POST UTME OSUSTECH 2020 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A radioactive sample decays with a half-life of $T_{1/2}$. What is the activity of the sample after a time $t$?
A. A_0 \left\( \frac{1}{2} \right \)^{t/T_{1/2}}
B. A_0 \left\( \frac{1}{2} \right \)^{T_{1/2}/t}
C. A_0 \left\( \frac{1}{2} \right \)^{t/T_{1/2}} + A_0
D. A_0 \left\( \frac{1}{2} \right \)^{T_{1/2}/t} + A_0
Question 2
A circuit consists of a $10, \Omega$ resistor, a $20, \Omega$ resistor, and a $5, \Omega$ resistor connected in series. If a voltage of $12, \text{V}$ is applied across the circuit, what is the current flowing through the $5, \Omega$ resistor?
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Question 3
A 50 Hz AC generator produces a \sinusoidal voltage given by \(v(t) = 100\sin\( 2\pi ft)\ \) V, where \(f\) is the frequency. Calculate the maximum voltage.
A. 50 V
B. 100 V
C. 200 V
D. 500 V
Question 4
A capacitor consists of two parallel plates, each of area 0.1 m^2, separated by a dis\tance of 0.01 m. The plates are charged to a potential difference of 10 V. Calculate the capaci\tance of the capacitor.
A. 0.01 F
B. 0.1 F
C. 1 F
D. 10 F
Question 5
A block of mass 5 kg is placed on a frictionless surface and connected to a spring with a spring cons\tant of 200 N/m. If the block is displaced by 0.2 m from its equilibrium position and released from rest, what is the maximum speed of the block?
A. 2 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s
Question 6
A 5 kg block of ice at 0°C is placed in a 10 kg block of copper at 100°C. Assuming no heat loss to the surroundings, what is the final temperature of the system?
A. 20°C
B. 30°C
C. 40°C
D. 50°C
Question 7
A lens of focal length $f = 10, \text{cm}$ is used to form an image of an object at a dis\tance of $d = 20, \text{cm}$. What is the magnification of the lens?
A. 0.5
B. 1
C. 2
D. 3
Question 8
A 2 μF capacitor is connected in series with a 3 μF capacitor. If a 12 V battery is connected across the combination, what is the equivalent capaci\tance?
A. 1.5 μF
B. 2.5 μF
C. 3.5 μF
D. 4.5 μF
Question 9
A heat engine operates between two reservoirs at temperatures $T_1 = 500, \text{K}$ and $T_2 = 300, \text{K}$. If the engine produces 500, J of work in one cycle, what is the efficiency of the engine?
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Question 10
A capacitor consists of two parallel plates of area $A$ separated by a dis\tance $d$. The plates are charged to a potential difference $V$. What is the capaci\tance of the capacitor?
A. \frac{\epsilon_0 A}{d}
B. \frac{\epsilon_0 A}{2d}
C. \frac{2\epsilon_0 A}{d}
D. \frac{\epsilon_0 A}{3d}
Question 11
A wave with a frequency of 50 Hz and an amplitude of 2 m is traveling through a medium with a speed of 300 m/s. What is the wavelength of the wave?
A. 6 m
B. 12 m
C. 15 m
D. 20 m
Question 12
A light ray passes from air into a glass of re\fractive index $n = 1.5$. If the angle of incidence is $30^\circ$, what is the angle of re\fraction?
A. 20^\circ
B. 25^\circ
C. 30^\circ
D. 35^\circ
Question 13
A convex lens of focal length 20 cm is used to form an image of an object placed 30 cm in front of it. What is the magnification of the lens?
A. 0.5
B. 1
C. 2
D. 3
Question 14
A radioactive sample decays at a rate given by the equation \(N(t) = N_0 e^{-\lambda t}\), where \(N_0\) is the initial number of nuclei, \(\lambda\) is the decay cons\tant, and \(t\) is time. If \(N_0 = 1000\) and \(\lambda = 0.1\) s^{-1}, calculate the number of nuclei remaining after 10 s.
A. 100
B. 200
C. 300
D. 400
Question 15
A particle of mass 2 kg is attached to a spring with a spring cons\tant of 100 N/m. If the particle is displaced by 0.5 m from its equilibrium position and released from rest, what is the maximum speed of the particle?
A. 0.5 m/s
B. 1.0 m/s
C. 1.5 m/s
D. 2.0 m/s

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