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POST UTME UNN 2020 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} ].

Correct A. -2

B. 2

C. 4

D. 6

Correct Answer: A

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Question 2 View Details

If the function [$f(x) =$$\frac{1}{x}$\) ] has a horizontal asymptote at [ $y = c$ ], find the value of [ c ].

A. 0

B. 1

C. -1

Correct D. ∞

Correct Answer: D

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Question 3 View Details

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

A. $\frac{1}{14}$\)

B. $\frac{1}{7}$\)

Correct C. $\frac{3}{14}$\)

D. $\frac{1}{2}$\)

Correct Answer: C

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Question 4 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 5 View Details

A company produces two products, A and B. The profit from the sale of one unit of product A is ₦100, and the profit from the sale of one unit of product B is ₦120. If the company produces 20 units of product A and 15 units of product B, what is the total profit?

A. ₦2500

Correct B. ₦2800

C. ₦3000

D. ₦3200

Correct Answer: B

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Question 6 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 is greater than 0.5.

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 7 View Details

A set of 10 students scored the following marks in a mathematics test: 85, 90, 78, 92, 88, 76, 95, 89, 91, 84. Calculate the mean and standard deviation of the marks.

Correct A. {mean: 87.5, std_dev: 5.5}

B. {mean: 88.5, std_dev: 6.5}

C. {mean: 89.5, std_dev: 7.5}

D. {mean: 90.5, std_dev: 8.5}

Correct Answer: A

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Question 8 View Details

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

Correct A. 10

B. -10

C. 2

D. -2

Correct Answer: A

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Question 9 View Details

A circle with center (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.

Correct A. $x^2$ + \$(y^2$$= 25$\)

B. $x^2$ + \$(y^2$$= 16$\)

C. $x^2$ + \$(y^2$$= 9$\)

D. $x^2$ + \$(y^2$$= 4$\)

Correct Answer: A

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Question 10 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2197

B. 2187

C. 2177

D. 2167

Correct Answer: A

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Question 11 View Details

Let ( f(x) = $\frac{x^2 - 4}{x - 2}$\)\) ). Find the derivative of ( f(x) ) using the chain rule.

Correct A. ( f'$(x) =$$\frac{2x^2 - 4}{$ x - 2 ^2}\)\) \)

B. ( f'$(x) =$$\frac{2x}{x - 2}$\) \)

C. ( f'$(x) =$$\frac{x^2 - 4}{$ x - 2 ^2}\)\) \)

D. ( f'$(x) =$$\frac{2x^2 - 4x}{$ x - 2 ^2}\)\) \)

Correct Answer: A

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Question 12 View Details

A set ( A ) contains the elements ( { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } ). Find the number of subsets of ( A ) that contain exactly 3 elements.

Correct A. $2^3 \$

B. $3^3 \$

C. $10 \$

D. $5 \$

Correct Answer: A

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Question 13 View Details

A sequence is defined by $a_n = 2n + 1$. Find the sum of the first 5 terms of the sequence.

A. $15 \$

B. $25 \$

C. $35 \$

Correct D. $45 \$

Correct Answer: D

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Question 14 View Details

A polynomial function is defined by ( f(x) = $x^3 - 6x^2 + 11x - 6$ ). Find the value of ( f(2) ).

Correct A. $0 \$

B. $2 \$

C. $4 \$

D. $6 \$

Correct Answer: A

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Question 15 View Details

A geometric progression is defined by $a_n = 2a_{n-1}$ with $a_1 = 2$. Find the sum of the first 5 terms of the progression.

Correct A. $62 \$

B. $63 \$

C. $64 \$

D. $65 \$

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi $cm^3$

B. 64\pi $cm^3$

Correct C. 96\pi $cm^3$

D. 128\pi $cm^3$

Correct Answer: C

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Question 17 View Details

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

A. $10^4$

Correct B. $10^8$

C. $10^12$

D. $10^16$

Correct Answer: B

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Question 18 View Details

Find the area under the curve $y = x^2 + 2x - 3$ from $x = 0$ to $x = 2$.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 3$ with initial term $a_1 = 2$. Find the sum of the first 5 terms of the sequence.

A. 35

B. 40

Correct C. 45

D. 50

Correct Answer: C

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Question 20 View Details

Solve the inequality $2x^2 - 5x - 3 > 0$.

Correct A. $-\infty, -1$ \cup $3, \infty$

B. $-\infty, -3$ \cup $1, \infty$

C. $-\infty, -2$ \cup $2, \infty$

D. $-\infty, -4$ \cup $4, \infty$

Correct Answer: A

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Question 21 View Details

A histogram is a graphical representation of a frequency distribution. What is the primary advantage of using a histogram over a bar chart?

Correct A. It allows for the visualization of continuous data

B. It is easier to read and understand

C. It can be used to display both categorical and numerical data

D. It is more aesthetically pleasing

Correct Answer: A

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Question 22 View Details

Solve for x in the equation $$1x \$ = $\frac{1}${$\sqrt{3}$}\) ).

A. 30°

Correct B. 60°

C. 45°

D. 90°

Correct Answer: B

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Question 23 View Details

Find the determinant of the matrix $egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}$.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 24 View Details

A sequence is defined as $a_n = 2n + 1$. Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 25 View Details

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

A. 800π

Correct B. 1000π

C. 1200π

D. 1600π

Correct Answer: B

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