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Mathematics
UTME / JAMB 2025
Triangles and Polygons
Diagram
Solution
Given the triangle XYZ above, calculate the value of Cot \(\theta\) and the length XY, respectively
A
\(\frac{\sqrt{48}}{13}\), \(\sqrt{48}\)
B
\(\frac{\sqrt{48}}{11}\), \(\sqrt{48}\)
C
\(\frac{\sqrt{13}}{11}\), \(\sqrt{13}\)
D
\(\frac{13}{\sqrt{48}}\), \(\sqrt{48}\)
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Geometric Construction
Solution
Which of the following angles cannot be constructed using a protractor, a compass, and a sharpened pencil?
A
135°
B
90°
C
145°
D
60°
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Differentiation
Solution
Find the limit of y = \(\frac{(x^3 - 2x^2 + 6x - 12)}{(x - 2)}\) as x goes to 2.
A
Infinity
B
10
C
0
D
12
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Differentiation
Solution
Find the derivatives of y = sin 4x
A
-4sin x
B
-4cos x
C
4sin4x
D
4cos4x
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Integration
Solution
Integrate y = 4x\(^3\) + 2x + cos x.
A
x\(^4\) - x\(^2\) - sin x + C
B
x\(^4\) + x\(^2\) + sin x + C
C
x\(^4\) - x\(^2\) + sin x + C
D
x\(^4\) + x\(^2\) - sin x + C
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Integration
Solution
Integrate the function y = 3x\(^2\) + 2x - 5 with respect to x.
A
x\(^3\) + x\(^2\) - 5x + C
B
x\(^2\) + 2x\(^2\) - 5x + C
C
x\(^2\) + 2x - 5 + C
D
x\(^3\) + 2x - 5 + C
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Statistics
Solution
The average weight of 15 iron bars is 1000 kg. If the heaviest iron bar is removed, the average weight is reduced by 5 kg. Find the weight in kg of the heaviest iron bar.
A
1170kg
B
1270kg
C
1070kg
D
1370kg
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Statistics
Diagram
Solution
The figure above is a pie chart. Use it to find in degrees those who are doctors
A
60\(^\circ\).
B
72\(^\circ\).
C
90\(^\circ\).
D
84\(^\circ\).
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Statistics
Diagram
Solution
The table above shows the weights of twelve mathematics students. Find the modal weight.
A
54
B
58
C
60
D
62
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Statistics
Diagram
Solution
From the table above, determine the upper - class boundary of the modal class
A
21.5
B
30.5
C
20.5
D
10.5
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Permutation and Combination
Solution
Find the number of permutations of the letters of the word SCHOOL.
A
600
B
360
C
480
D
300
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Permutation and Combination
Solution
The word HANDIER can be arranged in how many ways
A
3080
B
2650
C
4050
D
5040
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Probability
Solution
Find the probability of getting an even number in a single throw of a six-sided die.
A
\(\frac{1}{4}\)
B
\(\frac{1}{5}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{3}\)
medium Difficulty
Study Solution
Mathematics
UTME / JAMB 2025
Probability
Solution
If the probability of death is q and the probability of survival is p, find the probability of one death and one survival in an accident involving two persons
A
p/q
B
pq
C
p - q
D
p + q
medium Difficulty
Study Solution
Physics
UTME / JAMB 2025
Heat Energy & Temperature
Solution
5400kJ of heat energy was lost when some amount of steam condensed to water for drinking purposes at 15º C. What is the quantity of water collected? [L\(_f \) = 2.26 × 10\(^6\) Jkg\(^{-1}\), c\(_w\) = 4200 Jkg\(^{-1}K^{-1}\)]
A
0.95 kg
B
8.24 kg
C
1.84 kg
D
2.06 kg
medium Difficulty
Study Explanation