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Physics
UTME / JAMB 1985
Temperature, Thermometry & Thermal Expansion
Solution
Two divers G and H are at depths 20m and 40m respectively below the water surface in a lake. The pressure on G is P1 while the pressure on H is P2. If the atmospheric pressure is equivalent to 10m of water, then the value of \( \frac{p_2}{p_1} \) is?
A
0.50
B
0.60
C
1.67
D
2.00
E
3.0
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
pressure at H = 40m ; pressure at G, p1 = 20m
\(\frac{p_1}{p_1}\) = \(\frac{40 + 10}{20 + 10}\)
= \(\frac{50}{30}\)
≈ 1.67
Source: WAEC / JAMB / NECO Classroom Archive (Record #28569)
Physics
UTME / JAMB 1985
Temperature, Thermometry & Thermal Expansion
Solution
A quantity of gas occupies a certain volume when the temperature is -73oC and the pressure is 1.5 atmospheres. If the pressure is increased to 4.5 atmospheres and the volume is halved at the same time, what will be the new temperature of the gas?
A
573oC
B
327oC
C
300oC
D
110oC
E
27oC
medium Difficulty
Verified Correct Answer: Option E
Physical Principles & Numerical Solution
General Gas Law:
\(\frac{P_1 V_1}{T_1}\) = \(\frac{P_2 V_2}{T_2}\)
where T\(_1\) = -73 + 273 = 200k, T\(_2\) = ?,
V\(_1\) = 1, V\(_2\) = \(\frac{1}{2V}\),
P\(_1\) = 1.5, P\(_2\) = 4.5
T\(_2\) = \(\frac{P_2 V_2 T_1}{P_1 V_1}\)
T\(_2\) = \(\frac{4.5 * 1/2 * 200}{1.5 X 1}\)
T\(_2\) → 300k or 27ºC
Source: WAEC / JAMB / NECO Classroom Archive (Record #28593)
Physics
UTME / JAMB 1985
Atomic, Quantum, Nuclear Physics & Electronics
Solution
Which of the following features is NOT a characteristic of natural radioactivity?
A
Radioactivity is a nuclear phenomenon
B
Radioactivity is exhibited only by elements of mass number greater than 206
C
The radioactivity of an element is affected by electric and magnetic fields in the surroundings
D
Radioactive substances emits three types of radiations, a-rays, \(\beta\)-rays and y-rays
E
The radioactive element is transformed into a new element
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
Natural radioactivity is exhibited by elements of atomic numbers of 83 or more
Source: WAEC / JAMB / NECO Classroom Archive (Record #28658)
Physics
UTME / JAMB 1985
Atomic, Quantum, Nuclear Physics & Electronics
Solution
What is the number of neutrons in the Uranium isotope \(^{238}_{92}X\)?
A
92
B
146
C
238
D
330
E
119
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
No of neutrons = 238-92
=146
Source: WAEC / JAMB / NECO Classroom Archive (Record #28659)
Physics
UTME / JAMB 1985
Reflection, Refraction & Dispersion of Light
Solution
A narrow beam of white light can be split up into different colours by a glass prism. The correct explanation is that
A
white light is an electromagnetic wave
B
the prism has all the colours of the white light
C
white light has undergone total internal reflection in the prism
D
different colours of white light travel with different speeds in glass
E
white ligth consist of yellow, green and red colours
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
When white light passes through a prism, it is refracted (bent) at different angles depending on the wavelength (or color) of the light. This is because different colors of light travel at different speeds in the glass, leading to varying degrees of refraction. This phenomenon is known as dispersion.
Source: WAEC / JAMB / NECO Classroom Archive (Record #28635)
Chemistry
UTME / JAMB 1985
Periodic Table & Periodicity
Solution
A correct electrochemical series can be obtained from K, Na, Ca, Al, Mg, Zn, Fe, Pb, H, Cu, Hg, Ag, Au by interchanging?
A
Al and Mg
B
Zn and Fe
C
Zn and Pb
D
Pb and H
E
Au and Hg
medium Difficulty
Verified Correct Answer: Option A
Chemical Principles & Mechanism
The electrochemical series, also known as the activity series, is a list of metals listed in order of decreasing reactivity or in order of decreasing ease of oxidation.
Magnesium comes before Aluminium in the series
Source: WAEC / JAMB / NECO Classroom Archive (Record #14112)
Chemistry
UTME / JAMB 1985
Stoichiometry, Mole Concept & Volumetric Analysis
Solution
A colourless organic compound X was burnt in excess air to give two colourless and odourless gases, Y and Z, as products. X does not decolorize blue bromine vapour, Y turns lime milky while Z gives a blue colour with copper (ll) tetraoxosulphate (IV).
Compound X is?
A
an alkene
B
an alkane
C
an alkyne
D
tetrachloromethane
E
dichloromethane
medium Difficulty
Verified Correct Answer: Option B
Chemical Principles & Mechanism
Burning the alkane in the presence of sufficient air or oxygen; it produces carbon dioxide, water, and a huge amount of heat as a product.
If carbon dioxide is bubbled through limewater, the limewater turns milky or cloudy white.
Anhydrous CuSO4 is used to test the presence of water in any liquid because it changes its colour from white to blue in the presence of water.
Source: WAEC / JAMB / NECO Classroom Archive (Record #14127)
Mathematics
UTME / JAMB 1985
Fractions, Decimals, Percentages & Approximations
Solution
If three numbers P, Q, R are in ratio 6 : 4 : 5, find the value of \(\frac{3p - q}{4q + r}\)
A
\(\frac{3}{2}\)
B
\(\frac{2}{3}\)
C
2
D
3
E
18
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
P : Q : r = 6 : 4 : 5
5 = 6 + 4 + 5
= 15
P = \(\frac{6}{15}\), q = \(\frac{4}{15}\), r = \(\frac{5}{15}\) = \(\frac{1}{3}\)
To find \(\frac{3p - q}{4q + r}\)
3p - q = 3 x \(\frac{6}{15}\) - \(\frac{4}{15}\)
\(\frac{18}{15}\) - \(\frac{4}{15}\) = \(\frac{14}{15}\)
∴ 4q + r = 4 x \(\frac{4}{15}\) + \(\frac{5}{15}\)
\(\frac{16}{15}\) = \(\frac{16}{15}\) + \(\frac{5}{15}\)
= \(\frac{21}{15}\)
\(\frac{14}{15}\) x \(\frac{15}{21}\) = \(\frac{14}{21}\)
= \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #32180)
Mathematics
UTME / JAMB 1985
Fractions, Decimals, Percentages & Approximations
Solution
Arrange the following numbers in ascending order of magnitude \(\frac{6}{7}\), \(\frac{13}{15}\), 0.8650
A
\(\frac{6}{7}\) < 0.865 < \(\frac{13}{15}\)
B
\(\frac{13}{15}\) < \(\frac{6}{7}\) < 0.865
C
\(\frac{6}{7}\) < \(\frac{13}{15}\) < 0.865
D
0.865 < \(\frac{6}{7}\) < \(\frac{13}{15}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{6}{7}\), \(\frac{13}{15}\), 0.8650
In ascending order, we have 0.8571, 0.8650, 0.8666
i.e. \(\frac{6}{7}\) < 0.8650 < \(\frac{13}{15}\)
Source: Myschool Past Questions Archive (Record #32191)
Mathematics
UTME / JAMB 1985
Fractions, Decimals, Percentages & Approximations
Solution
A sum of money was invested at 8% per annum simple interest. If after 4 years the money amounts to N330.00. Find the amount originally invested
A
N180.00
B
N165.00
C
N150.00
D
N250.00
E
N200.00
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
S.I = \(\frac{PTR}{100}\)
T = 4yrs, R = 8%, a = N330.00
330 - P = \(\frac{PTR}{100}\), A = P + I
i.e. A = P + \(\frac{PTR}{100}\)
330 = P + \(\frac{P(4) (8)}{100}\)
33000 = 32P + 100P
132P = 33000
P = N250.00
Source: Myschool Past Questions Archive (Record #32197)
Mathematics
UTME / JAMB 1985
Number Bases & Modular Arithmetic
Solution
In the equation below, Solve for x if all the numbers are in base 2: \(\frac{11}{x}\) = \(\frac{1000}{x + 101}\)
A
101
B
11
C
110
D
111
E
10
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{11}{x}\) = \(\frac{1000}{x + 101}\) = 11(x + 101)
1000x = 11x + 1111
1000x - 11x = 1111
101x = 1111
x = \(\frac{1111}{101}\)
x = 11
Source: Myschool Past Questions Archive (Record #32200)
Mathematics
UTME / JAMB 1985
Inequalities & Linear Programming
Solution
List all integers satisfying the inequality -2 \(\leq\) 2 x -6 < 4
A
2, 3, 4, 5
B
2, 3, 4
C
2, 5
D
3, 4, 5
E
4, 5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
-2 \(\leq\) 2x - 6 < 4 = 2x - 6 < 4
= 2x < 10
= x < 5
2x \(\geq\) -2 + 6 \(\geq\)
= x \(\geq\) 2
∴ 2 \(\leq\) x < 5 [2, 3, 4]
Source: Myschool Past Questions Archive (Record #32203)
Mathematics
UTME / JAMB 1985
Plane Geometry, Polygons & Circle Theorems
Solution
Find correct to two decimals places 100 + \(\frac{1}{100}\) + \(\frac{3}{1000}\) + \(\frac{27}{10000}\)
A
100.02
B
1000.02
C
100.22
D
100.01
E
100.51
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
100 + \(\frac{1}{100}\) + \(\frac{3}{1000}\) + \(\frac{27}{10000}\)
\(\frac{1000,000 + 100 + 30 + 27}{10000}\) = \(\frac{1,000.157}{10000}\)
= 100.02
Source: Myschool Past Questions Archive (Record #32204)
Mathematics
UTME / JAMB 1985
Fractions, Decimals, Percentages & Approximations
Solution
John gives one-third of his money to Janet who has N105.00. He then finds that his money is reduced to one-fourth of what Janet now has. Find how much money john has at first
A
N45.00
B
N48.00
C
N52.00
D
N60.00
E
N58.00
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let x be John's money, Janet already had N105, \(\frac{1}{3}\) of x was given to Janet
Janet now has \(\frac{1}{3}\)x + 105 = \(\frac{x + 315}{3}\)
John's money left = \(\frac{2}{3}\)x = \(\frac{1}{4} \times\frac{ x + 315}{3}\)
cross multiplying
24x = 3x + 945
∴ x = 45
Source: Myschool Past Questions Archive (Record #32209)
Mathematics
UTME / JAMB 1985
Plane Geometry, Polygons & Circle Theorems
Solution
Write h in terms of a, b, c, d if a = \(\frac{b(1 - ch)}{1 - dh}\)
A
h = \(\frac{a - b}{ad}\)
B
h = \(\frac{1 - b}{ad - bc}\)
C
h = \(\frac{(a - b)^2}{ad - bc}\)
D
h = \(\frac{a - b}{ad - bc}\)
E
h = \(\frac{b - a}{ab - dc}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
a = \(\frac{b(1 - ch)}{1 - dh}\)
a = \(\frac{b - bch}{1 - dh}\)
a - adh = b - bch
a - b = -bch + adh
a - b = adh - bch
a - b = h(ad - bc)
h = \(\frac{a - b}{ad - bc}\)
Source: Myschool Past Questions Archive (Record #32216)