POST UTME COAL CITY UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 2
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = 0, pi, 2pi \)
B. \( x = \frac{pi}{2}, \frac{3pi}{2} \)
C. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)
D. \( x = \frac{pi}{6}, \frac{5pi}{6}, \frac{7pi}{6}, \frac{11pi}{6} \)
Question 3
A fair six-sided die is rolled. If the outcome is an even number, a second die is rolled. Find the probability that the sum of the two dice is 7.
A. \( \frac{1}{12} \)
B. \( \frac{1}{6} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{3} \)
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) for ( x ) in the interval \( -infty, infty \ \) ).
A. \frac{-5 + \sqrt{49}}{4}
B. \frac{-5 - \sqrt{49}}{4}
C. \frac{-5 + \sqrt{25 + 24}}{4}
D. \frac{-5 - \sqrt{25 + 24}}{4}
Question 5
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
A. 0
B. 10
C. 20
D. 30
Question 6
A rec\tangular box has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the box in cubic centimeters.
A. 400
B. 500
C. 600
D. 800
Question 7
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 4.
A. 40
B. 60
C. 80
D. 100
Question 8
Solve the system of linear equations u\sing substitution: [ \begin{cases} x + 2y = 6 \\ 2x - 3y = -3 \end{cases} \].
A. \begin{pmatrix} x = 2 \\ y = 2 \end{pmatrix}
B. \begin{pmatrix} x = 3 \\ y = 1 \end{pmatrix}
C. \begin{pmatrix} x = 4 \\ y = 0 \end{pmatrix}
D. \begin{pmatrix} x = 5 \\ y = -1 \end{pmatrix}
Question 9
A particle moves along the x-axis with a velocity given by $v(t) = 2t^2 - 5t + 1$. Find the acceleration of the particle at time $t = 2$ seconds.
A. 4
B. -10
C. -6
D. 6
Question 10
Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, 54, ... ).
A. 126
B. 128
C. 130
D. 132
Question 11
Find the volume of the sphere with radius \( r = 4 \) cm.
A. \( \frac{4}{3} pi \( 4 \ \)^3 )
B. \( \frac{4}{3} pi \( 4 \ \)^2 )
C. \( \frac{4}{3} pi \( 4 \ \) )
D. \( \frac{4}{3} pi \( 4 \ \)^2 )
Question 12
Find the sum of the first five terms of the geometric series \( 2 + 6 + 18 + 54 + ldots \).
A. 242
B. 242
C. 242
D. 242
Question 13
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and \( -2, 3 \).
A. \( x^2 + y^2 + 4x - 8y + 5 = 0 \)
B. \( x^2 + y^2 - 4x + 8y + 5 = 0 \)
C. \( x^2 + y^2 + 8x - 4y + 5 = 0 \)
D. \( x^2 + y^2 - 8x + 4y + 5 = 0 \)
Question 14
Find the value of ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{3\pi}{4}
Question 15
Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...
A. 120
B. 150
C. 180
D. 200

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