POST UTME PAN-ATLANTIC UNIVERSITY 2020 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in parallel. If the voltage across the circuit is 20 V, calculate the current through the 10 Ω resistor.
A. 2 A
B. 4 A
C. 6 A
D. 8 A
Question 2
A beam of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, calculate the angle of re\fraction.
A. 20°
B. 25°
C. 30°
D. 35°
Question 3
A radioactive sample has a half-life of 10 years. If the initial activity is 100 Bq, calculate the activity after 20 years.
A. 25 Bq
B. 50 Bq
C. 75 Bq
D. 100 Bq
Question 4
A particle of mass $m$ is confined to a one-dimensional box of length $L$. The ground state wave function of the particle is given by (psi(x) = \sqrt{\frac{2}{L}} \sinleft\( \frac{pi x}{L}\right \)). What is the expectation value of the position operator $x$ in the ground state?
A. \frac{L}{2}
B. \frac{L}{4}
C. \frac{3L}{4}
D. \frac{L}{3}
Question 5
A lens has a focal length of $f$. A light ray passes through the lens and is re\fracted. The angle of incidence is $i$, the angle of re\fraction is $r$, and the angle of deviation is $D$. What is the relationship between these angles?
A. D = i + r
B. D = i - r
C. D = \frac{i}{f}
D. D = \frac{i}{2f}
Question 6
A beam of light passes from air into a glass slab of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 25°
C. 30°
D. 35°
Question 7
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The impedance of the circuit is given by $Z = \sqrt{R^2 + \( \omega L - \frac{1}{\omega C} \)^2}$. What is the condition for resonance to occur?
A. \omega L - \frac{1}{\omega C} = 0
B. \omega L + \frac{1}{\omega C} = 0
C. \omega L - \frac{1}{\omega C} = \frac{1}{2}
D. \omega L + \frac{1}{\omega C} = \frac{1}{2}
Question 8
A radioactive sample decays with a half-life of $T_{1/2} = 10$ years. If the initial activity is $A_0 = 100$ Bq, what is the activity of the sample after $t = 20$ years?
A. 50 Bq
B. 25 Bq
C. 12.5 Bq
D. 6.25 Bq
Question 9
A magnetic field of 0.5 T is applied to a coil of wire with 100 turns. If the coil has a resis\tance of 10 Ω, calculate the induced emf in the coil.
A. 0.5 V
B. 1 V
C. 2 V
D. 3 V
Question 10
A particle of mass ( m ) is moving in a circular path of radius ( r ) with a cons\tant speed ( v ). The particle is subject to a centripetal force \( F_c \) given by \( F_c = \frac{mv^2}{r} \). If the particle's speed is doubled, what is the new centripetal force required to keep the particle in its circular path?
A. \( \frac{mv^2}{r} \)
B. \( \frac{2mv^2}{r} \)
C. \( \frac{4mv^2}{r} \)
D. \( \frac{8mv^2}{r} \)
Question 11
A capacitor with a capaci\tance of 10 μF is connected to a 12 V battery. If the capacitor is initially uncharged, calculate the time it takes for the capacitor to reach a voltage of 9 V.
A. 1 s
B. 2 s
C. 3 s
D. 4 s
Question 12
A light ray passes through a prism and is re\fracted. The angle of incidence is $i$, the angle of re\fraction is $r$, and the angle of deviation is $D$. What is the relationship between these angles?
A. D = i + r
B. D = i - r
C. D = i + 2r
D. D = i - 2r
Question 13
A coil of wire with 100 turns is placed in a magnetic field of strength 0.5 T. If the current in the coil is 2 A, what is the magnitude of the torque acting on the coil?
A. 0.1 Nm
B. 0.2 Nm
C. 0.3 Nm
D. 0.4 Nm
Question 14
A magnetic field of 0.5 T is applied to a coil of 100 turns and radius 0.1 m. If the current is 2 A, calculate the torque on the coil.
A. 0.1 Nm
B. 0.2 Nm
C. 0.3 Nm
D. 0.4 Nm
Question 15
A particle of mass $m$ is moving in a circular path with a radius of $r$. If the particle is subject to a centripetal force of magnitude $F_c = \frac{mv^2}{r}$, what is the magnitude of the acceleration of the particle?
A. \frac{v^2}{r}
B. \frac{2v^2}{r}
C. \frac{3v^2}{r}
D. \frac{4v^2}{r}

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