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POST UTME BABCOCK UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(x = \frac{\pi}{2}\)

B. \(x = \frac{\pi}{4}\)

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

D. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 2 View Details

A random variable X has a probability distribution given by \(P X = x \\) = \(frac{1}{2}\)\) ) for \\(frac{1}{2})\(x = 1, 2, 3, 4\). Find the expected value of X.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 3 View Details

In the diagram below, ( ABC ) is a right-angled triangle with angle (B = 90\^circ\). If \\((B = 90^circ\(AB = 3\) and \(BC = 4\), find the length of ( AC ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 4 View Details

A histogram of the heights of students in a class is shown below. If the class has 50 students, find the median height.

A. 160

Correct B. 170

C. 180

D. 190

Correct Answer: B

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Question 5 View Details

A circle with center ( C ) and radius ( r ) is shown below. If \(OC = 6\), find the length of ( AB ).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 6 View Details

A cylindrical tank with a radius of 5m and a height of 10m is filled with water. If the density of water is 1000 \(kg/m\^3\\(tank with a radius of 5m and a height of 10m is filled with water. If the density of water is 1000 (kg/m\), calculate the volume of water in the \tank.

Correct A. 785.4 \(m^3\)

B. 785.4 \(m^2\)

C. 785.4 m

D. 785.4 \(km^3\)

Correct Answer: A

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Question 7 View Details

Solve the inequality: \(\frac{x-2}{x+1}\)\\() > 0\)

Correct A. x < -1 or \(x > 2\)

B. x < -1 or \(x < 2\)

C. x > -1 or \(x < 2\)

D. x > -1 or \(x > 2\)

Correct Answer: A

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Question 8 View Details

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

Correct A. 14.67

B. 14.67 \(m^2\)

C. 14.67 \(km^2\)

D. 14.67 \(cm^2\)

Correct Answer: A

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Question 9 View Details

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

A. 0.375

Correct B. 0.375 or \(3/8\)

C. 0.375 or \(1/3\)

D. 0.375 or \(1/2\)

Correct Answer: B

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Question 10 View Details

The mean of 5 numbers is 12. If one of the numbers is 15, what is the mean of the remaining 4 numbers?

Correct A. 11.25

B. 11.25 or \(45/4\)

C. 11.25 or \(3/4\)

D. 11.25 or \(1/4\)

Correct Answer: A

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Question 11 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 12 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 13 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \(x - 3\)^2 + \(y - 4\)^\(2 = 25\)

B. \(x - 4\)^2 + \(y - 3\)^\(2 = 25\)

C. \(x - 3\)^2 + \(y - 4\)^\(2 = 30\)

D. \(x - 4\)^2 + \(y - 3\)^\(2 = 30\)

Correct Answer: A

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Question 14 View Details

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

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

B. \(\frac{24}{25}\)\)

C. \(\frac{24}{25}\)\)

D. \(\frac{24}{25}\)\)

Correct Answer: A

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Question 15 View Details

Find the sum of the first 10 terms of the geometric series with first term \(a = 2\) and common ratio \(r = 3\).

Correct A. 59049

B. 59049

C. 59049

D. 59049

Correct Answer: A

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Question 16 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 17 View Details

Solve the system of linear equations using matrices:\n\(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix}\)

Correct A. \(egin{bmatrix} 1 \ 2 \end{bmatrix}\)

B. \(egin{bmatrix} 2 \ 1 \end{bmatrix}\)

C. \(egin{bmatrix} 3 \ 4 \end{bmatrix}\)

D. \(egin{bmatrix} 4 \ 3 \end{bmatrix}\)

Correct Answer: A

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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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 16\) )

D. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 19 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 \(km/h\\((km/h) and returns at an average speed of 40\). If the distance between the two cities is 240 km, what is the average speed for the round trip?

A. 48

B. 50

Correct C. 52

D. 54

Correct Answer: C

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Question 20 View Details

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

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 21 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.

A. 12.5%

Correct B. 15%

C. 17.5%

D. 20%

Correct Answer: B

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Question 22 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 23 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 24 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 10 terms of the sequence.

A. 110

B. 120

Correct C. 130

D. 140

Correct Answer: C

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Question 25 View Details

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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