Two identical particles have to be distributed among three energy levels. Let rB, rF and rC represent the ratios of probability of finding two particles to that of finding one particle in a given energy state. The subscripts B, F and C correspond to whether the particles are Bosons, Fermions and classical particles, respectively. The rB : rF : rC is equal to

The difference between fermions and bosons is that bosons do not obey ______

A

Aufbau principle

B

Pauli’s Exclusion Principle

C

Hund’s Rule of Maximum Multiplicity

D

Heisenberg’s Uncertainty Principle

The difference between fermions and bosons is that bosons’ wave function is _______

A

Continuous

B

Single Valued

C

Symmetric

D

Differentiable

A particle of mass m is attached to a thin uniform rod of length a and mass 4m. The distance of the particle from the centre of mass of the rod is $$\frac{a}{2}.$$
Classical Mechanics mcq question image

The moment of inertia of the combination about an axis passing through a normal to the rod is

A

$$\frac{{64}}{{48}}m{a^2}$$

B

$$\frac{{91}}{{48}}m{a^2}$$

C

$$\frac{{27}}{{48}}m{a^2}$$

D

$$\frac{{51}}{{48}}m{a^2}$$

A system has energy level E₀, 2E₀, 3E₀, . . . . . , where the excited states are triply degenerated. Four non-interacting bosons are placed in this system. If the total energy of these bosons is 5E₀, the number of microstates is

A

2

B

3

C

4

D

5

Which of the following statements are true?
1. The classical approach to probability theory requires that the total number of possible outcomes be known or calculated and that each of the outcomes be equally likely.
2. A marginal probability is also known as unconditional probability.
3. For three independent events, the joint probability of the three events, P (ABC) = P (A) × P (B/A) × P (C/AB)
4. Two events are mutually exclusive, exhaustive and equally likely, the probability of either event A or B or both occurring P(A or B) = P(A) + P(B)

A

Both 1 and 3

B

Both 3 and 4

C

1, 2 and 4

D

All of the above

The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.

A

Both statements are correct

B

Both statements are incorrect

C

Statement I is correct while Statement II is incorrect

D

Statement I is incorrect while Statement II is correct

The mass of particle A is double the mass of particle B and the charge on both the particles is equal. If both the particles are moving perpendicular to the magnetic field B with equal speed, then the ratio of the magnetic force on particle A to particle B will be:

A

1 : 1

B

1 : 2

C

2 : 1

D

1 : 4

Which property distinguishes bosons from fermions?

A

spin

B

Electrical charge

C

Mass

D

Stability of nucleus

There are two classes of three figures each. Class 'A' figures differ in certain way from figures in Class 'B'. Which two of the four Answer Figures belong to Class 'A'?
Grouping of Identical Figures mcq question image

Grouping of Identical Figures mcq question image

A

1 and 3

B

1 and 2

C

2 and 4

D

2 and 3

In the following figure, Triangle represent school, Square represent college, Circle represent Students, Rectangle represent Private college, and Trapezium represent Distance learning. Which set of letter represent college student that opted for distance learning.

A

G

B

H

C

Both 1 and 2

D

K

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