POST UTME BABCOCK UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( y = 2 \) about the x-axis.
A. \( \frac{8}{3} pi \)
B. \( \frac{16}{3} pi \)
C. \( \frac{32}{3} pi \)
D. \( \frac{64}{3} pi \)
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. \text{Volume: } \frac{16}{3} \pi
B. \text{Volume: } \frac{32}{3} \pi
C. \text{Volume: } \frac{64}{3} \pi
D. \text{Volume: } \frac{128}{3} \pi
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( -\frac{1}{2}, \infty \right \)
D. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
Question 4
Solve the system of equations: \( egin{cases} x + y + z = 6 \ 2x - 3y + z = 3 \ x - 2y + 3z = 2 \end{cases} \).
A. x = 1, y = 2, z = 3
B. x = 2, y = 1, z = 3
C. x = 3, y = 2, z = 1
D. x = 1, y = 3, z = 2
Question 5
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. 0
B. -2
C. -4
D. 2
Question 6
Find the equation of the circle with center at (2, 3) and radius 4.
A. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16
C. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 7
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. \text{Solution: } x \leq -1 \text{ or } x \geq \frac{3}{2}
B. \text{Solution: } x < -1 \text{ or } x > \frac{3}{2}
C. \text{Solution: } x \leq -1 \text{ or } x < \frac{3}{2}
D. \text{Solution: } x > -1 \text{ or } x \geq \frac{3}{2}
Question 8
A circle has a radius of 4. Find the area of the circle.
A. 16
B. 25.13
C. 50.27
D. 100.54
Question 9
Find the value of \( \log_{10} \( x^2 \) given that \( \log_{10} x = 2 \).
A. \text{Value: } 4
B. \text{Value: } 6
C. \text{Value: } 8
D. \text{Value: } 10
Question 10
A rec\tangular prism has a length of 8, a width of 5, and a height of 3. Find the volume of the prism.
A. 120
B. 150
C. 180
D. 200
Question 11
A rec\tangular box has a length of ( 6 ) cm, a width of ( 4 ) cm, and a height of ( 3 ) cm. Find the volume of the box.
A. ( 72 ) cm\( ^3 \)
B. ( 48 ) cm\( ^3 \)
C. ( 36 ) cm\( ^3 \)
D. ( 24 ) cm\( ^3 \)
Question 12
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3 or 5?
A. 1/3
B. 1/2
C. 2/3
D. 5/6
Question 13
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that they are of different colors?
A. 1/2
B. 1/3
C. 2/5
D. 3/7
Question 14
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 cm
B. 6 cm
C. 10 cm
D. 12 cm
Question 15
Solve the inequality \( |x-2| geq 3 \).
A. \( x leq -1 \) or ( x geq 5 )
B. ( x leq 1 ) or ( x geq 5 )
C. \( x leq -1 \) or ( x geq 4 )
D. ( x leq 1 ) or ( x geq 4 )

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