POST UTME MOUNTAIN TOP UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A number is divisible by 3 if the sum of its digits is divisible by 3. Find the smallest number greater than 1000 that is divisible by 3.
A. 1002
B. 1005
C. 1008
D. 1011
Question 2
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 3
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{2} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{6} \)
Question 4
Find the mean of the following data set: 2, 4, 6, 8, 10.
A. 5
B. 6
C. 7
D. 8
Question 5
A car travels from City A to City B at an average speed of 60 km/h and returns at an average speed of 40 km/h. If the dis\tance between the two cities is 240 km, what is the average speed of the car for the entire trip?
A. \( \frac{2 cdot 240}{60 + 40} \)
B. \( \frac{2 cdot 240}{60 - 40} \)
C. \( \frac{240}{60 + 40} \)
D. \( \frac{240}{60 - 40} \)
Question 6
Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \ \).
A. 0
B. 10
C. 20
D. 30
Question 7
A random variable X has a probability distribution given by P\( X=1 \)=0.3, P\( X=2 \)=0.4, P\( X=3 \)=0.3. Find the expected value of X.
A. 1
B. 2
C. 3
D. 4
Question 8
Solve the equation \( 2x^3 - 5x^2 + 3x - 1 = 0 \) u\sing the Rational Root Theorem.
A. \( x = 1 \)
B. \( x = -1 \)
C. \( x = \frac{1}{2} \)
D. \( x = -\frac{1}{2} \)
Question 9
A coin is tossed 5 times. What is the probability that exactly 3 heads appear?
A. 1/32
B. 5/32
C. 10/32
D. 15/32
Question 10
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 11
Find the derivative of ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{x^2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{1}{\( x^2 + 1 \ \)^2} )
Question 12
A set of numbers has a mean of 10 and a s\tandard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 13
Solve for x in the equation \log_{10}\( x^2 \)=4.
A. 10
B. 100
C. 1000
D. 10000
Question 14
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the cross product formula.
A. \( egin{pmatrix} 6 \ -4 \end{pmatrix} \)
B. \( egin{pmatrix} 4 \ -6 \end{pmatrix} \)
C. \( egin{pmatrix} 3 \ -2 \end{pmatrix} \)
D. \( egin{pmatrix} 2 \ -3 \end{pmatrix} \)
Question 15
A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.
A. 6
B. 10
C. 12
D. 15

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