POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a circle of radius 6, a chord of length 8 is drawn. If the chord is ext\ended by 4 units, what is the length of the new chord?
A. 12
B. 10
C. 8
D. 6
Question 2
Find the volume of the solid formed by revolving the region bounded by the curves y = 2x^2, y = 0, and x = 2 about the x-axis.
A. \frac{256\pi}{15}
B. \frac{512\pi}{15}
C. \frac{256\pi}{3}
D. \frac{512\pi}{3}
Question 3
A right-angled triangle has a hypotenuse of length 10 cm and one of the acute angles is 45°. Find the length of the side opposite the 45° angle.
A. 5 cm
B. 7.07 cm
C. 10 cm
D. 15 cm
Question 4
Solve the inequality [ 2x^2 + 5x - 3 > 0 ].
A. x < -1 or x > 3/2
B. x < 1 or x > -3/2
C. x < -3/2 or x > 1
D. x < 3/2 or x > -1
Question 5
Solve the system of equations \( x + y = 3 \) and \( xy = 2 \).
A. x = 2, y = 1
B. x = 1, y = 2
C. x = -1, y = -2
D. x = 2, y = -1
Question 6
A random experiment has two indep\endent events (A) and (B) with probabilities (P(A) = 0.4) and (P(B) = 0.6). Find the probability that both events occur.
A. 0.2
B. 0.24
C. 0.28
D. 0.32
Question 7
A sequence is defined by the formula [ a_n = 2n + 1 ]. Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 8
In a triangle $ABC$, if $\tan A = \frac{1}{3}$ and $\tan B = \frac{1}{2}$, find $\tan C$.
A. \frac{7}{4}
B. \frac{4}{7}
C. \frac{5}{12}
D. \frac{12}{5}
Question 9
Find the derivative of the function [ f(x) = \frac{1}{x^2 + 1} ].
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 10
A survey of 100 students found that 60% of them preferred Mathematics, 20% preferred Science, and 20% preferred English. If 10 students preferred both Mathematics and Science, and 5 students preferred both Mathematics and English, find the number of students who preferred only Mathematics.
A. 40
B. 45
C. 50
D. 55
Question 11
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. x in \( -infty, -3 \) cup (3, infty)
B. x in \( -infty, -3 \) cup (3, infty) cup (0, 3)
C. x in \( -infty, -3 \) cup (0, 3)
D. x in \( -infty, -3 \) cup (3, infty) cup \( -3, 0 \)
Question 12
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. If 3 more numbers are added to the set, the new mean is 12. What is the sum of the 3 additional numbers?
A. 30
B. 60
C. 90
D. 120
Question 13
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).
A. 10
B. 12
C. 14
D. 16
Question 14
A rec\tangular solid has dimensions 5 cm, 6 cm, and 7 cm. Find the volume of the solid.
A. 210 cm^3
B. 240 cm^3
C. 270 cm^3
D. 300 cm^3
Question 15
Find the value of x in the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. 2
B. -3
C. -2
D. 1

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