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POST UTME UNILORIN 2020 Mathematics | Objective

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Question 1 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 80?

Correct A. 0.9772

B. 0.6827

C. 0.3413

D. 0.1587

Correct Answer: A

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Question 2 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the third side?

Correct A. 8

B. 6

C. 10

D. 12

Correct Answer: A

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Question 4 View Details

A company produces two products, A and B. The profit on product A is ₦100 per unit and the profit on product B is ₦150 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?

Correct A. ₦65,000

B. ₦70,000

C. ₦75,000

D. ₦80,000

Correct Answer: A

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Question 5 View Details

A car travels from city A to city B at an average speed of 60 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). What is the average speed for the round trip?

A. 48

Correct B. 50

C. 52

D. 54

Correct Answer: B

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Question 6 View Details

Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. \(\frac{1}{3} \pi 4^2 + 2^2 + 4 \cdot 2 \cdot 4 \\) )

B. \(\frac{1}{3} \pi 4^2 + 2^2 - 4 \cdot 2 \cdot 4 \\) )

C. \(\frac{1}{3} \pi 4^2 + 2^2 + 2 \cdot 4 \cdot 2 \\) )

D. \(\frac{1}{3} \pi 4^2 + 2^2 - 2 \cdot 4 \cdot 2 \\) )

Correct Answer: A

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Question 7 View Details

Solve for x in the equation \(\sin^2 x + \cos^2 x = 1\).

Correct A. \(x = \frac{\pi}{4}\)

B. \(x = \frac{\pi}{2}\)

C. \(x = \frac{3\pi}{4}\)

D. \(x = \frac{\pi}{6}\)

Correct Answer: A

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Question 8 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{64}{3}\)

B. \(\frac{32}{3}\)

C. \(\frac{16}{3}\)

D. \(\frac{8}{3}\)

Correct Answer: A

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Question 9 View Details

Solve the matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

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

C. \(x = 3, y = 4\)

D. \(x = 4, y = 3\)

Correct Answer: A

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Question 10 View Details

Find the surface area of the sphere with radius 5 cm.

Correct A. ( 100pi )

B. ( 50pi )

C. ( 25pi )

D. ( 10pi )

Correct Answer: A

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Question 11 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12 View Details

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

Correct A. \(x = 1\), \(y = 3\)

B. \(x = 2\), \(y = 2\)

C. \(x = 3\), \(y = 1\)

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 13 View Details

A random variable ( X ) has a probability distribution given by: \(P X = x \\) = \begin{cases} \(\frac{1}{2}\)\) & text{if } \(x = 1\) \\(text{if} (x = 1\ \(\frac{1}{4}\)\) & text{if } \(x = 2\) \\(text{if} (x = 2\ \(\frac{1}{4}\)\) & text{if } \(x = 3\) \\(text{if}\((x = 3\)\ \end{cases} ). Find the probability that ( X ) takes a value greater than 2.

A. \(\frac{1}{2}\)\)

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

Correct C. \(\frac{3}{4}\)\)

D. \(\frac{1}{8}\)\)

Correct Answer: C

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Question 14 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 15 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.

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

B. \(\frac{1}{2}\)\)

C. \(\frac{3}{4}\)\)

Correct D. \(\frac{2}{3}\)\)

Correct Answer: D

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Question 16 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{pmatrix} ].

A. 13

Correct B. -13

C. 0

D. 1

Correct Answer: B

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Question 17 View Details

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

A. 0

Correct B. -2

C. 2

D. -4

Correct Answer: B

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Question 18 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. \(y = 2x - 3\)

D. \(y = 2x + 3\)

Correct Answer: A

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Question 19 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ).

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 20 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).

A. 3

Correct B. 6

C. 9

D. 12

Correct Answer: B

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Question 21 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 22 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 23 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 24 View Details

A die is rolled twice. Find the probability that the sum of the two numbers is 7.

A. \(1/6\)

Correct B. \(1/12\)

C. \(1/36\)

D. \(1/24\)

Correct Answer: B

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Question 25 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. \(y = -2x + 7\)

D. \(y = 2x - 7\)

Correct Answer: A

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