POST UTME LEAD CITY UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $x$ in the equation $\log_{10} \( x^2 \) = 4$.
A. 2
B. 4
C. 8
D. 16
Question 2
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
A. 1
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{3}{4} \)
Question 3
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the third side?
A. 8
B. 10
C. 12
D. 14
Question 4
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. \( \frac{2x\( x^2 + 1 \ \) - x^2(2x)}{\( x^2 + 1 \)^2} )
B. \( \frac{2x\( x^2 + 1 \ \) + x^2(2x)}{\( x^2 + 1 \)^2} )
C. \( \frac{2x\( x^2 + 1 \ \) - x^2(2x)}{\( x^2 + 1 \)^2} )
D. \( \frac{2x\( x^2 + 1 \ \) + x^2(2x)}{\( x^2 + 1 \)^2} )
Question 5
A cylindrical \tank has a height of 10 m and a radius of 4 m. If the \tank is filled with water to a height of 6 m, find the volume of water in the \tank.
A. 1500\pi
B. 1200\pi
C. 1000\pi
D. 800\pi
Question 6
The mean of a set of five numbers is 15. If one of the numbers is 10, find the sum of the remaining four numbers.
A. 50
B. 60
C. 70
D. 80
Question 7
Find the vector [ mathbf{a} ] such that [ mathbf{a} cdot mathbf{b} = 10 ] and [ mathbf{a} cdot mathbf{c} = 5 ], where [ mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix} ] and [ mathbf{c} = egin{pmatrix} 1 \ 2 \end{pmatrix} ].
A. \begin{pmatrix} 1 \ 2 \end{pmatrix}
B. \begin{pmatrix} 2 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ 4 \end{pmatrix}
D. \begin{pmatrix} 4 \ 5 \end{pmatrix}
Question 8
Find the value of $\int_{0}^{\pi} \sin^2(x) \cos^2(x) dx$.
A. 0
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}
Question 9
A sequence is defined by the recurrence relation [ a_n = 2a_{n-1} + 3 ] with initial term [ a_1 = 2 ]. Find the sum of the first five terms of the sequence.
A. 55
B. 65
C. 75
D. 85
Question 10
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 0
B. -2
C. 2
D. -1
Question 11
Find the value of $x$ in the equation $2^x + 2^{x+2} = 2^{x+3}$.
A. 1
B. 2
C. 3
D. 4
Question 12
Solve the inequality $\frac{1}{x-2} + \frac{1}{x+2} \leq \frac{1}{2}$.
A. x \in \( -\infty, -2 \) \cup \( 2, \infty \)
B. x \in \( -\infty, -2 \) \cup (2, 4]
C. x \in \( -\infty, -2 \) \cup (2, \infty]
D. x \in \( -\infty, -2] \cup \( 2, \infty \ \)
Question 13
A survey of 100 people found that 60% of them preferred coffee, 20% preferred tea, and 20% preferred neither. Find the probability that a person chosen at random prefers coffee.
A. 0.6
B. 0.4
C. 0.3
D. 0.2
Question 14
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{array} ].
A. -3
B. 3
C. -1
D. 1
Question 15
Solve the system of linear equations \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( egin{bmatrix} 1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} 2 \ 3 \end{bmatrix} \)
C. \( egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} 4 \ 5 \end{bmatrix} \)

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