JAMB UTME - Physics - 1992

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The fraction of a radioactive material that has decayed after three half-lives is represented by the second option:

1

3

Explanation: The half-life of a radioactive material is the amount of time it takes for half of the radioactive atoms to decay. After one half-life, half of the original radioactive material has decayed. After two half-lives, only one-fourth (1/2 x 1/2) of the original radioactive material remains. After three half-lives, only one-eighth (1/2 x 1/2 x 1/2) of the original radioactive material remains, meaning that seven-eighths (1 - 1/8 = 7/8) of the material has decayed. Therefore, the fraction of radioactive material that has decayed after three half-lives is 7/8.

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R.d = $\frac{0.4}{0.5}$ = 0.8

0.8 = $\frac{\text{Density of oil}}{\text{Density of water}}$

0.8 = $\frac{\text{Density of oil}}{1000}$

Density of oil = 800kgm3

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The properties that make a convex mirror useful as a driving mirror are: - The image formed by the mirror is virtual, meaning it is not real, but appears to be behind the mirror. This is the opposite of a real image, which is formed in front of the mirror. So, statement i is incorrect. - The image formed by the mirror is erect, meaning it is not inverted. This is important for a driving mirror because it allows the driver to quickly and easily interpret the image without confusion. So, statement ii is correct. - The mirror has a wide field of view, which means that it can reflect light from a larger area compared to a flat mirror or concave mirror. This allows the driver to see more of the surroundings, making it easier to spot potential hazards. So, statement iii is correct. - The image formed by a convex mirror is smaller than the object itself. This is the opposite of magnification, which would make the image larger. So, statement iv is incorrect. Therefore, the correct answer is option ii and iii.

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In alternating current (AC) theory, impedance is measured in ohms, r.m.s. voltage is measured in volts, and resonance frequency is measured in hertz. Impedance is the opposition to the flow of electric current in an AC circuit, similar to resistance in a DC circuit. R.m.s. voltage is the equivalent steady DC voltage that produces the same heating effect as the AC voltage. Resonance frequency is the frequency at which an AC circuit exhibits the greatest impedance. Therefore, the correct option is: ohms, volt and hertz.

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Range = $\frac{U^{2}sin2\theta }{g}$

RangeQ = $\frac{U^{2}sin150}{g}$

RangeR = $\frac{U^{2}sin30}{g}$

Since, sin30o = sin150o

therefore, RQ = RR

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The critical angle is the angle of incidence at which the angle of refraction is 90 degrees, meaning that the refracted ray travels along the surface of the medium rather than entering it. The formula for calculating the critical angle is: critical angle = sin⁻¹ (1/n) where n is the refractive index of the medium. In this question, the refractive index of the medium in air is given as 2.0. Plugging this value into the formula, we get: critical angle = sin⁻¹ (1/2.0) Using a calculator, we can find that sin⁻¹ (1/2.0) is approximately 30 degrees. Therefore, the correct option is 30o.

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The question is asking about the average power output of a man who climbs a set of stairs. Power is the rate at which work is done or energy is transferred, and it is calculated by dividing the work or energy by the time taken to do it. In this case, the work done is equal to the force exerted by the man (800N) multiplied by the distance he climbs (15m), which is equal to 12,000 joules (J). The time taken to climb the stairs is given as 12.5 seconds. Therefore, the man's average power output is the work done divided by the time taken, which is equal to 960 watts (W). So the answer is 960W.

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The variation in the length of the steel bridge can be calculated using the formula: ΔL = LαΔT where ΔL is the variation in length, L is the original length of the bridge, α is the linear expansivity of steel, and ΔT is the difference in temperature. In this case, the bridge is 600m long, the linear expansivity of steel is 0.000012C^-1, and the difference in temperature between night and day is 25°C (35°C - 10°C). Substituting these values into the formula: ΔL = (600m)(0.000012C^-1)(25°C) = 0.18m Therefore, the daily variation in the length of the steel bridge is 0.18m or 18cm. So the correct option is 0.18cm.

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The energy stored in a capacitor is given by the formula: E = 1/2 * C * V^2 where E is the energy stored, C is the capacitance and V is the voltage across the capacitor. From the given information, the capacitance is 10µF and the voltage across the capacitor is 12V. Substituting these values in the formula, we get: E = 1/2 * 10µF * (12V)^2 E = 1/2 * 10^-5F * 144V^2 E = 7.2 x 10^-4 J Therefore, the energy stored in the capacitor is 7.2 x 10^-4 J. The option closest to this value is 7.2 x 10-4J.

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The force (F) acting on an electron in an electric field is given by the equation F = qE, where q is the charge of the electron and E is the electric field intensity. Substituting the given values, we have: F = (1.6 x 10^-19 C) x (10^8 V/m) F = 1.6 x 10^-11 N Therefore, the force acting on the electron is 1.6 x 10^-11 N, which is option (A). Note that the force is very small due to the small charge of the electron and the relatively weak electric field intensity.

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The amount of heat absorbed by the copper block can be calculated using the formula: Q = mcΔT where Q is the amount of heat absorbed, m is the mass of the block, c is the specific heat capacity of copper, and ΔT is the change in temperature. Substituting the given values, we have: Q = (0.05 kg)(390 J/kg.K)(70°C - 20°C) Q = (0.05 kg)(390 J/kg.K)(50°C) Q = 975 J Therefore, the amount of heat absorbed by the copper block is 975 J. So, the correct option is: - 9.75 x 102J

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F = $\frac{uv}{u+v}$

v = 3u

18 = $\frac{3u\times u}{3u+u}$

u = 24cm

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Bi-metallic strips are made of two different metals bonded together, with different coefficients of thermal expansion. When the strip is heated, the two metals expand at different rates, causing the strip to bend. This bending action can be used to control a switch, which is the basis for a thermostat. As the temperature changes, the bi-metallic strip bends, causing the switch to turn on or off, controlling the heating or cooling system. Therefore, the correct answer is "a thermostat".

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The angle between the direction of the earth's magnetic field and the horizontal is called the "angle of dip". This angle is also known as the inclination angle and it measures the vertical angle between the Earth's magnetic field lines and the horizontal plane. The angle of dip changes depending on the location on Earth and it is used to determine the latitude of the location.

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When an object is placed very close to the pole of a concave mirror, the virtual image obtained is enlarged and upright. A concave mirror is a mirror that curves inward, and the focal point of the mirror is the point at which all light rays parallel to the axis of the mirror converge. When an object is placed very close to the pole of the mirror, the light rays from the object diverge and do not converge at the focal point. However, the diverging rays appear to originate from a virtual object behind the mirror, and these rays converge at the focal point. As a result, a virtual, enlarged and upright image of the object is formed.

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Resistivity = $\frac{\text{Resiatance x Area}}{length}$

1.6 x 10-6 = $\frac{15\times Area}{0.27}$

Area = 1.0 x 10-4m2

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I = $\frac{P}{V}$ = $\frac{60}{240}$ = 0.25A

I = $\frac{P}{V}$ = $\frac{60}{40}$ = 1.5A

I = $\frac{P}{V}$ = $\frac{40}{12}$ = 3.3A

I = $\frac{P}{V}$ = $\frac{40}{5}$ = 8A

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The charge stored in a capacitor is given by the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage across the capacitor. Initially, the capacitor is uncharged, so Q = 0. When the 5-volt battery is connected to the plates of the capacitor, the voltage across the capacitor becomes 5 V. Therefore, the charge on the capacitor becomes: Q = CV = (2.0 μF)(5 V) = 10.0 μC The charge on the capacitor will not change after a long time because a capacitor is an ideal device that stores charge without dissipating it. Therefore, the correct answer is 10.0μC.

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When an ebolite rod is rubbed with fur, it gains extra electrons from the fur, which causes the rod to have a surplus of negative charges, making it negatively charged. Therefore, the correct answer is "a negative charge".

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When the block of ice floats on water, a part of it is submerged in the water and the remaining part is above the water. When the ice melts, it turns into water, and its volume decreases. However, the mass of the ice is equal to the mass of the water produced after melting. Therefore, the water produced from the melting of the ice will occupy the same volume as the submerged part of the ice. As a result, the water level in the container will remain the same after the ice melts, and so the correct answer is "remain the same".

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The speed of light changes as it passes through different media with different refractive indices. The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. The formula for finding the speed of light in a medium is: Speed of light in a medium = (Speed of light in a vacuum) / (Refractive index of the medium) In this question, the speed of light in air is given as 3 x 10^8 ms^-1, and the refractive index of the glass is given as 1.50. So, we can use the formula to find the speed of light in glass: Speed of light in glass = (Speed of light in air) / (Refractive index of glass) = (3 x 10^8) / 1.50 = 2 x 10^8 ms^-1 Therefore, the answer is option C, 2.0 x 10^8 ms^-1.

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The frequency of the sound produced by a siren is determined by the number of sound waves produced per second, which depends on the number of times the sound source completes a full cycle of motion per second. For a siren with a rotating disc and multiple holes, the frequency of the sound produced is equal to the product of the number of holes on the disc and the number of revolutions per second. In this case, the siren has 32 holes on the disc and makes 25 revolutions per second, so the frequency of the sound produced would be: Frequency = 32 holes/disc * 25 revolutions/second = 800 Hz Therefore, the correct answer is option C) 800Hz.

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In music, the term "octave" refers to the interval between two notes where the frequency of one note is double the frequency of the other. So, in the sentence, "A note is the octave of another note if it has," the correct option is "a frequency twice that of the first note." This means that if one note has a certain frequency, the note that is an octave higher will have a frequency that is exactly double that of the first note. For example, if one note has a frequency of 440 Hz, the note that is an octave higher will have a frequency of 880 Hz.

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The question is asking for the value of the resistor R that needs to be connected to a galvanometer G of internal resistance 10 ohms, to convert it into a voltmeter with a maximum reading of 100V. The maximum current that can flow through the galvanometer is given as 0.05A. To convert the galvanometer into a voltmeter, a resistor needs to be connected in series with it. The value of this resistor can be calculated using the formula: R = (Vmax/Ig) - Rg Where R is the value of the resistor to be connected, Vmax is the maximum voltage that the voltmeter can read (in this case, 100V), Ig is the maximum current that can flow through the galvanometer (0.05A), and Rg is the internal resistance of the galvanometer (10 ohms). Substituting the given values, we get: R = (100/0.05) - 10 R = 1990 ohms Therefore, the value of the resistor R that needs to be connected in series with the galvanometer G is 1990 ohms. It should be connected in series with the galvanometer to convert it into a voltmeter. So, the correct answer is "1990 ohms in series".

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$\frac{500\times 1.5}{100.0}$ x 100%

= 75%

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When the pressure of a gas is kept constant, the density of the gas will only be affected by changes in its temperature and volume. As the temperature of the gas increases, the density decreases, since the gas molecules move faster and take up more space. As the volume of the gas increases, the density decreases, since the same mass of gas is spread over a larger volume. Therefore, the correct option is: "inversely proportional to its temperature."

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The least count of a measuring instrument is the smallest measurement that can be made with it. The least count of a rule is the distance between two adjacent graduations. A rule graduated in centimeters usually has the smallest graduation of 1 mm or 0.1 cm. Therefore, the least possible error in using a rule graduated in centimeters is 0.1 cm.

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The parallel ray is not before the retina, but behind the retina for a long sighted person.

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y = 0.005 sin[x(0.5X - 200t)]

compare to Y = A sin(kx - wt)

$\lambda$ = $\frac{2\pi }{k}$ and F = $\frac{w}{2\pi }$

V= $\lambda$F

= $\frac{2\pi }{0.5}$ x $\frac{200}{2\pi }$

= 400ms-1

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100oC .... 5.5

$\theta$oC .... 5.3

0oC .... 5.0

$\frac{\theta -0}{100-0}$ = $\frac{5.5-5.0}{5.5-5.0}$

$\theta$ = 40oC

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