POST UTME COAL CITY UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Find the median of the data set ( { 1, 3, 5, 7, 9 } ).
A. 5
B. 7
C. 9
D. 11
Question 4
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 2
D. y = x + 2
Question 5
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 6
Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{pmatrix} \).
A. 14
B. -14
C. 21
D. -21
Question 7
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 8
Solve the equation $x^2 + 5x + 6 = 0$ u\sing the quadratic formula.
A. x = -2 or x = -3
B. x = 2 or x = 3
C. x = -3 or x = 2
D. x = 3 or x = -2
Question 9
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 10
Find the value of $\frac{d}{dx}\left\( \frac{1}{x^2}\right \)$.
A. -\frac{2}{x^3}
B. +\frac{2}{x^3}
C. -\frac{1}{x^3}
D. +\frac{1}{x^3}
Question 11
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
A. \( egin{pmatrix} -\frac{11}{13} \ \frac{24}{13} \end{pmatrix} \)
B. \( egin{pmatrix} \frac{11}{13} \ -\frac{24}{13} \end{pmatrix} \)
C. \( egin{pmatrix} -\frac{24}{13} \ \frac{11}{13} \end{pmatrix} \)
D. \( egin{pmatrix} \frac{24}{13} \ -\frac{11}{13} \end{pmatrix} \)
Question 12
A firm produces two products, A and B. Product A requires 2 hours of labor and 3 hours of capital, while product B requires 3 hours of labor and 2 hours of capital. If the firm has 120 hours of labor and 100 hours of capital, how many units of product A and product B should the firm produce to maximize profit?
A. (20, 30)
B. (30, 20)
C. (25, 25)
D. (35, 15)
Question 13
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 14
Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...
A. 120
B. 150
C. 180
D. 200
Question 15
Let \( S = { 1, 2, 3, 4, 5 } \). Find the number of subsets of ( S ) that contain exactly three elements.
A. 10
B. 15
C. 20
D. 25

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