POST UTME CALEB UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector ( mathbf{a} ) has a magnitude of 5 and a direction of 30°. If a vector ( mathbf{b} ) has a magnitude of 3 and a direction of 60°, what is the magnitude of the sum of the two vectors?
A. 4
B. 5
C. 6
D. 7
Question 2
A set ( A ) contains 5 elements. If ( A ) has 3 subsets, what is the number of elements in the power set of ( A )?
A. 10
B. 15
C. 20
D. 25
Question 3
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 4
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). If \( a = 2 \) and \( b = 3 \), what is the result of the operation?
A. 13
B. 14
C. 15
D. 16
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 sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first five terms of the sequence.
A. 55
B. 65
C. 75
D. 85
Question 7
A survey of 100 students found that 60% of them preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the number of students who preferred only Mathematics?
A. 36
B. 40
C. 42
D. 44
Question 8
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 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
Let \( S = {1, 2, 3, 4, 5, 6} \). Find the number of subsets of ( S ) that contain exactly three elements.
A. 10
B. 15
C. 20
D. 25
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
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 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )
B. \( \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \ \) )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )
Question 14
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 15
Find the value of ( x ) in the equation \( 2^x = 16 \).
A. \( x = 2 \)
B. \( x = 4 \)
C. \( x = 1 \)
D. \( x = 3 \)

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