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POST UTME BOWEN UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\)

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 2 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\)

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 3 View Details

Find the value of (\(12\theta\) given that \\((\)12theta\(\(1\theta = \frac{3}{5}\) and 1\\(theta =\)\(\frac{4}{5}\)\)

Correct A. \(\frac{24}{25}\)\)

B. \(\frac{16}{25}\)\)

C. \(\frac{20}{25}\)\)

D. \(\frac{12}{25}\)\)

Correct Answer: A

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Question 4 View Details

Solve the system of linear equations \(egin{cases} x + y = 2 \ 2x - y = 3 \end{cases}\)

Correct A. (1, 1)

B. (2, 0)

C. \(3, -1\)

D. \(4, -2\)

Correct Answer: A

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Question 5 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) )

Correct A. \(y = 2x + 1\)

B. \(y = 2x - 1\)

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 6 View Details

A cylindrical \tank with a radius of 5m and height of 10m is filled with water. Find the volume of water in the \tank, given that the water level is 8m above the base of the \tank.

A. 160\pi \text{m}^3

Correct B. 200\pi \text{m}^3

C. 240\pi \text{m}^3

D. 280\pi \text{m}^3

Correct Answer: B

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Question 7 View Details

Solve the equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.

Correct A. \(x = -2 \pm \sqrt{2}\)

B. \(x = -2 \pm \sqrt{3}\)

C. \(x = -2 \pm \sqrt{4}\)

D. \(x = -2 \pm \sqrt{5}\)

Correct Answer: A

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Question 8 View Details

A circle has a diameter of 14cm. Find the area of the circle.

A. 22\pi \text{cm}^2

Correct B. 49\pi \text{cm}^2

C. 98\pi \text{cm}^2

D. 196\pi \text{cm}^2

Correct Answer: B

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Question 9 View Details

A rectangular prism has a length of 6cm, width of 4cm, and height of 3cm. Find the volume of the prism.

A. 48 \text{cm}^3

Correct B. 72 \text{cm}^3

C. 96 \text{cm}^3

D. 108 \text{cm}^3

Correct Answer: B

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Question 10 View Details

A cone has a radius of 4cm and height of 6cm. Find the volume of the cone.

A. 16\pi \text{cm}^3

Correct B. 32\pi \text{cm}^3

C. 48\pi \text{cm}^3

D. 64\pi \text{cm}^3

Correct Answer: B

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Question 11 View Details

Let \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) and \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\). Find ( det(AB) ) if ( det(A) = -1 ) and ( det(B) = 2 ).

Correct A. -2

B. 2

C. 4

D. -4

Correct Answer: A

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Question 12 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 13 View Details

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?

Correct A. \(\frac{3}{8}\)\)

B. \(\frac{1}{4}\)\)

C. \(\frac{3}{14}\)\)

D. \(\frac{1}{7}\)\)

Correct Answer: A

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Question 14 View Details

Find the derivative of ( f(x) = \(3x^2 - 2x + 1\) ) using the chain rule.

Correct A. 6x - 2

B. \(3x^2 - 2\)

C. \(2x^2 + 1\)

D. \(x^2 - 1\)

Correct Answer: A

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Question 15 View Details

Solve the equation \(\log_2 x \\) + \log_2\(x^2 = 5\) ).

Correct A. \(x = 16\)

B. \(x = 8\)

C. \(x = 4\)

D. \(x = 2\)

Correct Answer: A

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Question 16 View Details

A random sample of 25 students from a large population has a mean height of 175 cm with a standard deviation of 5 cm. Calculate the probability that a randomly selected student from this sample has a height greater than 180 cm.

A. 0.1587

B. 0.3413

Correct C. 0.4772

D. 0.6915

Correct Answer: C

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Question 17 View Details

Solve for x in the equation \(\log_{10} x^2\)\(= 4\)\).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 18 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \(x+2\)^2 + \(y-3\)^\(2 = 16\)

B. \(x-2\)^2 + \(y+3\)^\(2 = 16\)

C. \(x+2\)^2 + \(y+3\)^\(2 = 16\)

D. \(x-2\)^2 + \(y-3\)^\(2 = 16\)

Correct Answer: A

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Question 19 View Details

Solve the system of equations \(\begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases}\).

Correct A. \{ (1, 3), (2, 2) \}

B. \{ (1, 2), (2, 3) \}

C. \{ (2, 1), (3, 2) \}

D. \{ (3, 1), (4, 2) \}

Correct Answer: A

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Question 20 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 21 View Details

In a base-8 number system, what is the value of the digit (x\) in the number \(x_{8}\\((x) in the number\) if it is known that \(x_{8} + 12_{8} = 23_{8}\)?

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 22 View Details

Let \(A = egin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}\) and \(B = egin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix}\). Find the determinant of the matrix \(AB\).

A. -12

Correct B. -16

C. -20

D. -24

Correct Answer: B

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Question 23 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.68

B. 0.76

Correct C. 0.84

D. 0.92

Correct Answer: C

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Question 24 View Details

Solve for \(x\): \(\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 25 View Details

A binary operation (\circ\) is defined as \\((circ\(a circ b = ab + a + b\). Find the value of \(2 \\(circ b = ab + a + b). Find the value of \circ 3\).

A. 9

B. 10

Correct C. 11

D. 12

Correct Answer: C

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