POST UTME AL-HIKMAH UNIVERSITY 2025 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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_0(x) = \sqrt{\frac{2}{L}} \sinleft\( \frac{pi x}{L}\right \)$. What is the expectation value of the position operator $hat{x}$ in the ground state?
A. 0
B. \frac{L}{2}
C. L
D. \frac{L}{\pi}
Question 2
A lens of focal length 20 cm is used to form an image of an object placed 30 cm from the lens. If the object is moved to a dis\tance of 60 cm from the lens, what is the new image dis\tance?
A. 40 cm
B. 60 cm
C. 80 cm
D. 120 cm
Question 3
A gas is confined to a cylinder of volume 2 m^3 at a temperature of 300 K. If the gas is heated to a temperature of 400 K, what is the new volume of the gas?
A. 2.5 m^3
B. 3.0 m^3
C. 3.5 m^3
D. 4.0 m^3
Question 4
A wave with a frequency of 100 Hz and an amplitude of 2 m is traveling along a string. If the wave is reflected off a fixed \end, what is the amplitude of the reflected wave?
A. -2 m
B. 0 m
C. 1 m
D. 2 m
Question 5
A particle of mass 2 kg is projected from the origin with an initial velocity of 10 m/s at an angle of 60° to the horizontal. Assuming the acceleration due to gravity is 9.8 m/s², calculate the time taken for the particle to reach its maximum height.
A. 1.5 s
B. 2.0 s
C. 2.5 s
D. 3.0 s
Question 6
A 10 Ω resistor is connected in series with a 20 Ω resistor and a 30 Ω resistor. If a 12 V DC source is connected across the circuit, what is the current in the circuit?
A. 0.5 A
B. 1 A
C. 1.5 A
D. 2 A
Question 7
A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. If the particle is subject to a centripetal force of 12 N, what is the angular frequency of the particle?
A. 1.5 rad/s
B. 2.0 rad/s
C. 2.5 rad/s
D. 3.0 rad/s
Question 8
A projectile is launched from the origin with an initial velocity $v_0$ at an angle $\theta$ above the horizontal. What is the projectile's range?
A. \frac{v_0^2}{g} \sin 2\theta
B. \frac{v_0^2}{g} \cos 2\theta
C. \frac{v_0^2}{g} \sin \theta
D. \frac{v_0^2}{g} \cos \theta
Question 9
A 10 μF capacitor is connected in series with a 20 Ω resistor and a 5 V battery. If the switch is closed at t = 0, what is the charge on the capacitor after 5 seconds?
A. 50 μC
B. 100 μC
C. 200 μC
D. 500 μC
Question 10
A parallel plate capacitor has plates of area $A$ and separation $d$. If the capaci\tance is $C$, what is the charge on the plates when a potential difference of $V$ is applied?
A. CV
B. \frac{CV}{2}
C. \frac{C}{V}
D. \frac{V}{C}
Question 11
A wave of wavelength $\lambda$ and frequency $f$ is traveling through a medium with speed $v$. If the wave is reflected from a fixed \end, what is the new wavelength of the wave?
A. \frac{\lambda}{2}
B. \frac{\lambda}{4}
C. \frac{\lambda}{3}
D. \frac{\lambda}{5}
Question 12
A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. The particle is subjected to a centripetal force $F_c = \frac{mv^2}{r}$. If the particle is moving in a clockwise direction, what is the direction of the force $F_c$?
A. towards the center
B. away from the center
C. perp\endicular to the radius
D. along the radius
Question 13
A 10 μF capacitor is connected in parallel with a 20 Ω resistor and a 5 V battery. If the switch is closed at t = 0, what is the charge on the capacitor after 5 seconds?
A. 50 μC
B. 100 μC
C. 200 μC
D. 500 μC
Question 14
A 2 kg block is moving with a velocity of 4 m/s on a frictionless surface. If a force of 10 N is applied to the block, calculate the acceleration of the block.
A. 0.5 m/s^2
B. 1 m/s^2
C. 2 m/s^2
D. 5 m/s^2
Question 15
A radioactive sample has a half-life of 10 years. If the initial activity is 100 Bq, calculate the activity after 20 years.
A. 12.5 Bq
B. 25 Bq
C. 50 Bq
D. 100 Bq

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