POST UTME UNILORIN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of 5 numbers has an average of 10. If one of the numbers is 15, what is the sum of the remaining 4 numbers?
A. 40
B. 45
C. 50
D. 55
Question 2
A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.
A. 100π
B. 200π
C. 400π
D. 800π
Question 3
The set of all real numbers (x) such that \( |x-2|+|x-6| = 6 \) is given by the interval ([a,b]). Find the value of \( a+b \).
A. 4
B. 8
C. 10
D. 12
Question 4
Solve for y in the equation \( 2^y = 64 \).
A. 3
B. 4
C. 5
D. 6
Question 5
Determine the value of x in the equation \( \sin\( 2x \ \) = \frac{1}{2} ) given that ( 0 leq x leq 2pi ).
A. \( \frac{pi}{6} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{2} \)
Question 6
A fair six-sided die is rolled. Find the probability that the number rolled is greater than 4.
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 7
In a normal distribution with mean \( mu = 50 \) and s\tandard deviation \( sigma = 10 \), find the probability that a randomly selected value lies between 40 and 60.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 8
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi
B. 32\pi
C. 40\pi
D. 48\pi
Question 9
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 10
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 11
Simplify the expression \( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} \).
A. 1
B. 2
C. 3
D. 4
Question 12
A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{4} ) for \( x = 1, 2, 3, 4 \). Find the expected value of X.
A. 2
B. 3
C. 4
D. 5
Question 13
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 u\sing the Pythagorean theorem.
A. 8 cm
B. 12 cm
C. 14 cm
D. 16 cm
Question 14
In a geometric sequence with first term (a) and common ratio (r), the sum of the first five terms is given by \( S_5 = \frac{a\( 1-r^5 \ \)}{1-r}). If \( S_5 = 246.5 \) and \( r = \frac{1}{2} \), find the value of (a).
A. 120
B. 240
C. 480
D. 960
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )

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