POST UTME LASU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation [ 2x^2 + 5x - 3 = 0 ] u\sing the quadratic formula.
A. -1
B. 1
C. 2
D. 3
Question 2
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. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 3
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 4
Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = 4 \).
A. \( mathbf{v} = 3mathbf{i} + 4mathbf{j} \)
B. \( mathbf{v} = 4mathbf{i} + 3mathbf{j} \)
C. \( mathbf{v} = 3mathbf{i} - 4mathbf{j} \)
D. \( mathbf{v} = 4mathbf{i} - 3mathbf{j} \)
Question 5
Solve for x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 6
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 = x - 1
D. y = x + 1
Question 7
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \( \frac{1}{2} \)
B. \( \frac{2}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{4}{5} \)
Question 8
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 9
Solve for x in the equation \( 2^x + 2^{x+1} = 2^{x+2} + 1 \).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 10
Let A be a 2x2 matrix given by [A = egin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix}]. Find the determinant of A.
A. 1
B. 2
C. 3
D. 4
Question 11
A random variable ( X ) has probability density function ( f(x) = \frac{1}{2}e^{-|x|} ). Find the expected value of ( X ).
A. ( E(X) = 0 )
B. ( E(X) = 1 )
C. ( E(X) = -1 )
D. ( E(X) = 2 )
Question 12
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 192\pi cm^3
D. 256\pi cm^3
Question 13
A circle with center ( C(2, 3) ) and radius \( r = 4 \) has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 ). Find the equation of the line pas\sing through the point ( P(6, 7) ) that is \tangent to the circle.
A. \( y - 7 = \frac{1}{4}\( x - 6 \ \) )
B. \( y - 7 = -\frac{1}{4}\( x - 6 \ \) )
C. \( y - 7 = \frac{1}{2}\( x - 6 \ \) )
D. \( y - 7 = -\frac{1}{2}\( x - 6 \ \) )
Question 14
Evaluate the integral [ \int_0^1 x^2 dx ].
A. 1
B. 2
C. 3
D. 4
Question 15
A population of bacteria grows according to the \logistic equation \( \frac{dP}{dt} = rP left\( 1 - \frac{P}{K} \right \ \) ), where \( r = 0.5 \) and \( K = 100 \). Find the equilibrium population.
A. \( P = 0 \)
B. \( P = 50 \)
C. \( P = 100 \)
D. \( P = 200 \)

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