23. Consider two inertial frames, S and S', with S' moving along the +x axis of frame S at speed v. A particle, when viewed in frame S', travels at speed u' at angle θ' to the +x direction of frame S'. The angle θ of the particle's velocity (viewed by frame S) relative to the +x axis of frame S satisfies
(A) tan θ =
(B) tan θ' =
(C) tan θ =
(D) tan θ' =

19. In an experiment on Newton's rings as shown in the figure, where we consider a lens of maximum thickness t and refractive index n. The radius of curvature of the spherical surface is R. When a light of wavelength A is incident from the top, the observed radius of the 3th bright fringe is given by (A) (B) (C) (D) 2Rλ/t.

20. A Rydberg atom is an atom with one of its electrons being excited to a state of a very large principle quantum number n, called a Rydberg state. For a Rydberg hydrogen atom whose diameter is approximately 1 µm, estimate the corresponding principle quantum number n: (Hint: For the ground state, n = 1, the diameter of a hydrogen atom is approximately 1 Å.)(A) 80 (B) 100 (C) 120 (D) 140.

21. Alice is initially on the moon and takes a rocket of speed 0.8 c to the earth. How long does it take for Alice to arrive at the earth according to Alice's watch supposing the moon-to-earth distance is approximately 4 × 10⁵ km? (A) 0.01 s (B) 0.1 s (C) 1 s (D) 10 s.

22. Consider an electron contained in a one-dimensional box of size L. What is the wavelength of the emitted photon corresponding to a transition from n = 3 to n = 2?(A)(B) (C)(D)

24. Which of the following statements regarding the photoelectric effect is false? (A) No electrons are emitted if the incident light falls below some cutoff frequency f₀ regardless of intensity. The cutoff frequency is characteristic of the material being illuminated. (B) Electrons are emitted almost instantaneously, even at very low light intensities. (C) As the light intensity incident on the metal is increased, the electrons should be ejected with more kinetic energy. (D) The maximum kinetic energy of the photoelectrons increases with increasing light frequency.

25. Estimate the thermal de Broglie wavelength of a hydrogen atom at 300 K: (A) 10⁻⁸ m (B) 10⁻⁹ m(C) 10⁻¹⁰ m (D) 10⁻¹¹ m.

1. Which of the following is the probable sequence in which organisms evolved? (A) Prokaryotic bacteria → eukaryotic algae → cyanobacteria → land plants (B) Eukaryotic bacteria → cyanobacteria → eukaryotic algae → land plants (C) Cyanobacteria → prokaryotic bacteria → eukaryotic algae → land plants (D) Cyanobacteria → eukaryotic algae → prokaryotic bacteria → land plants (E) Prokaryotic bacteria → cyanobacteria → eukaryotic algae → land plants

2. Respiration breaks down glucose and transfers its energy to: (A) carbohydrate. (B) starch. (C) water. (D) ATP. (E) chlorophyll.

3. Concerning the interactions among organisms, which of the following term with its definition is NOT correct? (A) Neutralism: neither organism benefits or is harmed. (B) Mutualism: both organisms benefit. (C) Competition: both organisms harm each other. (D) Predation: one organism benefits by harming another. (E) Amensalism: one organism benefits whereas the other is neither harmed nor helped.

4. Oily seeds, such as peanuts, that store energy in fat molecules can convert that fat to the carbohydrates needed for growth in: (A) nuclei. (B) chloroplasts. (C) dictyosomes. (D) glyoxysomes. (E) peroxisomes.