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POST UTME EKSU 2021 Mathematics | Objective

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Question 1 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 2 View Details

A bag contains 5 red balls, 4 blue balls, and 3 green balls. If a ball is drawn at random, what is the probability that it is either red or blue?

A. \(\frac{3}{6}\)\)

B. \(\frac{5}{12}\)\)

Correct C. \(\frac{7}{12}\)\)

D. \(\frac{9}{12}\)\)

Correct Answer: C

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Question 3 View Details

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

Correct A. \left( -\(\frac{3}{2}\)\), \(\frac{1}{2}\)\) \right]

B. \left( -\infty, \(\frac{1}{2}\)\) \right]

C. \left( -\infty, -\(\frac{3}{2}\)\) \right]

D. \left( -\infty, \infty \right]

Correct Answer: A

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Question 4 View Details

Find the derivative of the function: \(f(x) = \frac{1}{x^2 + 1}\).

A. \(\frac{-2x}{x^2 + 1\) ^2}\)\)

Correct B. \(\frac{2x}{x^2 + 1\) ^2}\)\)

C. \(\frac{-2}{x^2 + 1\) ^2}\)\)

D. \(\frac{2}{x^2 + 1\) ^2}\)\)

Correct Answer: B

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Question 5 View Details

A set of exam scores has a mean of 75 and a standard deviation of 10. If a new score of 90 is added to the set, what is the new mean?

A. 76

B. 77

Correct C. 78

D. 79

Correct Answer: C

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Question 6 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 7 View Details

Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8 View Details

Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 9 View Details

A binary operation ( ast ) is defined as \(a ast b = ab + 1\). Find the value of ( 2 ast 3 ).

A. 7

Correct B. 8

C. 9

D. 10

Correct Answer: B

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Question 10 View Details

Find the value of ( x ) in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 11 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. 48\pi \(cm^3\)

B. 64\pi \(cm^3\)

Correct C. 80\pi \(cm^3\)

D. 96\pi \(cm^3\)

Correct Answer: C

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Question 12 View Details

A histogram of exam scores has a mean of 75 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 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 13 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\).

A. -2

Correct B. -3

C. 2

D. 3

Correct Answer: B

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Question 14 View Details

Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, ...

A. 55

Correct B. 60

C. 65

D. 70

Correct Answer: B

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Question 15 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 16 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

Correct A. 0

B. -1

C. 1

D. 2

Correct Answer: A

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Question 17 View Details

Solve for x in the equation [ \\((x^2 + 5x + 6\)\(= 0\)\) ].

A. -2

Correct B. -1

C. 1

D. 2

Correct Answer: B

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Question 18 View Details

Find the volume of the cylinder with radius 4 cm and height 10 cm.

Correct A. 400\pi

B. 500\pi

C. 600\pi

D. 800\pi

Correct Answer: A

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Question 19 View Details

Solve the trigonometric equation [ 2 \\(\sin^2\) x + 3 \cos \(x - 1 = 0\) \].

A. \(\frac{\pi}{6}\)\)

Correct B. \(\frac{\pi}{4}\)\)

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

D. \(\frac{\pi}{2}\)\)

Correct Answer: B

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Question 20 View Details

Find the surface area of the sphere with radius 6 cm.

A. 288\pi

B. 360\pi

Correct C. 432\pi

D. 576\pi

Correct Answer: C

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Question 21 View Details

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 22 View Details

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

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 23 View Details

Solve the system of equations \(\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}\).

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

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

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

D. \(x = 4\), \(y = 5\)

Correct Answer: A

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Question 24 View Details

Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 25 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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