Physics: CUET Mock Test - 3 - CUET MCQ

If the normal points in the opposite direction of the field, then θ = 180^o and the flux is taken as negative. If the magnetic field is pointing opposite the direction of the surface area then the value of this flux is negative.

The relationship between resistivity and temperature for a semiconductor material is given by the following equation:

s =

where s₀ is the resistivity at absolute zero temperature, Eg is the bandgap energy of the semiconductor material, k is Boltzmann's constant, and T is the temperature in Kelvin.

• This equation is known as the Arrhenius equation and describes the temperature dependence of the resistivity of semiconductors.
• As the temperature increases, the resistivity of a semiconductor decreases exponentially due to the increasing number of thermally excited charge carriers (electrons and holes).
• Since, the decay is exponential, the resistivity decreases as the temperature increases.
• So, the graph representing resistivity vs temperature would be exponential decay and represented by,

The correct answer is option (3)

Concept:

The radius of the trajectory of a charged particle moving in a uniform magnetic field is given by the formula:

r = (mv)/(qB)

where:

r is the radius of the trajectory
m is the mass of the particle
v is the velocity of the particle
q is the charge of the particle
B is the magnetic field strength
The ratio of the radii of the trajectories of a proton and an alpha particle can be found by dividing their respective radii:

r_(proton) / r_(alpha) = [(m_protonv_proton)/(q_protonB)] / [(m_alphav_alpha)/(q_alphaB)] ------(1)

Since both particles have the same kinetic energy, we can use the fact that the kinetic energy of a particle is given by:

K = (1/2)mv²

Thus, we have:

v_proton =
v_alpha =

Substituting these expressions into the ratio of radii equation(1),and Plugging in the values for the masses and charges of the particles, we get

r(proton) / r(alpha) = [(1/4)*(2/1)]*sqrt(4/1) = 1/2 * 2 = 1

Therefore, the ratio of the radii of the trajectories of the proton and the alpha particle is 1:1 or simply 1.

This means that the radii of their trajectories will be the same.

The correct answer is option (1)

Concept:

• When an electron is projected in a uniform magnetic field along the direction of the field lines, the electron will experience a force perpendicular to both its velocity and the magnetic field direction, known as the Lorentz force.
• The direction of the Lorentz force can be determined using the "right-hand rule."

Right-hand rule:

• Point your right thumb in the direction of the electron's velocity, point your fingers in the direction of the magnetic field, and the direction in which your palm faces gives you the direction of the force experienced by the electron.
• Since the velocity and magnetic field are both along the same direction, the angle between them is 0 degrees. Therefore, the force experienced by the electron will be zero, and the electron will continue to move along its original path without any deviation

The correct answer is option (3).

CONCEPT:

• The Current-Carrying Conductor produces a magnetic Field Around it.

Biot-Savarts Law:

The direction and Magnitude of this magnetic field can be obtained from Biot-Savarts Law.

Where dB = Magnetic Field produced due to small wire of length dl, I = Current in wire, μ0 = Permittivity of free space, dl = Small Current Element

• The magnetic field generated due to the current-carrying circular conductor at its center is given as:

• This result has been obtained from Biot Savarts Law.

EXPLANATION:

• The Magnetic Field Produced due to the Semi-Circular wire is half of that of Circular wire.
• So, the magnetic field produced at the center "O" of the wire will be

Hence option 2 is the correct option.

Concept:

Since the electron is shot into the magnetic field normal to the direction of the field, it will experience a force perpendicular to both its velocity and the magnetic field direction. This force will cause the electron to move in a circular path with a radius given by:

r =

where:

r is the radius of the circular orbit in meters (m)
v is the velocity of the electron in meters per second (m/s)
Since the force on the electron is always perpendicular to its velocity, the electron will move in a circular path with a constant speed. This means that the frequency of revolution of the electron is given by:

f =

Substituting the expression for r from above, we get:

f =

where:

f is the frequency of revolution in Hertz (Hz)
B is the magnitude of the magnetic field in Tesla (T)
q is the charge of the electron in Coulombs (C)
m is the mass of the electron in kilograms (kg)

Since v cancels out from the equation, the frequency of revolution of the electron is independent of its initial velocity and only depends on the magnitude of the magnetic field, the charge and mass of the electron.

Therefore, the frequency of revolution of the electron in its circular orbit is solely dependent on the strength of the magnetic field and the properties of the electron, as given by the above equation.

The correct answer is option (1)

Concept:

• Plano- concave lens: It is the type of lens that has one side as a plane surface and the other side as a concave lens.
• Its focal length is always negative.
• The power of a lens is specified as the inverse of the focal length in meters, or P/1/f

Explanation:

Given, focal length, f = 10 cm = 0.1 m

Then power of the lens is P = 1/f = 1/0.1 = 10 D

• When the lens is cut in to two equal parts then there will be no effect on focal length as the radius of curvature will remain same and then the focus will be same.
• Then the power of each part is equal to the original lens.
• P = 10 D

The correct answer is option 1):(Iron)

Concept:
Semiconductor:

• A semiconductor is a substance that has resistivity in between the conductor and insulator.
• A semiconductor has 4 valance electrons that are C, Si, Ge, Sn, and Pb,Te
• Here Iron is not a semiconductor.It is a conductor
• Type of semiconductors are

• Semiconductors that are chemically pure, in other words, free from impurities are termed as intrinsic semiconductors
• Extrinsic semiconductors are semiconductors that are doped with specific impurities. The impurity modifies the electrical properties of the semiconductor and makes it more suitable for electronic devices such as diodes and transistors

Concept:

• The Refractive index also called the index of refraction measures the bending of a ray of light when passing from one medium into another.

• If i is the angle of incidence of a ray in vacuum (the angle between the incoming ray and the perpendicular to the surface of a medium, called the normal) and r is the angle of refraction (the angle between the ray in the medium and the normal),
• Then the refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction.
• 
• Refractive index of combined media = --- (1)
• Critical angle, C = sin^-1(μ^-1) --- (2)

Calculation:

Given, the refractive index of water,

Refractive index of a glass slab,

Refractive index of combined media =

From equation 1,

From equation 2 Critical angle,

Electric dipole moment:

• The electric dipole moment is a measure of the separation of positive and negative electrical charges.
• It consists of two equal and opposite charges that are infinitely close together.
• Its magnitude is equal to the product of the charge and the distance between the charges and having direction from the negative to the positive charge along the line between the charges.

Electric dipole moment p = qd

Where,

q = charge (Coulomb)

d = distance between charges (meter)

Concept:

Young's double slit experiment

• In the double slits experiment, we use two long parallel slits as the sources of light in place of pin holes.
• The light coming out of the two slits is intercepted on a screen placed parallel to the plane of the slits.
• The slits are illuminated by a parallel beam of a monochromatic light.
• A series of dark and bright strips, called fringes, are observed on the screen.
• The fringe-width is given by,
• Where, β = fringe width, λ = wavelength of light, D = distance of screen from slits, d = distance between slits.

Calculation:

Given, λ = 5898 Å, number of fringes = 92

Let the length of the screen on which the fringes are obtained be L₀
​⇒ 92 × β₁ = L₀

⇒
⇒

⇒ --- (1)

Now for λ = 5461 Å, Let the number of fringes = n

⇒ β₂ = --- (2)

From equation 1, and 2

⇒

⇒ n = 99

Motional electromotive is the emf induced by the motion of the conductor across the magnetic field. The expression for motional electromotive force is given by:
E = -vLB
This equation is true as long as the velocity, magnetic field, and length are mutually perpendicular to each other. The negative sign is associated with Lenz’s law.

The reactance of an inductor in a dc circuit is zero.
For dc → f = 0
X_L = 2π f L
X_L = 0
Therefore, the reactance of an inductor in a dc circuit is zero.

In an AC circuit, we can define three types of power, namely, Instantaneous power, Average power, and Apparent power. A circuit element produces or dissipates power according to the equation → P = IV, where I is the current through the element and V is the voltage across it.

Transformers are used to convert low alternating voltage to a high alternating voltage and vice versa. Transformers are based on the phenomena of mutual induction. A transformer consists of a soft iron coil with two coils wound around it which are not connected to one another. The other statements are not valid.

Factors on which the angle of deviation depends are → the angle of incidence, the material of the prism, the wavelength of light used, and the angle of the prism. So, the factor on which the angle of deviation that does not depend on is the angle of reflection.

Length (L) = 0.7 m; Speed (v) = 1 m/s; Magnetic field (B) = 20 T
The required equation E = -vLB (The negative sign only applies to the direction)
E = 1 × 0.7 × 20
E = 0.7 × 20
E = 14 V
Therefore, the motional emf in the bar and rails is 14 V.

For a purely inductive circuit, Φ = ± (π/2)
Power factor = cos (±(π/2))
Power factor = 0
Therefore, the power factor will be minimum for an inductive circuit.

Instantaneous power is defined as the power in an AC circuit at any instant of time. It is equal to the product of values of alternating voltage and alternating current at that time. And, because instantaneous power varies in both magnitude and sign over a cycle, it seldom has any practical importance.

Refractive index of the prism material is μ = 

μ = √3.

L = 0.15 m; B = 40 T; v = 5 m/s; R1 = 10 Ω; R2 = 10 Ω; R3 = 5 Ω
Emf (E) = vLB = 5 × 0.15 × 40
E = 5 × 6
E = 30 V
R1 and R2 are in parallel ➔ 
R_TOT = R + R3 = 10 + 5 = 15 Ω
Therefore, current (I) = E/R
I = 30/15
I = 2 A

When the frequency of an ac is doubled → The inductive reactance (X_L) gets doubled.
This is because inductive reactance is directly proportional to the frequency of an alternating current circuit.

Average power can be defined as the power averaged over one full cycle of alternating current. It is also known as true power. The expression for average power is given by:
P_av=V_rmsI_rmscos⁡Φ = (V₀I₀/2)(cosΦ)

For a step-up transformer, the voltage at the second terminal is greater than the primary terminal, i.e. → V_s > V_p. Similarly, the current in the secondary coil is lesser than that current flowing the primary coil, i.e. → I_s < I_p. Also, the number of turns in the secondary winding is greater than that in the primary winding, i.e. → N_s > N_p. So the transformation ratio will be greater than 1. So, the correct combination is given as:
k > 1; V_s > V_p, I_s < I_p, N_s > N_p

The reason is that for a given angle f incidence, the reflection is the same for all the wavelengths of white light while the angle of refraction is different for different wavelengths. Therefore, this is how dispersion is caused.

Van de Graff generator is used to create a large amount of static electricity. A Van de Graff generator uses static electricity and a moving belt to charge a large metal sphere to a very high voltage. As the belt moves, electrons move from the rubber belt to the silicon roller, causing the belt to become positively charged and the roller to become negatively charged. As a result, it builds up positive charge.

f = X_L/2πL
f = 3500/(2×3.14×2.5)
f = 222.9 Hz ≈ 223 Hz
Therefore, the frequency of a coil having reactance of 3500 Ω is 223 Hz.

A Van de Graff generator, by means of a moving belt and suitable brushes, transfers charge continuously to a large spherical conducting shell. As a result, a potential difference of the order of several million volts is built up and this can be used for accelerating charged particles.

Van de Graff generator was invented by Robert Jemison Van de Graff on November 28, 1933. Robert Jemison invented the Van de Graff generator, which is a kind of high-voltage electrostatic generator that accelerates particles, while he was doing his PhD in Princeton University.

When light passes from a rarer to a denser medium, the wavelength of light changes but the frequency remains unchanged. Therefore, there is no change in the frequency of light, only the wavelength changes.