POST UTME CRAWFORD UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 2
A circle has a radius of 4 cm and passes through the points (0, 0) and (3, 4). Find the equation of the circle in the form \( x - h \)^2 + \( y - k \)^2 = r^2.
A. \( x - 1 \)^2 + \( y - 2 \)^2 = 16
B. \( x + 1 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 1 \)^2 + \( y + 2 \)^2 = 16
D. \( x + 1 \)^2 + \( y + 2 \)^2 = 16
Question 3
Find the equation of the line pas\sing through the points ( P(1,2) ) and ( Q(3,4) ).
A. \( y = x + 1 \)
B. \( y = 2x - 1 \)
C. \( y = -x + 3 \)
D. \( y = x - 2 \)
Question 4
A die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 5
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A and B).
A. 0.24
B. 0.36
C. 0.48
D. 0.64
Question 6
Solve for x in the matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix} \).
A. x = 1, y = 1
B. x = 2, y = 1
C. x = 1, y = 2
D. x = 2, y = 2
Question 7
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm
Question 8
Find the sum of the first 10 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).
A. 2x + 3x^2 + 4x^3 + ldots + 20x^9
B. 2x + 3x^2 + 4x^3 + ldots + 21x^9
C. 2x + 3x^2 + 4x^3 + ldots + 22x^9
D. 2x + 3x^2 + 4x^3 + ldots + 23x^9
Question 9
A histogram shows the distribution of exam scores for a class of 100 students. The histogram has 5 bars, each representing a different score range. If the tallest bar represents 30 students, what is the probability that a randomly selected student scored between 70 and 80?
A. 0.3
B. 0.4
C. 0.5
D. 0.6
Question 10
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 11
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a range of scores. The heights of the bars are 8, 12, 15, 10, and 5 units. Find the mean score of the class.
A. 10
B. 12
C. 15
D. 18
Question 12
Solve the inequality \( 2x - 5 > 3 \).
A. \( x > 4 \)
B. \( x < 4 \)
C. \( x > 2 \)
D. \( x < 2 \)
Question 13
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. x \leq -1 \text{ or } x \geq \frac{3}{2}
B. x \leq -1 \text{ or } x \leq \frac{3}{2}
C. x \geq -1 \text{ or } x \geq \frac{3}{2}
D. x \geq -1 \text{ or } x \leq \frac{3}{2}
Question 15
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = x \) about the x-axis.
A. \frac{\pi}{6}
B. \frac{\pi}{3}
C. \frac{\pi}{2}
D. \frac{\pi}{4}

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