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POST UTME NOUN 2017 Mathematics | Objective

Are you preparing for POST UTME NOUN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

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

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

In the diagram below, ( ABC ) is a right-angled triangle with \( angle B = 90^{circ} \). If \( AB = 6 \) 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

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

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 \( x_1, y_1 \ \) ), what is the value of \( x_1 \) if \( y_1 = 7 \)?

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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