority carriers Correct answer.
  3. no mobile charge carriers
  4. equal numbers of electrons and holes

Explanation

Boron is trivalent and acts as an acceptor impurity in silicon. Each boron atom creates a vacancy, or hole, that can accept an electron, making holes the majority carriers and producing p-type silicon. The material remains electrically neutral overall.

Question 21Physics

The acceleration due to gravity at a height h above the Earth's surface becomes one-fourth of its value at the surface. Taking the Earth's radius as R and neglecting the Earth's rotation, h is equal to

  1. 2R
  2. R/2
  3. 3R
  4. R Correct answer.

Explanation

At a height h, g_h = g[R/(R+h)]². Setting g_h = g/4 gives R/(R+h) = 1/2, so R + h = 2R and h = R. The result assumes a spherical, non-rotating Earth.

Question 22Physics

A metallic wire of length L and radius r is stretched by a force F, producing an elongation ΔL. If the radius of the wire is doubled while its length and the applied force are kept the same, the elongation becomes

  1. ΔL/4 Correct answer.
  2. 4ΔL
  3. ΔL/2
  4. 2ΔL

Explanation

For a stretched wire, Young's modulus gives ΔL = FL/(πr²Y), so elongation is inversely proportional to the square of the radius. Doubling the radius increases the cross-sectional area four times, reducing the elongation to ΔL/4.

Question 23Physics

A solid body floats in water with three-fourths of its volume submerged. The density of the body is (density of water = 1000 kg/m³)

  1. 500 kg/m³
  2. 250 kg/m³
  3. 1000 kg/m³
  4. 750 kg/m³ Correct answer.

Explanation

For a floating body, weight equals the buoyant force: ρ_body V g = ρ_water (3V/4) g. Cancelling V and g gives ρ_body = (3/4)(1000) = 750 kg/m³.

Question 24Physics

A Carnot engine operates between a source and a sink at 300 K. If the efficiency of the engine is 40%, the temperature of the source is

  1. 480 K
  2. 420 K
  3. 450 K
  4. 500 K Correct answer.

Explanation

Carnot efficiency is η = 1 - T_sink/T_source. Substituting η = 0.40 and T_sink = 300 K gives 0.40 = 1 - 300/T_source, so 300/T_source = 0.60 and T_source = 500 K.

Question 25Physics

A particle executes simple harmonic motion with amplitude A. At the instant its displacement is A/2 from the mean position, the ratio of its kinetic energy to its potential energy is

  1. 3:1 Correct answer.
  2. 2:1
  3. 1:3
  4. 1:2

Explanation

In SHM, total energy E = ½mω²A², potential energy U = ½mω²x², and kinetic energy K = E - U. At x = A/2, U = E/4, so K = 3E/4 and K:U = 3:1.

Question 26Physics

A pipe closed at one end has a fundamental frequency of 100 Hz. The frequency of its first overtone is

  1. 300 Hz Correct answer.
  2. 100 Hz
  3. 400 Hz
  4. 200 Hz

Explanation

A pipe closed at one end supports only odd harmonics: f, 3f, 5f, and so on. The first overtone is the next allowed frequency, 3f = 3 × 100 = 300 Hz.

Question 27Physics

Two capacitors of 2 μF and 3 μF are connected in series across a 10 V battery. The charge on each capacitor is

  1. 30 μC
  2. 12 μC Correct answer.
  3. 20 μC
  4. 6 μC

Explanation

For capacitors in series, 1/C_eq = 1/2 + 1/3, giving C_eq = 1.2 μF. The charge is Q = C_eq V = 1.2 μF × 10 V = 12 μC, and series capacitors carry equal charge.

Question 28Physics

A cell of emf 2 V and internal resistance 1 Ω is connected to an external resistance of 9 Ω. The terminal voltage of the cell is

  1. 1.6 V
  2. 2.2 V
  3. 1.8 V Correct answer.
  4. 2.0 V

Explanation

The current is I = emf/(R + r) = 2/(9 + 1) = 0.2 A. The terminal voltage is V = emf - Ir = 2 - 0.2 × 1 = 1.8 V, which also equals IR = 0.2 × 9.

Question 29Physics

A galvanometer of resistance 100 Ω gives full-scale deflection for a current of 1 mA. To convert it into a voltmeter of range 10 V, the resistance to be connected in series with it is

  1. 10000 Ω
  2. 100 Ω
  3. 900 Ω
  4. 9900 Ω Correct answer.

Explanation

For a voltmeter, a series resistance R_s limits the current to the galvanometer's full-scale value: R_s = V/I_g - G. Here R_s = 10/0.001 - 100 = 10000 - 100 = 9900 Ω.

Question 30Physics

The de Broglie wavelength of an electron accelerated from rest through a potential difference of 100 V is approximately

  1. 0.123 Å
  2. 1.23 Å Correct answer.
  3. 12.3 Å
  4. 123 Å

Explanation

For an electron accelerated through V volts, λ = 12.27/√V Å. With V = 100 V, √V = 10, so λ ≈ 12.27/10 = 1.23 Å.

Question 31Physics

The dimensional formula of the coefficient of viscosity η is

  1. [M L^-2 T^-1]
  2. [M L^-1 T^-2]
  3. [M L^-1 T^-1] Correct answer.
  4. [M L T^-1]

Explanation

For streamline flow, viscous force is F = η A (dv/dx), so η = F/[A(dv/dx)]. Substituting dimensions gives MLT^-2 divided by L^2·T^-1, which reduces to M L^-1 T^-1. Thus the coefficient of viscosity has dimensions of pressure multiplied by time.

Question 32Physics

The moment of inertia of a uniform circular disc of mass M and radius R about an axis through its centre and perpendicular to its plane is

  1. (1/4)MR^2
  2. MR^2
  3. (1/2)MR^2 Correct answer.
  4. (2/5)MR^2

Explanation

For a uniform disc, each mass element at radius r contributes r^2 dm, and integrating over the disc gives I = (1/2)MR^2. The result MR^2 applies to a thin ring about the same axis, while (2/5)MR^2 is for a solid sphere about a diameter. Hence the disc has half the moment of inertia of a ring of the same mass and radius.

Question 33Physics

The output of a two-input AND gate is high

  1. only when both are high Correct answer.
  2. when any one input is low
  3. when the two inputs differ
  4. when both inputs are low

Explanation

An AND gate produces a high output only for the input combination 1,1; for 0,0, 0,1, and 1,0 its output is low. It is therefore equivalent to a series switching path, where both switches must be closed for the lamp to glow. The other listed conditions correspond to NOR or XOR behaviour, not AND.

Question 34Physics

An electric dipole of dipole moment p is placed in vacuum. At a far point on the axial line on the side of the positive charge, the electric field due to the dipole is

  1. (1/4πε0)(2p/r^3), along p Correct answer.
  2. (1/4πε0)(p/r^3), opposite to p
  3. (1/4πε0)(2p/r^2), along p
  4. (1/4πε0)(p/r^2), opposite to p

Explanation

On the axial line, the fields of the two charges are in the same direction, so they add. For r much larger than the dipole separation, the resultant is E = (1/4πε0)(2p/r^3) and points along the dipole moment from the negative to the positive charge. The equatorial field is half this magnitude and opposite to p.

Question 35Physics

A projectile launched at 45° with speed u has maximum horizontal range R. Neglecting air resistance, if the same speed is used at launch angles 30° and 60°, the horizontal ranges are

  1. equal, and each is equal to R
  2. equal, and each is less than R Correct answer.
  3. different, with the 60° range greater
  4. different, with the 30° range greater

Explanation

The range is R(θ) = u^2 sin2θ/g. Since sin60° = sin120°, the angles 30° and 60° give the same range, and because sin60° is less than sin90° = 1, that common range is less than the maximum range at 45°. Thus complementary angles have equal ranges below the 45° maximum.

Question 36Physics

In a metre bridge, a resistance of 6 Ω in the left gap balances against an unknown resistance in the right gap at a balance length of 40 cm from the left end. The unknown resistance is

  1. 15 Ω
  2. 4 Ω
  3. 9 Ω Correct answer.
  4. 6 Ω

Explanation

For a metre bridge, R_left/R_right = l/(100 - l), where l is measured from the left end. Substituting 6/R = 40/60 gives R = 6 × 60/40 = 9 Ω. The balance condition follows from equal potential at the galvanometer junctions.

Question 37Physics

Two thin lenses of powers +5 D and -2 D are placed in contact. The focal length of the combination is

  1. +20.0 cm
  2. +14.3 cm
  3. -33.3 cm
  4. +33.3 cm Correct answer.

Explanation

Powers of thin lenses in contact add, so P = +5 D + (-2 D) = +3 D. The focal length is f = 1/P = 1/3 m ≈ +33.3 cm. The positive sign means the combination is converging.

Question 38Physics

Two long straight parallel wires separated by a distance d carry currents I1 and I2 in the same direction. The force per unit length on each wire is

  1. attractive, of magnitude μ0I1I2/(4πd)
  2. repulsive, of magnitude μ0I1I2/(4πd)
  3. attractive, of magnitude μ0I1I2/(2πd) Correct answer.
  4. repulsive, of magnitude μ0I1I2/(2πd)

Explanation

The magnetic field of one wire at the other is B = μ0I/(2πd), so the force per unit length is F/L = BI2 = μ0I1I2/(2πd). Parallel currents in the same direction attract each other, as given by the direction of the magnetic force. The 4πd form would apply to a different geometry, not two long parallel wires.

Question 39Physics

A metal surface has work function φ. Light of frequency ν produces a stopping potential V0. If the frequency is increased to 2ν, with both frequencies above the threshold, the new stopping potential is

  1. 2V0
  2. 2V0 + hν/e
  3. V0 + hν/e Correct answer.
  4. V0 + 2hν/e

Explanation

The photoelectric equation gives eV0 = hν - φ. At frequency 2ν, eV' = 2hν - φ = (hν - φ) + hν = eV0 + hν, so V' = V0 + hν/e. The stopping potential increases linearly with frequency, not by doubling the original value.

Question 40Physics

A monatomic ideal gas initially at temperature T is compressed adiabatically and reversibly to half its initial volume. Its final temperature is

  1. T/2
  2. 2T
  3. 2^(2/3) T Correct answer.
  4. 2^(5/3) T

Explanation

For an adiabatic process, TV^(γ-1) is constant. A monatomic gas has γ = 5/3, so Tf = T(Vi/Vf)^(2/3) = T(2)^(2/3). The temperature rises on compression because work is done on the gas with no heat loss.

Question 41Physics

The SI unit of magnetic flux is

  1. tesla
  2. henry
  3. farad
  4. weber Correct answer.

Explanation

Magnetic flux is measured in weber, which equals one tesla multiplied by one square metre. The other units listed measure magnetic flux density, inductance, and capacitance respectively.

Question 42Physics

For a body projected from the Earth's surface, the escape velocity depends on which of the following?

  1. mass of the Earth Correct answer.
  2. mass of the projectile
  3. angle of projection
  4. speed of projection

Explanation

Escape velocity is given by v_e = sqrt(2GM/R), where M and R are the mass and radius of the Earth. It is independent of the projectile's mass, speed of projection, and angle of projection.

Question 43Physics

When a p-n junction diode is forward biased, the width of the depletion region

  1. becomes infinite
  2. increases
  3. decreases Correct answer.
  4. remains unchanged

Explanation

Forward bias lowers the potential barrier across the junction, allowing majority carriers to diffuse more easily. This reduces the uncovered charge layers and hence the depletion width.

Question 44Physics

A uniform wire of total resistance R is bent into an equilateral triangle. The equivalent resistance between any two vertices of the triangle is

  1. R/9
  2. 2R/9 Correct answer.
  3. R/3
  4. 2R/3

Explanation

Each side of the triangle has resistance R/3. Between two vertices, one side is in parallel with the other two sides in series, giving (R/3 × 2R/3)/(R) = 2R/9.

Question 45Physics

A body of mass 2 kg moving at 3 m/s collides head-on and perfectly inelastically with a stationary body of mass 4 kg. The loss in kinetic energy of the system is

  1. 12 J
  2. 3 J
  3. 6 J Correct answer.
  4. 9 J

Explanation

Momentum conservation gives the common speed as (2×3)/(2+4) = 1 m/s. Initial kinetic energy is 9 J and final kinetic energy is 3 J, so the loss is 6 J.

Question 46Physics

A convex lens of focal length 20 cm forms a real image of the same size as the object on a screen. The distance between the object and the screen is

  1. 60 cm
  2. 20 cm
  3. 80 cm Correct answer.
  4. 40 cm

Explanation

A convex lens forms a real image of the same size when the object is at 2f and the image is also at 2f. Thus the object-screen distance is 2f + 2f = 4f = 80 cm.

Question 47Physics

The rms speed of gas molecules at 27°C is v. At what temperature will the rms speed become 2v?

  1. 327°C
  2. 1200°C
  3. 108°C
  4. 927°C Correct answer.

Explanation

The rms speed is proportional to sqrt(T), so doubling the speed requires T to become 4 times the original absolute temperature. Since 27°C = 300 K, the new temperature is 1200 K = 927°C.

Question 48Physics

A circular coil of radius r carrying current I produces magnetic field B at its centre. The same wire is rewound into a coil of radius r/2 and carries the same current. The magnetic field at its centre becomes

  1. 2B
  2. B/4
  3. B/2
  4. 4B Correct answer.

Explanation

The wire length is fixed, so halving the radius doubles the number of turns. The field at the centre is proportional to NI/r, so the new field is (2N)(I)/(r/2) = 4 times the original.

Question 49Physics

A parallel-plate capacitor of capacitance C is charged to potential difference V and then disconnected from the battery. A dielectric slab of dielectric constant K is inserted so that it fills the entire space between the plates. The magnitude of the change in stored energy is

  1. ½CV²(1 − K)
  2. ½CV²(1 − 1/K²)
  3. CV²(K − 1)/K
  4. ½CV²(1 − 1/K) Correct answer.

Explanation

With the battery disconnected, the charge Q remains constant and the energy is U = Q²/(2C). Inserting the dielectric makes the capacitance KC, so the new energy is U/K and the magnitude of the change is ½CV²(1 − 1/K).

Question 50Physics

In Young's double-slit experiment, the slit separation is d and the screen distance is D. A thin transparent film of thickness t and refractive index μ is placed in front of one slit. The fringe pattern shifts by

  1. (μ + 1)tD/d
  2. (μ − 1)d/D
  3. (μ − 1)t d/D
  4. (μ − 1)tD/d Correct answer.

Explanation

The film introduces an additional optical path difference (μ − 1)t at that slit. The corresponding linear shift on the screen is this extra path multiplied by D/d.