POST UTME DELSU 2018 Mathematics | Objective

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Question 1
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 2
A rec\tangular box has dimensions ( x ) cm by ( y ) cm by ( z ) cm. If the surface area of the box is 600 cm^2, and the volume is 1200 cm^3, find the value of \( x + y + z \).
A. 20
B. 25
C. 30
D. 35
Question 3
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the cross product formula.
A. \( egin{pmatrix} 6 \ -4 \end{pmatrix} \)
B. \( egin{pmatrix} -6 \ 4 \end{pmatrix} \)
C. \( egin{pmatrix} 4 \ 6 \end{pmatrix} \)
D. \( egin{pmatrix} -4 \ -6 \end{pmatrix} \)
Question 4
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 5
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 6
Solve the trigonometric equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) u\sing the Pythagorean identity.
A. \( \sin\( x \ \) = pm 1 )
B. \( \cos\( x \ \) = pm 1 )
C. \( \sin\( x \ \) = pm \frac{1}{\sqrt{2}} )
D. \( \cos\( x \ \) = pm \frac{1}{\sqrt{2}} )
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > 1 \)
C. \( x < 1 \) or \( x > -\frac{3}{2} \)
D. \( x < -\frac{3}{2} \) or \( x < 1 \)
Question 8
A number is represented in base 8 as 1234. What is the value of this number in base 10?
A. 512
B. 1024
C. 1536
D. 2048
Question 9
A vector \( \vec{a} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \) is given. Find the magnitude of the vector.
A. 3
B. 4
C. 5
D. 6
Question 10
A particle moves in a straight line with a velocity of \( mathbf{v} = 2t , mathbf{i} + 3t^2 , mathbf{j} \) m/s, where ( t ) is in seconds. Find the position vector of the particle at time \( t = 2 \) seconds.
A. 8\mathbf{i} + 12\mathbf{j}
B. 4\mathbf{i} + 12\mathbf{j}
C. 8\mathbf{i} + 8\mathbf{j}
D. 4\mathbf{i} + 8\mathbf{j}
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -3 or x > 1
B. x < -1 or x > 3
C. x < 1 or x > 3
D. x < -3 or x < 1
Question 12
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 14
Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ).
A. 6x - 2
B. 6x + 2
C. 3x^2 - 2
D. 3x^2 + 2
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}

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