POST UTME AFE BABALOLA UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
If \vec{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} and \vec{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}, find the cross product \vec{a} \times \vec{b}.
A. \begin{pmatrix} -1 \ 8 \ -5 \end{pmatrix}
B. \begin{pmatrix} 1 \ -8 \ 5 \end{pmatrix}
C. \begin{pmatrix} -1 \ -8 \ 5 \end{pmatrix}
D. \begin{pmatrix} 1 \ 8 \ -5 \end{pmatrix}
Question 2
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. \( y = -2x + 1 \)
D. \( y = -2x - 1 \)
Question 3
Solve the equation \(\sin^2 x + \cos^2 x = 1\) for x in the interval \([0, 2\pi]\).
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{3\pi}{4}
D. \pi
Question 4
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. ( 1 )
B. \( -1 \)
C. ( 2 )
D. ( 3 )
Question 5
In the diagram below, a right-angled triangle has a hypotenuse of length 10 cm. If the length of the vertical leg is 6 cm, find the length of the horizontal leg u\sing the Pythagorean theorem.
A. \( x = \sqrt{100 - 36} = \sqrt{64} = 8 \) cm
B. \( x = \sqrt{100 + 36} = \sqrt{136} = 11.66 \) cm
C. \( x = \sqrt{100 - 6^2} = \sqrt{64} = 8 \) cm
D. \( x = \sqrt{100 + 6^2} = \sqrt{136} = 11.66 \) cm
Question 6
Find the value of ( x ) in the equation \( x^2 + 2x - 3 = 0 \).
A. \( x = -3 \) or \( x = 1 \)
B. \( x = -1 \) or \( x = 3 \)
C. \( x = 1 \) or \( x = -3 \)
D. \( x = -1 \) or \( x = -3 \)
Question 7
Solve for x in the equation [ 2^x + 3^x = 5^x ].
A. 1
B. 2
C. 3
D. 4
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
C. \( x < -\frac{1}{2} \) or \( x < \frac{3}{2} \)
D. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 9
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg u\sing the Pythagorean theorem.
A. \( x = \sqrt{100 - 36} = \sqrt{64} = 8 \) cm
B. \( x = \sqrt{100 + 36} = \sqrt{136} = 11.66 \) cm
C. \( x = \sqrt{100 - 6^2} = \sqrt{64} = 8 \) cm
D. \( x = \sqrt{100 + 6^2} = \sqrt{136} = 11.66 \) cm
Question 10
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 14 )
B. ( 28 )
C. ( 42 )
D. ( 56 )
Question 11
A solid cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.
A. 523.6
B. 523.6
C. 523.6
D. 523.6
Question 12
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experimenter wins a prize. If the number rolled is odd, the experimenter loses a prize. If the probability of winning a prize is 0.5, find the probability of lo\sing a prize.
A. \( P\( \text{winning} \ \) = 0.5 implies P\( \text{lo\sing} \) = 0.5 )
B. \( P\( \text{winning} \ \) = 0.5 implies P\( \text{lo\sing} \) = 0.25 )
C. \( P\( \text{winning} \ \) = 0.5 implies P\( \text{lo\sing} \) = 0.75 )
D. \( P\( \text{winning} \ \) = 0.5 implies P\( \text{lo\sing} \) = 0.25 )
Question 13
A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.3. If Y is another random variable such that Y = 2X - 1, find P\( Y = 3 \).
A. 0.4
B. 0.3
C. 0.2
D. 0.1
Question 14
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. x^2 + y^2 - 6x - 4y + 12 = 0
B. x^2 + y^2 + 2x - 4y + 5 = 0
C. x^2 + y^2 + 4x + 2y - 6 = 0
D. x^2 + y^2 - 2x + 4y - 8 = 0
Question 15
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. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³

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