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Mathematics
UTME / JAMB 2019
Variations
Solution
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.
A
12
B
8
C
9
D
16
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(p \propto \frac{1}{\sqrt{q}}\)
\(\implies p = \frac{k}{\sqrt{q}}\)
when p = 3, q = 16.
\(3 = \frac{k}{\sqrt{16}}\)
\(k = 3 \times 4 = 12\)
\(\therefore p = \frac{12}{\sqrt{q}}\)
when p = 4,
\(4 = \frac{12}{\sqrt{q}} \implies \sqrt{q} = \frac{12}{4}\)
\(\sqrt{q} = 3 \implies q = 3^2 \)
\(q = 9\)
Source: Myschool Past Questions Archive (Record #55053)
Mathematics
UTME / JAMB 2019
Fractions, Decimals, Percentages & Approximations
Solution
Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.
A
43.6% loss
B
35% profit
C
63.2% profit
D
28% loss
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
200 mangoes at 4 for N2.50
\(\implies\) Total cost price = \(\frac{200}{4} \times N 2.50\)
= N 125.00
Since 30 mangoes got spoilt \(\implies\) Left over = 200 - 30
= 170 mangoes
170 mangoes at 2 for N 2.40
\(\implies\) Total selling point = \(\frac{170}{2} \times N 2.40\)
= N 204.00
Profit : N (204.00 - 125.00) = N 79.00
% profit = \(\frac{79}{125} \times 100%\)
= 63.2% profit.
Source: Myschool Past Questions Archive (Record #55055)
Mathematics
UTME / JAMB 2019
Fractions, Decimals, Percentages & Approximations
Solution
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number.
A
19%
B
20%
C
25%
D
16.3%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
S.I = \(\frac{PRT}{100}\)
\(\implies\) N 4890 = \(\frac{8550 \times 3 \times x}{100}\)
\(x = \frac{4890 \times 100}{8550 \times 3}\)
\(x = 19.06%\)
\(x \approxeq 19%\)
Source: Myschool Past Questions Archive (Record #55062)
Physics
UTME / JAMB 2019
Scalars, Vectors & Relative Motion
Solution
The limiting frictional force between two surface depends on
I. the gaseous reaction between the surfaces
II. the nature of the surfaces in contact
III. the relative velocity between the surfaces
A
I only
B
I & IV only
C
II only
D
III only
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
- Friction depends on the nature of the surfaces in contact
Source: Myschool Past Questions Archive (Record #54954)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
If a body moves with a constant speed and at the same time undergoes an acceleration, its motion is said to be
A
circular
B
oscillatory
C
rectilinear
D
rotational
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
Circular motion has uniform
Source: Myschool Past Questions Archive (Record #54957)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
When blue and green colours of light are mixed, the resultant colour is
A
cyan
B
magenta
C
black
D
yellow
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
Cyan is a bluish-green colour
Source: Myschool Past Questions Archive (Record #54959)
Physics
UTME / JAMB 2019
Atomic, Quantum, Nuclear Physics & Electronics
Solution
A metal rod has a length of 100cm at 200\(^oC\). At what temperature will its length be 99.4cm. If the linear expansivity of the material of the rod is 2 x 10\(^{-5}C^{-1}\)
A
200\(^o\)C
B
300\(^o\)C
C
100\(^o\)C
D
-100\(^o\)C
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
L\(_1\) = 100cm, T\(_1\) = 200\(^o\)C
L\(_2\) = 99.4cm,T\(_2\) = ?
\(\alpha\) = 2 x 10\(^{-5}\)C\(^{-1}\)
\(\alpha\) = \(\frac{L_2 - L_1}{L_1(T_2 - T_1)}\)
2 x 10\(^{-5} = \frac{99.4 - 100}{100( T_2 - 200)} = \frac{-0.6}{100(T_2 - 200)}\)
2 x 10\(^{-5}\) x \(100(T_2 - 200) = -0.6\)
\(T_2 - 200 = \frac{-0.6}{0.002} = - 300^oC\)
\(T_2 = 200 - 300 = -100^oC\)
Source: Myschool Past Questions Archive (Record #54963)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
According to kinetic molecular model, in gases
A
The particles are closely packed together, they occupy minimum space & are usually arranged in a regular pattern
B
The particles occur in clusters with molecules slightly farther apart
C
The molecule are very fast apart & occupy all the space made available
D
The particle vibrate about fixed positions and are held together by the strong intermolecular bonds between them
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
In kinetic molecular model, gases are energized and thus moves freely, fast as they occupy specific space
Source: Myschool Past Questions Archive (Record #54973)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
The value of T in the figure above is
A
30N
B
10.0N
C
20N
D
40N
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
Tsin30 + Tsin30 =40
2Tsin30 = 40
Tsin30 = 40/2 = 20
T(\(\frac{1}{2}\)) = 20
T = 20 x 2 = 40N
Source: Myschool Past Questions Archive (Record #54981)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
A train has an initial velocity of 44m/s and an acceleration of -4m/s\(^2\). Calculate its velocity after 10 seconds
A
10m/s
B
6m/s
C
8m/s
D
4m/s
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
V = u _ at, at u = 44m/s
44 + [-4]10
4m/s
Source: Myschool Past Questions Archive (Record #54982)
Physics
UTME / JAMB 2019
Atomic, Quantum, Nuclear Physics & Electronics
Solution
Lamps in domestic lightings are usually in
A
series
B
divergent
C
convergent
D
parallel
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
Lamps in lightenings are arranged to reduce the heat losses
- resultant resistance is small for parallel arrangement which indicate low heat losses [Heat \(\alpha\) R]
Source: Myschool Past Questions Archive (Record #54984)
Physics
UTME / JAMB 2019
Calorimetry, Latent Heat & Change of State
Solution
During the transformation of matter from the solid to the liquid state, the heat supplied does not produce temperature increase because
A
all the heat is used to break the bonds holding the molecules of the solid together
B
the heat capacity has become very large as the substance melts
C
the heat energy is quickly conducted away
D
the heat gained is equal to the heat lost by the substance
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
During the transformation of the matter from the solid to the liquid state, the heat supplied does not produce a temperature increase because all the heat is used to break the bonds holding the molecules of the solid together
Source: Myschool Past Questions Archive (Record #54986)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
In a slide wire bridge, the balance is obtained at a point 25cm from one end of wire 1m long. The resistance to be tested is connected to that end and a standard resistance of 3.6\(\Omega\) is connected to the other end of the wire. Determine the value of the unknown resistance
A
3.2\(\Omega\)
B
1.4\(\Omega\)
C
3.21\(\Omega\)
D
1.2\(\Omega\)
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
\(\frac{R}{3.6} = \frac{75}{25} = \frac{1}{3}\)
3R = 3.6
R = 1.2\(\Omega\)
Source: Myschool Past Questions Archive (Record #54989)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
Electrons were discovered by
A
Dalton
B
James Charwick
C
J.J. Thompson
D
Niels Bohr
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
Electron was discovered J.J Thompson in 1879
Source: Myschool Past Questions Archive (Record #54990)
Physics
UTME / JAMB 2019
Current Electricity & Electric Circuits
Solution
Which of the following is/are the limitations to the Rutherford's atomic models?
I. It is applicable when energy is radiated as electrons are revolving
II. It is applicable when energy is radiated in a continuous mode
III. It is applicable to an atom with only one electron in the other shell
A
I only
B
II only
C
I & II only
D
I, II & III only
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
Rutherford assumed that (I) energy is radiated when electrons are revolving (II) energy is radiated in a continuous mode. These are limitations of Rutherford's model
Source: Myschool Past Questions Archive (Record #54991)