12. A force produces potential U(x) = ax⁴. where a = 1.43 J/m⁴ . What is the force and direction when the particle is at x = -0.78 m?
(A)ON
(B)-0.67 N
(C) 0.67N
(D) -2.7 N
(E) 2.7 N

8. A spherical ball contains a charge +q uniformly distributed over its surface. When its diameter is D, the electric field at its surface has magnitude E. What will the electric field be if its diameter changes to 2D without changing the charge? (A)E (B)2E (C)4E (D) E/2 (E) E/4

9. What is the total energy supplied while the current increases from zero to a final value I? Assume L is the inductance. (A)(B)LI2 (C) 2LI2 (D)(E)4LI2

10. An object is placed between two mirrors of distance apart. If object  is distance away from mirror 1 (see the right figure), what is the distance of the second closest image of object  that appears in mirror 1? (Hint: The closest one is .) (A)(B)28/3 (C)  (D)4 (E) 5

11. Which of the following statements on radioactive decays is true? (A) The rate of decary is proportional to the number of undeeayed substance. (B) The rate of decay  is proportional to the half-life of the undecayed substance. (C) The decay constant is proportional to the half-life of the undecayed substance. (D) The half-life of a substance decreases with time. (E) None of the above. 

13. In vacuum, an electromagnetic wave traveling along the x axis has an electric field and a magnetic field whose magnitudes depend on x and t asE(x,t)=E0sin(kx一ωt),B(x,t)=B0sin(kx-ωt+Φ), where E0 and B0 are the amplitudes of . Which fact below is correct? (A) (B)The directions of  and   are arbitrary once they are perpendicular to x. (C)Φ=π/2 (D) ωk =c (E)This is a linearly polarized wave.

14. Which statement regarding total internal retlection is not true? (A) It cannot occur when the incident light is in the medium of lower index of refraction. (B) Total internal reflection oceurs for rays with their incident angles greater a critical angle. (C) It explains the phenomenon that the water-to-air interface looks like a mirror when an observer is in water. (D) It is used in transmission through optical fibers. (E) The effect is used to realize polarizers.

15. Which of the following statements on a wave functionφ(x,t) in quantum mechanics is correct? (A) The probability of finding the particle in region (B) The wave function can be determined via a series of measurements. (C) Since it is not a function of velocity, it does not carry the information of momentum. (D) All of the above. (E) None of the above.

16. Which type of titration is used to determine the concentration of calcium ions in a sample? (A) Acidity Titration (B) Alkalinity Titration (C) Redox Titration (D) Complexometric Titration (E) Ionic Strength Titration 

17. Which of the following is a cyclic organic compound with four nitrogen atoms? (A) Tetrazine(B) Diazine (C) Triazine (D) Benenze (E) None of the above

18. Which of the following organic compounds with the sum formula CroH4 exhibits two singlets in the 'H NMR spectrum and three signals in the 3C NMR spectrum?(A)(B)(C)(D)(E) None of the above