POST UTME PAN-ATLANTIC UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix} \).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 2
A right-angled triangle has a hypotenuse of 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.5 cm
C. 8.66 cm
D. 10 cm
Question 3
A s\tandard six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{4}
Question 4
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x, & 0 < x < 1 \ 0, & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2, & 0 < y < 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that \( X + Y < 1 \).
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 5
A company produces two products, A and B. The profit from the production of product A is ₦120 per unit, while the profit from the production of product B is ₦180 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?
A. ₦48,000
B. ₦54,000
C. ₦60,000
D. ₦66,000
Question 6
Solve the system of linear equations u\sing matrices: \( egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} \).
A. \( egin{pmatrix} 1 \ 2 \end{pmatrix} \)
B. \( egin{pmatrix} 2 \ -1 \end{pmatrix} \)
C. \( egin{pmatrix} 3 \ -2 \end{pmatrix} \)
D. \( egin{pmatrix} 4 \ -3 \end{pmatrix} \)
Question 7
Solve the quadratic equation: \( x^2 + 4x + 4 = 0 \).
A. \begin{cases} x = -2 \end{cases}
B. \begin{cases} x = 2 \end{cases}
C. \begin{cases} x = -1 \end{cases}
D. \begin{cases} x = 1 \end{cases}
Question 8
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. ( 13 )
B. ( 15 )
C. ( 17 )
D. ( 19 )
Question 9
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
A. -1
B. 1
C. 2
D. 3
Question 10
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. 0
B. \frac{pi}{2}
C. \pi
D. \frac{3pi}{2}
Question 11
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \].
A. -120
B. -150
C. -180
D. -200
Question 12
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30 cm³
B. 40 cm³
C. 50 cm³
D. 60 cm³
Question 13
Convert the \fraction [ \frac{3}{8} ] to base 6.
A. 101
B. 110
C. 111
D. 1000
Question 14
Solve for x in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 1
D. 2
Question 15
Let ( f(x) = egin{cases} x^2, & x < 0 \ x^3, & x \geq 0 \end{cases} ). Find the value of \( \int_{-1}^{1} f\( x \ \) \, dx ).
A. 0
B. 1
C. 2
D. 3

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