POST UTME LASU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = x^3 \sin x ) u\sing the product rule.
A. 3x^2 \sin x + x^3 \cos x
B. x^3 \cos x - 3x^2 \sin x
C. x^2 \sin x + 3x^2 \cos x
D. x^3 \cos x + 3x^2 \sin x
Question 2
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 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 4
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 5
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 6
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]
Question 7
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 8
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( x in \( -infty, -3 \ \) cup (2, infty) )
B. \( x in \( -infty, -3 \ \) cup (3, infty) )
C. \( x in \( -infty, -2 \ \) cup (2, infty) )
D. \( x in \( -infty, -2 \ \) cup (3, infty) )
Question 9
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 10
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ).
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
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
Find the derivative of ( 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{x}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-x}{\( x^2 + 1 \ \)^2} )
Question 14
Find the value of x in the equation \( \frac{x}{3} - 2 = 1 \).
A. 9
B. 11
C. 13
D. 15
Question 15
Two events A and B are indep\endent. If P(A) = 0.3 and P(B) = 0.4, find P\( A \cap B \).
A. 0.12
B. 0.24
C. 0.36
D. 0.48

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