POST UTME UI 2023 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A 2.0 Ω resistor is connected in series with a 4.0 Ω resistor and a 6.0 Ω resistor. If a 12 V battery is connected across the circuit, what is the current (I) flowing through the 2.0 Ω resistor?
A. 0.5 A
B. 1 A
C. 2 A
D. 3 A
Question 2
A quantum particle has a wave function given by \psi(x) = Ae^{-\alpha x^2}. If the particle is in a box of length 1 m, what is the probability of finding the particle in the region 0.5 m < x < 0.6 m?
A. \frac{A^2}{2\alpha} \( e^{-\alpha \( 0.5 \ \)^2} - e^{-\alpha (0.6)^2})
B. \frac{A^2}{2\alpha} \( e^{-\alpha \( 0.6 \ \)^2} - e^{-\alpha (0.5)^2})
C. \frac{A^2}{2\alpha} \( e^{-\alpha \( 0.5 \ \)^2} + e^{-\alpha (0.6)^2})
D. \frac{A^2}{2\alpha} \( e^{-\alpha \( 0.6 \ \)^2} + e^{-\alpha (0.5)^2})
Question 3
A \sinusoidal voltage source has a maximum voltage of $10$ V and a frequency of $50$ Hz. What is the rms voltage?
A. 5
B. 7.07
C. 10
D. 14.14
Question 4
A wave has a frequency of 50 Hz and a wavelength of 10 m. What is the speed of the wave?
A. 250 m/s
B. 500 m/s
C. 750 m/s
D. 1000 m/s
Question 5
A wave has a frequency of 50 Hz and a wavelength of 0.2 m. If the wave is traveling in the positive x-direction, what is the direction of the particle velocity?
A. in the positive x-direction
B. in the negative x-direction
C. perp\endicular to the wave
D. in the positive y-direction
Question 6
A charged particle of mass $m$ and charge $q$ is moving in a magnetic field $B$ with velocity $v$. Determine the force exerted on the particle.
A. q\vec{v} \times \vec{B}
B. \vec{v} \times \vec{B}
C. q\vec{B}
D. \vec{B} \times \vec{v}
Question 7
A radioactive sample decays from $100$ g to $50$ g in $10$ years. What is the half-life of the sample?
A. 5
B. 10
C. 20
D. 30
Question 8
A photon of energy $E$ is incident on a metal surface. Determine the maximum kinetic energy of the ejected electron.
A. E - W
B. E + W
C. W - E
D. E \times W
Question 9
A light ray passes through a prism with an angle of incidence of 30°. If the re\fractive index of the prism is 1.5, find the angle of re\fraction.
A. 20°
B. 25°
C. 30°
D. 35°
Question 10
A radioactive sample has a half-life of 10 years. If the initial activity of the sample is 100 Bq, what is the activity of the sample after 20 years?
A. 12.5 Bq
B. 25 Bq
C. 50 Bq
D. 100 Bq
Question 11
A particle of mass 2.0 kg is moving in a circular path of radius 1.5 m with a speed of 4.0 m/s. What is the magnitude of the force acting on the particle?
A. 10 N
B. 20 N
C. 30 N
D. 40 N
Question 12
A quantum particle has a wave function given by \psi(x) = Ae^{-ikx}. If the particle is observed at x = 0, what is the probability of finding the particle at that point?
A. 0
B. 1
C. A^2
D. e^{-2ikx}
Question 13
A capacitor is charged to a potential difference of 12 V. If the capaci\tance is 2 μF, what is the energy stored in the capacitor?
A. 0.144 J
B. 1.44 J
C. 14.4 J
D. 144 J
Question 14
A thermodynamic system undergoes a process from state A to state B, where the internal energy (U) increases by 100 J. If the system is heated by 50 J of heat energy (Q), what is the change in the system's entropy (ΔS)?
A. 0.5 J/K
B. 1 J/K
C. 2 J/K
D. 5 J/K
Question 15
A radioactive sample decays from 100 mg to 50 mg in 10 minutes. What is the half-life \( t1/2 \) of the sample?
A. 5 min
B. 10 min
C. 15 min
D. 20 min

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