POST UTME CALEB UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a circle of radius 5 units, a chord of length 8 units subt\ends an angle of 60 degrees at the centre. Find the area of the sector.
A. 20π
B. 30π
C. 40π
D. 50π
Question 2
Solve the equation \(x^2 + 5x + 6 = 0\) u\sing the quadratic formula.
A. \(-3\)
B. \(-2\)
C. \(1\)
D. \(3\)
Question 3
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from the set is greater than 12.
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 4
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{-2x}{\( x^2 + 1 \)^3}
D. \frac{2x}{\( x^2 + 1 \)^2}
Question 5
Solve the inequality \( left| x - 2 \right| geq 3 \).
A. \( x leq -1 \) or ( x geq 5 )
B. ( x leq 1 ) or ( x geq 5 )
C. \( x leq -1 \) or ( x geq 4 )
D. ( x leq 1 ) or ( x geq 4 )
Question 6
A histogram has a mean of 25 and a s\tandard deviation of 6. If the histogram has 12 bars, what is the range of the histogram?
A. 20
B. 30
C. 40
D. 50
Question 7
Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find ( AB ) u\sing the rule of Sarrus.
A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
B. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
C. \begin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix}
D. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}
Question 8
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 9
A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.
A. 256\pi cm^3
B. 512\pi cm^3
C. 768\pi cm^3
D. 1024\pi cm^3
Question 10
Find the area of the triangle formed by the points ( (0, 0) ), ( (3, 4) ), and ( (6, 0) ).
A. 12
B. 15
C. 18
D. 20
Question 11
In a circle of radius 4 units, a chord of length 6 units subt\ends an angle of 90 degrees at the centre. Find the length of the chord.
A. 4
B. 5
C. 6
D. 7
Question 12
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8 cm
B. 12 cm
C. 14 cm
D. 16 cm
Question 13
Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), what is the probability that both events occur?
A. 0.1
B. 0.2
C. 0.3
D. 0.4
Question 14
A sequence \( a_n \) is defined as \( a_n = \frac{1}{n} \). Find the sum of the first 5 terms of the sequence.
A. 1
B. 2
C. 3
D. 4
Question 15
Solve the inequality \(2x - 5 > 3x + 2\).
A. \(x < -\frac{7}{2}\)
B. \(x > -\frac{7}{2}\)
C. \(x < \frac{7}{2}\)
D. \(x > \frac{7}{2}\)

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