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POST UTME UNIOSUN 2017 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 2\) about the x-axis.

Correct A. \(\frac{32\pi}{5}\)\)

B. \(\frac{16\pi}{3}\)\)

C. \(\frac{64\pi}{5}\)\)

D. \(\frac{128\pi}{5}\)\)

Correct Answer: A

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Question 2 View Details

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

Correct A. \(-\infty, -1\) \cup \(3, \infty\)

B. \(-\infty, -3\) \cup \(1, \infty\)

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

D. \(-\infty, 1\) \cup \(3, \infty\)

Correct Answer: A

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Question 3 View Details

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

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 4 View Details

Solve the system of linear equations \(x + y = 2\) and 2x - 3y = -3 using the method of substitution.

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

B. \(x = -1\), \(y = 3\)

C. \(x = 2\), \(y = 0\)

D. \(x = 0\), \(y = 2\)

Correct Answer: A

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Question 5 View Details

Find the area under the curve \(y = x\^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 2\).

A. \(\frac{16}{5}\)\)

Correct B. \(\frac{32}{5}\)\)

C. \(\frac{48}{5}\)\)

D. \(\frac{64}{5}\)\)

Correct Answer: B

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Question 6 View Details

Determine the value of (n\) in the arithmetic sequence \(a_n = 2n + 5\\((n) in the arithmetic sequence\), given that \(a_1 = 9\) and \(a_{10} = 47\).

A. 5

Correct B. 7

C. 9

D. 11

Correct Answer: B

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Question 7 View Details

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 8 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

Correct A. 0.3413

B. 0.3415

C. 0.3417

D. 0.3419

Correct Answer: A

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Question 9 View Details

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

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 10 View Details

A binary operation (ast\) on the set of integers is defined by \(a ast b = a^2 + b^2\\((ast) on the set of integers is defined by\) for all integers \(a\) and \(b\). Find the value of \(x\) such that \(x ast 2 = 21\).

A. 3

B. 5

Correct C. 7

D. 9

Correct Answer: C

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Question 11 View Details

Let X be a random variable with probability density function (pdf) given by f(x) = \(\frac{1}{2}e^{-|x|}\) for -∞\(< x\)< ∞. Find the probability that X lies between -1 and 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 12 View Details

A histogram of exam scores is given below. If the mean score is 60, find the value of k.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 13 View Details

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

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

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

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

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

Correct Answer: A

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Question 14 View Details

Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\) using the factor theorem.

Correct A. \(x - 1\), x - 2\)\(x - 3 \\)\(= 0 )\)

B. \(x - 1\), x - 2\)\(x + 3 \\)\(= 0 )\)

C. \(x + 1\), x - 2\)\(x - 3 \\)\(= 0 )\)

D. \(x - 1\), x + 2\)\(x - 3 \\)\(= 0 )\)

Correct Answer: A

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Question 15 View Details

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

Correct A. \(egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0\)

B. \(egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 1\)

C. \(egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = -1\)

D. \(egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 2\)

Correct Answer: A

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Question 16 View Details

Determine the value of x in the equation \(2x^2 + 5x - 3 = 0\).

Correct A. \(x = -1\)

B. \(x = 3\)

C. \(x = -3\)

D. \(x = 1\)

Correct Answer: A

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Question 17 View Details

Find the volume of the frustum of a cone with height 10cm, lower base radius 5cm, and upper base radius 3cm.

A. ( 100pi ) cm³

Correct B. ( 150pi ) cm³

C. ( 200pi ) cm³

D. ( 250pi ) cm³

Correct Answer: B

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Question 18 View Details

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

A. \(x = 10\)

B. \(x = 100\)

C. \(x = 1000\)

Correct D. \(x = 10000\)

Correct Answer: D

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Question 19 View Details

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

A. ( 8 )

Correct B. ( 10 )

C. ( 12 )

D. ( 14 )

Correct Answer: B

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Question 20 View Details

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

A. ( 288pi ) cm²

B. ( 360pi ) cm²

Correct C. ( 432pi ) cm²

D. ( 480pi ) cm²

Correct Answer: C

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Question 21 View Details

Find the sum of the infinite geometric series \(sum_{n = 1}^{\infty} \frac{1}{2^n}\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22 View Details

A set of 10 students scored the following marks in a mathematics test: 23, 21, 19, 24, 22, 20, 25, 18, 26, 17. Calculate the mean, median, and mode of the data.

A. Mean: 22, Median: 22, Mode: 23

B. Mean: 22, Median: 23, Mode: 22

C. Mean: 23, Median: 22, Mode: 22

Correct D. Mean: 22, Median: 22, Mode: 22

Correct Answer: D

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Question 23 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. x > -1 or \(x < 3/2\)\)

C. x < -1 or \(x < 3/2\)\)

D. x > -1 or \(x > 3/2\)\)

Correct Answer: A

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Question 24 View Details

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

Correct A. \(1/2\)

B. \(2/3\)

C. \(3/4\)

D. \(4/5\)

Correct Answer: A

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Question 25 View Details

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

Correct A. 21

B. 22

C. 23

D. 24

Correct Answer: A

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