POST UTME EKSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In the diagram below, [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ] is a matrix. Find the determinant of the matrix.
A. 0
B. 1
C. 2
D. 3
Question 2
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( \cos^2 x \)
C. \( \sin^2 x \)
D. \( \cos x \)
Question 3
Find the equation of the circle with center at ( (2, 3) ) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 20
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 24
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 28
Question 4
Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ) for ( x ).
A. \( x > 10 \)
B. \( x < -10 \)
C. \( x > -10 \)
D. \( x < 10 \)
Question 5
Find the value of ( x ) in the equation \( x^3 - 2x^2 - 5x + 6 = 0 \).
A. 1
B. -1
C. 2
D. -2
Question 6
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{1}{\( x^2 + 1 \)^2}
D. \frac{-1}{\( x^2 + 1 \)^2}
Question 7
Find the sum of the first 10 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = \frac{1}{2} \).
A. \frac{1023}{512}
B. \frac{1024}{512}
C. \frac{1025}{512}
D. \frac{1026}{512}
Question 8
A sequence is defined as [ a_n = 2n^2 + 3n - 1 ]. Find the sum of the first 5 terms of the sequence.
A. 105
B. 115
C. 125
D. 135
Question 9
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \) for ( x ) and ( y ).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)
Question 10
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 2
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 1
C. \( x - 4 \)^2 + \( y - 5 \)^2 = 4
D. \( x - 5 \)^2 + \( y - 6 \)^2 = 9
Question 11
A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.
A. 6
B. 8
C. 10
D. 12
Question 12
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 13
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability P\( X > Y \).
A. 0.25
B. 0.5
C. 0.75
D. 1.0
Question 14
Solve the equation [ 2x^2 + 5x - 3 = 0 ] u\sing the quadratic formula.
A. -1
B. 1
C. -3
D. 3
Question 15
Find the area under the curve \( y = x^2 \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{\pi}{2} \).
A. \frac{1}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}

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