POST UTME BOWEN UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 2
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
A. 13
B. 15
C. 17
D. 19
Question 3
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. \boxed{x^2 + y^2 - 12x - 8y + 36 = 0}
B. x^2 + y^2 - 10x - 6y + 20 = 0
C. x^2 + y^2 - 14x - 10y + 40 = 0
D. x^2 + y^2 - 16x - 12y + 48 = 0
Question 4
Find the derivative of the function [f(x)=\frac{x^2+2x-3}{x^2-4}].
A. \frac{2x+2}{\( x^2-4 \)^2}
B. \frac{2x+2}{x^2-4}
C. \frac{2x-2}{x^2-4}
D. \frac{2x-2}{\( x^2-4 \)^2}
Question 5
In the circuit below, find the current through the 2-ohm resistor.
A. 1 A
B. 2 A
C. 3 A
D. 4 A
Question 6
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. 48\pi
B. 64\pi
C. 72\pi
D. 80\pi
Question 7
Solve the equation \( x^2 + 2x - 3 = 0 \).
A. \begin{pmatrix} x = -3 \\ x = 1 \end{pmatrix}
B. \begin{pmatrix} x = 1 \\ x = -3 \end{pmatrix}
C. \begin{pmatrix} x = -1 \\ x = 3 \end{pmatrix}
D. \begin{pmatrix} x = 3 \\ x = -1 \end{pmatrix}
Question 8
A cylindrical water \tank has a height of 10m and a radius of 4m. If the water level is 6m, find the volume of water in the \tank.
A. 1000\pi
B. 1200\pi
C. 1500\pi
D. 1800\pi
Question 9
Solve the inequality \( x+2 \ \)^2-4\( x-1 \)geq 0).
A. $x\leq -6$ or $x\geq 2$
B. $x\leq -2$ or $x\geq 4$
C. $x\leq -4$ or $x\geq 6$
D. $x\leq -8$ or $x\geq 8$
Question 10
A fair six-sided die is rolled. What is the probability that the result is a prime number?
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 11
Solve for ( x ) in the equation \( \sin \( 2x \ \) = \cos (x) ).
A. \( x = \frac{\pi}{4} \)
B. \( x = \frac{\pi}{2} \)
C. \( x = \frac{3\pi}{4} \)
D. \( x = \frac{\pi}{6} \)
Question 12
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \) u\sing the quadratic formula.
A. \boxed{x \leq -\frac{3}{2} \text{ or } x \geq \frac{1}{2}}
B. x \leq -\frac{3}{2} \text{ or } x \geq -\frac{1}{2}
C. x \leq -\frac{1}{2} \text{ or } x \geq \frac{3}{2}
D. x \leq -\frac{1}{2} \text{ or } x \geq -\frac{3}{2}
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( 16 + 12 - 8 = 20 \)
B. \( 8 + 12 - 8 = 12 \)
C. \( 16 + 12 - 8 = 20 \)
D. \( 8 + 12 - 8 = 12 \)
Question 14
Find the area under the curve [y=x^2-4x+3] from x=0 to x=3.
A. \frac{9}{2}
B. \frac{15}{2}
C. \frac{21}{2}
D. \frac{27}{2}
Question 15
Solve the equation [ x^2 + 4x + 4 = 0 ].
A. -2
B. -1
C. 1
D. 2

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