POST UTME LASU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has equation \(x^2 + y^2 - 6x + 4y - 12 = 0\). Find the center and radius of the circle.
A. \( 3, -2 \), 5
B. (3, 2), 5
C. (2, 3), 5
D. \( 2, -3 \), 5
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 3
A right triangle has legs of length 3 cm and 4 cm. Find the length of the hypotenuse.
A. 5
B. 6
C. 7
D. 8
Question 4
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 5
Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find ( AB ) if it exists.
A. \( egin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix} \)
B. \( egin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix} \)
C. \( egin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix} \)
D. \( egin{bmatrix} 23 & 26 \ 49 & 56 \end{bmatrix} \)
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. 2x
B. -2x
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^2}
Question 7
Solve the equation \( \log_2 \( x^2 + 1 \ \) = 3 ) for ( x ).
A. \( x = 7 \)
B. \( x = -7 \)
C. \( x = 5 \)
D. \( x = -5 \)
Question 8
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 9
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
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 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 11
Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 1 \end{cases} \).
A. {(1, 1)}
B. {\( 1, -1 \)}
C. {\( -1, 1 \)}
D. {\( -1, -1 \)}
Question 12
Simplify the expression \sqrt{64x^6y^4} u\sing the properties of radicals.
A. 8x^3y^2
B. 2^3x^3y^2
C. 2^6x^6y^4
D. 4x^3y^2
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 P\( X + Y < 1 \).
A. 1/2
B. 1/3
C. 2/3
D. 3/4
Question 14
A die is rolled twice. Find the probability that the sum of the two numbers is 7.
A. \( \frac{1}{6} \)
B. \( \frac{1}{12} \)
C. \( \frac{1}{36} \)
D. \( \frac{1}{24} \)
Question 15
Find the sum of the first ( n ) terms of the arithmetic progression \( 2, 5, 8, \ldots \).
A. \frac{n}{2} [2(2) + \( n - 1 \)3]
B. \frac{n}{2} [2(5) + \( n - 1 \)3]
C. \frac{n}{2} [2(8) + \( n - 1 \)3]
D. \frac{n}{2} [2(2) + \( n - 1 \)5]

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