POST UTME PAN-ATLANTIC UNIVERSITY 2017 Mathematics | Objective

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Question 1
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 2
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 3
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \ \) for ( x ) in the interval \( [0, 2\pi] \).
A. \left\{ 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \right\}
B. \left\{ 0, \frac{\pi}{4}, \frac{3\pi}{4}, \pi, \frac{5\pi}{4}, \frac{7\pi}{4} \right\}
C. \left\{ 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \right\}
D. \left\{ 0, \frac{\pi}{4}, \frac{3\pi}{4}, \pi, \frac{5\pi}{4}, \frac{7\pi}{4} \right\}
Question 4
A rec\tangular box has dimensions 5 cm, 8 cm, and 3 cm. Find the volume of the box in cubic centimeters.
A. 120
B. 150
C. 180
D. 200
Question 5
Solve the equation \( 2^x + 3^x = 5^x \) for ( x ).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)
Question 6
Solve the inequality \( 2x - 5 > 3 \)
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 7
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 6 \) and \( mathbf{a} cdot mathbf{c} = 3 \), where \( mathbf{b} = egin{bmatrix} 2 \ 3 \end{bmatrix} \) and \( mathbf{c} = egin{bmatrix} 1 \ 4 \end{bmatrix} \)
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 2 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 8
In a certain number base, the representation of the number 27 is 101. If the base is denoted by 'b', find the value of 'b' u\sing the equation \( b^2 - 5b - 6 = 0 \).
A. 4
B. 6
C. 8
D. 10
Question 9
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )
Question 10
A rec\tangular prism has a length of ( 10 ) cm, a width of ( 5 ) cm, and a height of ( 3 ) cm. Find its volume.
A. ( 150 ) cm\( ^3 \)
B. ( 300 ) cm\( ^3 \)
C. ( 500 ) cm\( ^3 \)
D. ( 1000 ) cm\( ^3 \)
Question 11
Find the magnitude of the vector \( \vec{a} = \langle 3, 4 \rangle \ \) and the vector \( \vec{b} = \langle -2, 1 \rangle \ \).
A. \( \sqrt{29} \)
B. \( \sqrt{5} \)
C. \( \sqrt{2} \)
D. \( \sqrt{3} \)
Question 12
Find the value of \( \sin (2x) \) when \( x = \frac{\pi}{6} \).
A. \frac{1}{2}
B. \frac{\sqrt{3}}{2}
C. \frac{\sqrt{2}}{2}
D. \frac{\sqrt{6}}{2}
Question 13
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 5 \ 1 & 2 & 3 \ 4 & 1 & 2 \end{array} ].
A. 0
B. 1
C. 2
D. 3
Question 14
Solve the equation \( x^2 + 4x + 4 = 0 \)
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 15
A matrix ( A ) is given by \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of ( A ).
A. 0
B. 2
C. 4
D. 6

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