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POST UTME NOUN 2017 Mathematics | Objective

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Question 1 View Details

Solve the inequality \(\frac{x}{x-2} > 0\) for ( x in mathbb{R} setminus {2} ).

Correct A. \(x < 0\) or \(x > 2\)

B. \(x < 2\)

C. \(x > 2\)

D. \(x = 2\)

Correct Answer: A

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Question 2 View Details

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that they are of different colors?

Correct A. \(\frac{5}{8}\)

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

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

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

Correct Answer: A

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Question 3 View Details

Find the sum of the first 10 terms of the geometric series \(2x^2 + 4x^3 + 8x^4 + ldots\).

Correct A. \(2x^2 \left \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \\) )

B. \(2x^2 \left \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \\) )

C. \(2x^2 \left \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \\) + \(4x^3\) )

D. \(2x^2 \left \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \\) + \(4x^3\) )

Correct Answer: A

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Question 4 View Details

In the diagram below, ( ABC ) is a right-angled triangle with angle (B = 90\^{circ}\). If \\((B = 90^{circ}\(AB = 6\) cm and \(BC = 8\) cm, find the length of ( AC ).

A. 10 cm

B. 12 cm

Correct C. 15 cm

D. 20 cm

Correct Answer: C

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Question 5 View Details

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

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\) or \(x = -3\)

D. \(x = 1\) or \(x = 3\)

Correct Answer: A

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Question 6 View Details

In the coordinate plane, the equation of a line is given by (y = \(\frac{3}{2}\)x - 2\). If the line passes through the point \\((y = frac{3}{2}x - 2\(x_1, y_1\) ), what is the value of \(x_1\\() ), what is the value of\) if \(y_1 = 7\)?

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 7 View Details

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice. Otherwise, the coin is flipped only once. What is the probability that the number of heads observed is odd?

A. \(1/4\)

B. \(1/2\)

Correct C. \(3/4\)

D. \(2/3\)

Correct Answer: C

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Question 8 View Details

The matrix \(A = egin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix}\) is multiplied by the matrix \(B = egin{bmatrix} 5 & 2 \ 1 & 3 \end{bmatrix}\). What is the value of the element in the first row and second column of the product matrix?

Correct A. 17

B. 19

C. 21

D. 23

Correct Answer: A

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Question 9 View Details

The mean of a set of numbers is 20. If the mean of a subset of these numbers is 15, what is the mean of the remaining numbers?

A. 10

B. 15

C. 20

Correct D. 25

Correct Answer: D

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Question 10 View Details

A circle with center ( (0, 0) ) and radius 4 passes through the point ( (3, 4) ). What is the equation of the circle?

Correct A. \(x^2 + y^2 = 16\)

B. \(x^2 + y^2 = 20\)

C. \(x^2 + y^2 = 24\)

D. \(x^2 + y^2 = 28\)

Correct Answer: A

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Question 11 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\) for ( x in mathbb{R} ).

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

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

C. \(-\infty, -3 \\) cup (3, infty) )

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

Correct Answer: A

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Question 12 View Details

Find the area under the curve \(y = \sin^2 x\) from \(x = 0\) to \(x = \frac{\pi}{2}\).

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

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

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

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

Correct Answer: A

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Question 13 View Details

Solve the system of equations \(egin{cases} x + y + z = 6 \ 2x + 2y + 3z = 12 \ 3x + 2y + z = 9 \end{cases}\).

Correct A. \(x = 1, y = 2, z = 3\)

B. \(x = 2, y = 1, z = 3\)

C. \(x = 3, y = 2, z = 1\)

D. \(x = 1, y = 3, z = 2\)

Correct Answer: A

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Question 14 View Details

Find the derivative of the function ( f(x) = \sin (2x) ).

Correct A. ( f'\((x) = 2\)\cos (2x) )

B. ( f'\((x) =\)\cos (2x) )

C. ( f'\((x) = 2\)\sin (2x) )

D. ( f'\((x) =\)\sin (2x) )

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. ( 0 )

B. ( 1 )

C. \(-1\)

D. ( 2 )

Correct Answer: A

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Question 16 View Details

Find the value of x in the quadratic equation \(x^2 + 5x + 6 = 0\).

A. 1

Correct B. -2

C. -3

D. 4

Correct Answer: B

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Question 17 View Details

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

A. -\(1 < x\)\(< 3\)

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

C. -\(3 < x\)\(< 1\)

D. x < -3 or \(x > 1\)

Correct Answer: B

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Question 18 View Details

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

Correct A. 6x + 2

B. 6x - 2

C. \(3x^2 + 2\)

D. \(3x^2 - 2\)

Correct Answer: A

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Question 19 View Details

Solve the system of equations \(x + y = 4\) and \(2x - y = 3\).

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 20 View Details

Find the sum of the infinite geometric series \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \\).

Correct A. 2

B. 4

C. 8

D. 16

Correct Answer: A

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Question 21 View Details

Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value greater than 0.5.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 22 View Details

Find the equation of the circle with center ( (2, 3) ) and radius 4.

Correct A. \(x^2 + y^2 - 4x - 6y + 25 = 0\)

B. \(x^2 + y^2 + 4x + 6y + 25 = 0\)

C. \(x^2 + y^2 - 4x + 6y + 25 = 0\)

D. \(x^2 + y^2 + 4x - 6y + 25 = 0\)

Correct Answer: A

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Question 23 View Details

Solve the equation \(2^x + 2^{-x} = 10\).

Correct A. \(x = 2\)

B. \(x = -2\)

C. \(x = 3\)

D. \(x = -3\)

Correct Answer: A

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Question 24 View Details

The mean of a set of 5 numbers is 10. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 25 View Details

Find the vector ( mathbf{a} ) such that \(\mathbf{a} \cdot 2 \mathbf{i} + 3 \mathbf{j} \\) = 10 ) and \(\mathbf{a} \cdot \mathbf{j} = 5\).

Correct A. \(2 \mathbf{i} + 5 \mathbf{j}\)

B. \(5 \mathbf{i} + 2 \mathbf{j}\)

C. \(10 \mathbf{i} + 5 \mathbf{j}\)

D. \(5 \mathbf{i} + 10 \mathbf{j}\)

Correct Answer: A

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