POST UTME UNN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 20
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 24
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 28
Question 2
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \frac{\pi}{6}
B. \frac{\pi}{12}
C. \frac{\pi}{18}
D. \frac{\pi}{24}
Question 3
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.3413
B. 0.6827
C. 0.9544
D. 0.9973
Question 4
A 2x2 matrix \begin{bmatrix} a & b \ c & d \end{bmatrix} has an inverse \begin{bmatrix} e & f \ g & h \end{bmatrix}. If the product of the two matrices is \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}, calculate the value of a.
A. 1
B. 2
C. 3
D. 4
Question 5
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.
A. 8
B. 8.16
C. 8.18
D. 8.20
Question 6
Solve the vector equation \overrightarrow{a} \cdot \overrightarrow{b} = 0.
A. \overrightarrow{a} = \overrightarrow{0} \text{ or } \overrightarrow{b} = \overrightarrow{0}
B. \overrightarrow{a} = \overrightarrow{b}
C. \overrightarrow{a} \perp \overrightarrow{b}
D. \overrightarrow{a} \parallel \overrightarrow{b}
Question 7
A right circular cone has a height of 20 cm and a radius of 10 cm. Find the volume of the cone in cubic centimeters.
A. 1000\pi
B. 2000\pi
C. 3000\pi
D. 4000\pi
Question 8
Solve for y in the equation \( y^2 + 4y - 5 = 0 \).
A. 1
B. -1
C. 2
D. -2
Question 9
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 10
A polynomial f(x) = x^3 + 2x^2 - 7x + 12 has a root at x = -1. Calculate the value of f\( -1 \).
A. 1
B. 2
C. 3
D. 4
Question 11
A solid sphere has a radius of 5 cm. Find the surface area of the sphere in square centimeters.
A. 314.16
B. 314.17
C. 314.18
D. 314.19
Question 12
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?
A. 0.2
B. 0.24
C. 0.36
D. 0.48
Question 13
Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 2x - 6} > 0.
A. \( -\infty, -3 \) \cup \( 1, \infty \)
B. \( -\infty, -2 \) \cup \( 1, \infty \)
C. \( -\infty, -3 \) \cup \( -2, \infty \)
D. \( -\infty, -2 \) \cup \( -3, \infty \)
Question 14
Simplify the expression \sqrt{8} + \sqrt{18} + \sqrt{32}.
A. 10\sqrt{2}
B. 12\sqrt{2}
C. 14\sqrt{2}
D. 16\sqrt{2}
Question 15
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = x^3 about the x-axis.
A. \frac{\pi}{6}
B. \frac{\pi}{12}
C. \frac{\pi}{24}
D. \frac{\pi}{48}

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