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POST UTME BOWEN UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

In a certain number base, the representation of the number 27 is 101. What is the value of the number base?

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 2 View Details

A set 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 will be between 70 and 80?

Correct A. 0.34

B. 0.68

C. 0.85

D. 0.95

Correct Answer: A

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Question 3 View Details

A binary operation * is defined as follows:\((a * b = a\)\^2 + \(b^2\)\). Find the value of \\((a * b = a^2 + b^2\(2 * 3\) * 4.

A. 32

B. 40

Correct C. 48

D. 64

Correct Answer: C

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Question 4 View Details

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

A. 70

Correct B. 75

C. 80

D. 85

Correct Answer: B

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Question 5 View Details

A vector →A is given by →\(A = 2\)→i + 3→j. Find the magnitude of →A.

A. \(√13\)

Correct B. \(√15\)

C. \(√17\)

D. \(√19\)

Correct Answer: B

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Question 6 View Details

In a certain number base, the digits 1, 2, and 3 represent the values 2, 5, and 8, respectively. What is the value of the number 432 in this base?

A. 19

Correct B. 21

C. 23

D. 25

Correct Answer: B

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Question 7 View Details

A right circular cone has a height of 12 cm and a base radius of 6 cm. If a smaller cone is formed by melting \(1/4\) of the original cone, what is the volume of the smaller cone?

Correct A. 288π \(cm^3\)

B. 384π \(cm^3\)

C. 576π \(cm^3\)

D. 768π \(cm^3\)

Correct Answer: A

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Question 8 View Details

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \(1/6\)

B. \(1/12\)

Correct C. \(1/18\)

D. \(1/36\)

Correct Answer: C

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Question 9 View Details

In a certain trigonometric identity, \sin\(x+y\) = \sin\(x)\cos(y\) + \cos(x)\sin(y\). If \\((x)sin(y\(x = 30)° and \(y = 60\)°, what is the value of \\()° and (y = 60\sin\(x+y\)?

Correct A. \\((√3/2\)\)

B. \(1/2\)

C. \\((√2/2\)\)

D. \(1/√2\)\)

Correct Answer: A

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Question 10 View Details

The area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 4\) can be calculated using the definite integral. What is the value of this integral?

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 11 View Details

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 using the cosine rule.

A. 8

Correct B. 12

C. 16

D. 20

Correct Answer: B

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Question 12 View Details

A random variable X has a probability distribution given by (P(X) = \begin{cases} 0.2 & \text{if}\(x = 1\), \\((P(X) = begin{cases} 0.2 & \ 0.3 & \text{if} x = 2, \\\( 0.3 & text{if} x = 2, \ 0.5 & \text{if} x = 3. \end{cases}\) Find the mean of X.

A. 1.5

B. 2.0

Correct C. 2.5

D. 3.0

Correct Answer: C

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Question 13 View Details

Solve the system of equations \(\begin{cases} x + y + z = 6, \\ 2x + 2y + 3z = 12. \end{cases}\) using matrices.

Correct A. \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \\ 5 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix}

Correct Answer: A

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Question 14 View Details

A polynomial function f(x) has a degree of 4 and the following properties:\(f(1) = 2\), f\(-1 = -2\),\(f(0) = 0\), f(2) = 10. Find the value of f(3).

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 15 View Details

Two events A and B are independent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. Find the probability that both events A and B occur.

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 16 View Details

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

Correct A. \boxed{ 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 17 View Details

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

Correct A. \boxed{ -\infty, -1 \cup 2, \infty }

B. \(-\infty, 2\) \cup \(2, \infty\)

C. \(-\infty, -1\) \cup \(1, \infty\)

D. \(-\infty, 1\) \cup \(2, \infty\)

Correct Answer: A

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Question 18 View Details

Find the value of \sum_{\(n = 1\)}^{\infty} \(\frac{1}{n^2}\)\)\).

Correct A. \boxed{\(\frac{\pi^2}{6}\)\)\)}

B. \(\frac{\pi^2}{12}\)\)\)

C. \(\frac{\pi^2}{24}\)\)\)

D. \(\frac{\pi^2}{48}\)\)\)

Correct Answer: A

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Question 19 View Details

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

Correct A. \boxed{\(y = 1x + 1\)}

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

C. \(y = x + 1\)

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

Correct Answer: A

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Question 20 View Details

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

Correct A. \boxed{\(x =\)\pm 10}

B. \(x = 10\)

C. \(x = -10\)

D. \(x = 5\)

Correct Answer: A

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Question 21 View Details

In a binary system, what is the decimal equivalent of the binary number 1011?

A. 11

Correct B. 13

C. 15

D. 17

Correct Answer: B

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Question 22 View Details

A histogram is a graphical representation of the distribution of a set of data. What is the primary purpose of a histogram?

A. To show the mean of the data

B. To show the median of the data

Correct C. To show the distribution of the data

D. To show the range of the data

Correct Answer: C

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Question 23 View Details

A vector Δπ is defined as Δπ = πₑ - πₒ. What is the magnitude of Δπ?

A. |Δπ| = |πₑ| - |πₒ|

B. |Δπ| = |πₑ| + |πₒ|

Correct C. |Δπ| = |πₑ| - |πₒ|

D. |Δπ| = |πₑ| × |πₒ|

Correct Answer: C

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Question 24 View Details

A polynomial function f(x) = \((x^3 - 6x^2 + 11x - 6\)\) is given. What is the value of f\(-1\\((x^3 - 6x^2 + 11x - 6) is given. What is the value of f\)?

Correct A. 1

B. -1

C. 0

D. 6

Correct Answer: A

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Question 25 View Details

A curve is defined by the equation (y = x\^2 + 2x - 3\). What is the area under the curve between x = -1 and \\((y = x^2 + 2x - 3\(x = 2\)?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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