JAM 2024 Physics Quiz

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Questions and Answers

What is the total number of Na and Cl ions per unit cell of a NaCl crystal?

2 (correct)

What is the sum of the binary numbers 10110.10, 11010.01, and 10101.11 in decimal?

69.50

70.25

70.50

70.75 (correct)

Which matrix is both Hermitian and unitary?

(0 (1+i); (1-i) 0)

(1 -i; i 1)

(0 i; i 0)

(0 -i; i 0) (correct)

What is the divergence of a 3-dimensional vector defined by $\hat{r}/r^3$?

Zero Signup and view all the answers

Which of the following statements about the magnitudes of spin magnetic moments is true?

$\mu_e < \mu_p < \mu_n$ Signup and view all the answers

For a particle with total energy E approaching x = 0 from x = -∞, which statement about the potential V(x) can be inferred?

The probability density P(x) increases as x approaches 0. Signup and view all the answers

In which scenario will the divergence of a vector field $\hat{r}/r^3$ not equal zero?

At x = 0 Signup and view all the answers

What can be concluded about the relative sizes of spin magnetic moments?

There exists a hierarchy: $\mu_e < \mu_p < \mu_n$. Signup and view all the answers

What is the charge Q at point A if Q = 2C?

2C Signup and view all the answers

What is the total distance between points A and B?

2d Signup and view all the answers

What is the radius of the semicircle MCL?

2d Signup and view all the answers

What is the angular frequency $ heta$ if $ heta = 100 rad/s$?

100 rad/s Signup and view all the answers

If the induced electric field at a distance of 0.07m from the axis of the solenoid is being calculated, what is the formula used to compute it?

E = -rac{dB}{dt} imes r Signup and view all the answers

What is the magnitude of the flux at the origin through a circular loop of radius 2?

$2\pi$ Signup and view all the answers

Which statement about the roots of the polynomial $f(z) = z^4 - 8z^3 + 27z^2 - 38z + 26$ is correct?

$z_1 + z_2 + z_3 + z_4 = -4$ and $z_1 z_2 z_3 z_4 = 19$ Signup and view all the answers

What assumption in classical theory led to the ultraviolet catastrophe?

Allowed frequencies have no upper limit. Signup and view all the answers

If the rest mass of an electron is 0.511 MeV/c^2, what is its speed as a fraction of the speed of light when it has 5.11 MeV of kinetic energy?

0.998 Signup and view all the answers

For a one-dimensional infinite square-well potential, what determines the ground state energy of the electron within it?

Both the width and mass Signup and view all the answers

Which condition describes a standing wave in a cavity?

Waves only exist at discrete frequencies without any cutoff. Signup and view all the answers

Which of the following statements is true regarding the energy levels in an infinite square well?

Energy levels are quantized and inversely proportional to the square of the quantum number. Signup and view all the answers

What impacts the number of allowed frequencies of standing waves in a cavity?

The dimensions of the cavity. Signup and view all the answers

What is the expression for the displacement vector in medium 2 when the electric field in medium 1 is given as 𝐸⃗1 = 3𝑥̂ + 2𝑦̂ + 4𝑧̂?

(3𝑥̂ + 6𝑦̂ + 8𝑧̂ )𝜀0 Signup and view all the answers

What is the correct equation for the velocity of water emerging from the hole at height ℎ1?

Velocity at ℎ1 is √2𝑔ℎ1 Signup and view all the answers

Which statement accurately describes the maximum horizontal distance D in relation to height ℎ1?

D will be maximum when ℎ1 = 2/3h Signup and view all the answers

How is the volume flow rate from an individual hole of the mesh calculated?

𝐴𝑜√𝑣𝑜2 + 2𝑔ℎ/n Signup and view all the answers

Which of the following statements about the maximum value of D is correct?

The maximum value of D is h. Signup and view all the answers

What is the volume flow rate for n circular holes of area 𝐴ℎ at the bottom of the pipe?

𝑛(𝐴𝑜 − 𝐴ℎ)√𝑣𝑜2 + 𝑔ℎ Signup and view all the answers

What is the relationship between the electric field and the permittivity of free space in determining displacement?

Displacement is directly proportional to the electric field multiplied by ε₀. Signup and view all the answers

What happens to the velocity of fluid when it passes through the mesh with circular holes?

Velocity decreases as energy is lost in the mesh. Signup and view all the answers

What is the correct expression for the component of velocity along the line joining the source and the observer?

$\frac{1}{2 \sqrt{a^2 \sin^2 \omega t + L^2}} a v_0 \sin(2\omega t)$ Signup and view all the answers

Under what condition will the observed frequency be f?

When the source is at $x = 0$ and $x = -a$ Signup and view all the answers

What is the work done during an isothermal expansion from $V_0$ to $2.5V_0$?

$R T_0 \ln(2.5)$ Signup and view all the answers

What is the change in internal energy during an isothermal process?

$0$ Signup and view all the answers

What would be the work done during an isobaric expansion to 2.5$V_0$?

$3 R T_0$ Signup and view all the answers

For the isobaric process, what is the correct change in internal energy?

$\frac{9}{2} R T_0$ Signup and view all the answers

What is the significance of the depletion width in n-side of a p-n junction?

It influences the breakdown voltage of the diode. Signup and view all the answers

If the acceptor and donor concentrations change, what will happen to the depletion width?

It will vary inversely with the square root of the doping concentrations. Signup and view all the answers

Study Notes

JAM 2024 Physics (PH) Study Notes

Question 1: The total number of Na and Cl ions per unit cell of the NaCl crystal is 4 (Option B).
Question 2: The sum of the three binary numbers 10110.10, 11010.01, and 10101.11, in the decimal system is 70.25 (Option B).
Question 3: The Hermitian and unitary matrix is (0 𝑖 )
𝑖 0* (Option B).
Question 4: The divergence of the 3-dimensional vector 𝑟̂ / 𝑟3 is zero (Option B).
Question 5: The magnitudes of spin magnetic moments of electron, proton, and neutron are 𝜇e, 𝜇p, and 𝜇n, respectively. The correct relation is 𝜇e > 𝜇p > 𝜇n (Option A).
Question 6: The magnitude of the flux of ∇×𝐹, through a circular loop of radius 2, centered at the origin, is 4𝜋 (Option C).
Question 16: The roots of the polynomial 𝑓(𝑧) = 𝑧 4 − 8𝑧 3 + 27𝑧 2 − 38𝑧 + 26, are 𝑧1 , 𝑧2 , 𝑧3 , & 𝑧4 . The correct statement is 𝑧1 + 𝑧2 + 𝑧3 + 𝑧4 4 =− 𝑧1 𝑧2 𝑧3 𝑧4 19 (Option A).
Question 17: The ultraviolet catastrophe in the classical (Rayleigh-Jeans) theory of cavity radiation is attributed to the assumption that the allowed frequencies of the standing waves inside the cavity have no upper limit (Option C).
Question 18: Given that the rest mass of electron is 0.511MeV/c2, the speed (in units of c) of an electron with kinetic energy 5.11MeV is closest to 0.993 (Option B).
Question 19: The electric field in medium 1 is 𝐸⃗1 = 3𝑥̂ + 2𝑦̂ + 4𝑧̂. The displacement vector 𝐷⃗ 2 in medium 2 is (9𝑥̂ + 6𝑦̂ + 16𝑧̂ )𝜀0 (Option C).
Question 24: A tank filled with water up to a height ℎ has a small hole at a height ℎ1 such that ℎ1 < ℎ. The correct statement is D will be maximum when ℎ1 = 2/3ℎ (Option C).
Question 25: An incompressible fluid flows through a vertical pipe with a thin mesh at the bottom having n circular holes. The volume flow rate from an individual hole of the mesh is given by 𝐴𝑜 √𝑣𝑜2 + 2𝑔ℎ 𝑛 (Option A).
Question 26: A ball is dropped from a height ℎ. The correct options are:
- 1 𝑎𝑣0 𝑣𝑃𝑆 (𝑡) = sin (2𝜔𝑡)
2 √𝑎2 𝑠𝑖𝑛2 𝜔𝑡 + 𝐿2* (Option A)
- The observed frequency will be f when the source is at 𝑥 = 0 and 𝑥 = ±𝑎 (Option B)
Question 40: One mole of an ideal monoatomic gas is expanded from an initial volume 𝑉𝑜 to 2.5𝑉𝑜. The correct statements are:
- When the process is isothermal, the work done is 𝑅𝑇𝑜 ln 2 (Option A)
- When the process is isothermal, the change in internal energy is zero (Option B)
- When the process is isobaric, the change in internal energy is 9 𝑅𝑇𝑜 2 (Option D)
Question 41: The value of the depletion width in the n-side is 0.16µm (Rounded off to the nearest integer).
Question 59: The value of the line integral ∫𝑀 𝐸⃗.⃗⃗⃗ 𝑑𝑙 along the path MCL is 4.5V.
Question 60: The amplitude of the induced electric field at a distance of 0.07m from the axis of the solenoid is 3.43 V/m (Rounded off to two decimal places).

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Test your knowledge with this JAM 2024 Physics quiz, covering key topics such as crystal structures, binary numbers, and vector calculus. Challenge yourself to answer questions about matrices, magnetic moments, and polynomial roots, all vital for Physics aspirants.