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Mathematics
UTME / JAMB 1985
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure POQ is the diameter of the circle PQR. If PSR = 145o, find xo
Attached Figure / Diagram
A
25o
B
35o
C
45o
D
125o
E
55o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
< PRQ = \(\frac{1}{2}\) < POQ = 90o
< PSR + < PQR = 180o
< PQR = 180o - 145o = 35o
\(\bigtriangleup\)PQR is a right angled triangle
x = 90 - < PQR
= 90o - 35o
= 55o
Source: Myschool Past Questions Archive (Record #32806)
Mathematics
UTME / JAMB 1985
Indices, Logarithms & Surds
Diagram
Solution
In the figure, GHIJKLMN is a cube of side a. Find the length of HN.
Attached Figure / Diagram
A
\(\sqrt{3a}\)
B
3a
C
3a2
D
a\(\sqrt{2}\)
E
a\(\sqrt{3}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
HJ2 = a2 + a2 = 2a2
HJ = \(\sqrt{2a^2} = a \sqrt{2}\)
HN2 = a2 + (a\(\sqrt{2}\))2 = a2 + 2a2 = 3a2
HN = \(\sqrt{3a^2}\)
= a\(\sqrt{3}\)cm
Source: Myschool Past Questions Archive (Record #32814)
Mathematics
UTME / JAMB 1985
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, PQ is the tangent from P to the circle QRS with SR as its diameter. If QPR = \(\theta\)o and RQP = \(\phi\)o, which of the following relationships between \(\theta\)o and \(\phi\)o is correct
Attached Figure / Diagram
A
\(\theta\)o + \(\phi\)o = 902
B
\(\phi\)o = 902 - 2\(\theta\)o
C
\(\theta\)o = \(\phi\)o
D
\(\phi\)o = 2\(\theta\)o
E
\(\theta\)o + 2\(\phi\)o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
180 - \(\phi\)o = \(\theta\)o + \(\phi\)o (Sum of opposite interior angle equal to its exterior angle)
180 = 2\(\phi\) + \(\theta\)o
Source: Myschool Past Questions Archive (Record #32818)
Mathematics
UTME / JAMB 1985
Indices, Logarithms & Surds
Diagram
Solution
In the figure, the area of the shaded segment is
Attached Figure / Diagram
A
3\(\pi\)
B
9\(\frac{\sqrt{3}}{4}\)
C
3 (\(\pi - 3 \frac{\sqrt{3}}{4}\))
D
\(\frac{(\sqrt{3 - \pi)}}{4}\)
E
\(\pi + \frac{9 \sqrt{3}}{4}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of sector = \(\frac{120}{360} \times \pi \times (3)^2 = 3 \pi\)
Area of triangle = \(\frac{1}{2} \times 3 \times 3 \times \sin 120^o\)
= \(\frac{9}{2} \times \frac{\sqrt{3}}{2} = \frac{9\sqrt {3}}{4}\)
Area of shaded portion = 3\(\pi - \frac{9\sqrt {3}}{4}\)
= 3 (\(\pi - 3 \frac{\sqrt{3}}{4}\))
Source: Myschool Past Questions Archive (Record #32831)
Mathematics
UTME / JAMB 1985
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, find angle x
Attached Figure / Diagram
A
100o
B
120o
C
60o
D
110o
E
140o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
In the figure, angle x = 20o + 80o + 40o
= 140o
Source: Myschool Past Questions Archive (Record #32832)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
Solution
In the question below choose the option opposite in meaning to the word underlined:
The chief was generous in his award of university scholarships
A
nobel
B
considerate
C
liberal
D
mean
E
honest
medium Difficulty
Verified Correct Answer: Option D
Grammar & Contextual Explanation
The underlined word "generous" means kind, giving, or willing to share resources freely. The opposite of generous is stingy or unwilling to give, which is best represented by "mean" in this context.
Source: Myschool Past Questions Archive (Record #4416)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
Solution
In the question below choose the option opposite in meaning to the word underlined:
To most people last Christmas was an austere period
A
prosperous
B
harsh
C
severe
D
sour
E
stern
medium Difficulty
Verified Correct Answer: Option A
Grammar & Contextual Explanation
In this context, austere means strict, harsh or lacking in comfort and luxury. It is associated with hardship or minimalism, especially due to economic difficulty. So, we need a word that is opposite in meaning—suggesting comfort, wealth, or abundance. Prosperous means wealthy, successful or thriving, especially in financial terms. This is clearly the opposite of austere.
Source: Myschool Past Questions Archive (Record #4417)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
Chidi is naturally taciturn
A
friendly
B
cheerful
C
dumb
D
lively
E
garrulous
medium Difficulty
Verified Correct Answer: Option E
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #4418)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
He is loved for his altruism.
A
benevolence
B
sincerity
C
selfishness
D
selflessness
E
kindness
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #4419)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
Solution
In the question below choose the option opposite in meaning to the word underlined:
The military Governor upheld the decision of his cabinet
A
held up
B
undercut
C
maintained
D
abolished
E
reversed
medium Difficulty
Verified Correct Answer: Option E
Grammar & Contextual Explanation
The correct answer is E. reversed. Uphold means to support, maintain or confirm a decision or action. The opposite of "uphold" would be to overturn, cancel or reverse the decision.
Source: Myschool Past Questions Archive (Record #4420)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
Many untrustworthy students gives evasive answers to questions which they fully understand.
A
direct
B
outspoken
C
simple
D
truthful
E
clever
medium Difficulty
Verified Correct Answer: Option A
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #4421)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
Solution
In the question below choose the option opposite in meaning to the word underlined:
The deafening noise of the two jet planes which flew across our compound yesterday made people fear that an assault on the country might be imminent
A
impending
B
ahead
C
remote
D
eminent
E
threatening
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
The word "imminent" means something that is about to happen very soon or likely to occur at any moment. We are asked to find the opposite in meaning — that is, a word meaning not happening soon or unlikely to happen. "Remote" (when used for time or likelihood) means unlikely to happen soon or far off, which is opposite to "imminent.
Source: Myschool Past Questions Archive (Record #4422)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
Disgruntled people are indifferent to any plans to rid the society of evil
A
different from
B
diffirent about
C
in agreement with
D
interested in
E
opposed to
medium Difficulty
Verified Correct Answer: Option D
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #4423)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
the severity of the harmattan helped me to complete my writing assignment in record time because i had no choice but to lock my self indoors
A
warmth
B
mildness
C
moderation
D
leniency
E
gentility
medium Difficulty
Verified Correct Answer: Option B
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #4424)
English Language
UTME / JAMB 1985
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
The increase in transport fares deterred our club from planning an excursion this year
A
deferred
B
irritated
C
impelled
D
restricted
E
encouraged
medium Difficulty
Verified Correct Answer: Option E
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #4425)