POST UTME LASU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x: 2^x + 3^x = 5^x.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 2
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. \frac{32\pi}{5}
B. \frac{64\pi}{5}
C. \frac{128\pi}{5}
D. \frac{256\pi}{5}
Question 3
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{6} \)
Question 4
Determine the sum of the infinite geometric series with first term \( a = \frac{1}{2} \) and common ratio \( r = \frac{1}{3} \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{2}{3} \)
Question 5
A particle moves in a straight line with its position given by ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity at time t = 2 seconds.
A. 4t^2 - 10t + 3
B. 6t^2 - 10t + 2
C. 2t^2 - 5t + 1
D. t^2 - 5t + 2
Question 6
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
D. \left\( x - 3 \right \)^2 + \left\( y + 2 \right \)^2 = 16
Question 7
Find the equation of the circle with center ( (2,3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 8
A set of 5 consecutive integers has a median of 8. What is the sum of the integers?
A. 120
B. 125
C. 130
D. 135
Question 9
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that both balls are blue?
A. 1/8
B. 1/7
C. 1/6
D. 1/5
Question 10
Evaluate the definite integral \( int_{0}^{1} x^2 , dx \).
A. \( \frac{1}{3} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{4} \)
Question 11
Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ldots ).
A. ( 62 )
B. ( 64 )
C. ( 66 )
D. ( 68 )
Question 12
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 13
Find the sum of the first 5 terms of the geometric series \( 2x^2 + 3x + 1 \).
A. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1
B. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1
C. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1
D. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{64}{3} \)
D. \( \frac{128}{3} \)
Question 15
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2 \)
B. \( x = -3 \)
C. \( x = 2 \)
D. \( x = 3 \)

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