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POST UTME UNILAG 2020 Mathematics | Objective

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Question 1 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 2 View Details

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

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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Question 3 View Details

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

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 4 View Details

A histogram is shown below. What is the mode of the data set?

A. A

Correct B. B

C. C

D. D

Correct Answer: B

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Question 5 View Details

Solve the equation $x^2 + 4x + 4 = 0$.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 6 View Details

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

A. 48\pi $cm^3$

B. 64\pi $cm^3$

Correct C. 80\pi $cm^3$

D. 96\pi $cm^3$

Correct Answer: C

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Question 7 View Details

A circle passes through the points (2, 3), (4, 1), and (6, 5). Find the equation of the circle.

Correct A. $x^2$ + \$(y^2 - 4x - 2y + 5$$= 0$\)

B. $x^2$ + \$(y^2 + 4x + 2y - 5$$= 0$\)

C. $x^2$ + \$(y^2 - 6x + 2y - 5$$= 0$\)

D. $x^2$ + \$(y^2 + 6x - 2y - 5$$= 0$\)

Correct Answer: A

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Question 8 View Details

Solve the equation $\frac{x^2 - 4x + 4}{x^2 - 4x + 3}$\)\) = $\frac{x + 2}{x - 1}$\)

Correct A. $x = 2$

B. $x = 3$

C. $x = 4$

D. $x = 5$

Correct Answer: A

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Question 9 View Details

Find the area of the region bounded by the parabola (y = x\^2\), the x-axis, and the line \$(y = x^2\(x = 2$.

A. $\frac{8}{3}$\)

Correct B. $\frac{16}{3}$\)

C. $\frac{24}{3}$\)

D. $\frac{32}{3}$\)

Correct Answer: B

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Question 10 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11 View Details

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

A. 24\pi

B. 36\pi

Correct C. 48\pi

D. 60\pi

Correct Answer: C

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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 inequality |x - 2|$> 3.$

Correct A. $-\infty, -1$ \cup $4, \infty$

B. $-\infty, 1$ \cup $4, \infty$

C. $-\infty, -1$ \cup $1, \infty$

D. $-\infty, 1$ \cup $2, \infty$

Correct Answer: A

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Question 14 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio $\frac{1}{2}$\).

A. 1.9999

Correct B. 2.0000

C. 2.0001

D. 2.0002

Correct Answer: B

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Question 15 View Details

Solve the equation \log_2 $x + 1 = 3$.

A. 7

Correct B. 8

C. 9

D. 10

Correct Answer: B

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Question 16 View Details

Given that $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix}$, find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. 0.6

B. 0.8

C. 1.2

D. 1.6

Correct Answer: A

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Question 17 View Details

A random variable ( X ) has a probability density function ( f(x) = begin{cases} 2x & \text{if } $0 < x\\(begin{cases} 2x & text{if}$$< 1$\ 0 & \text{otherwise} \end{cases} ). Find the expected value of ( X ).

A. 0.25

Correct B. 0.5

C. 0.75

D. 1.0

Correct Answer: B

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Question 18 View Details

The graph of the function $y = \frac{1}{x} \$ has a horizontal asymptote at $y = \boxed{?}$.

A. 0

B. 1

Correct C. ∞

D. -∞

Correct Answer: C

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Question 19 View Details

A polynomial ( p(x) ) has roots at $x = -2, 3, \$ and ( 5 ). Write the polynomial in factored form.

Correct A. $x + 2$, x - 3\)$x - 5$

B. $x - 2$, x + 3\)$x + 5$

C. $x + 2$, x - 3\)$x + 5$

D. $x - 2$, x + 3\)$x - 5$

Correct Answer: A

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Question 20 View Details

A set of data has a mean of 25 and a standard deviation of 3. If the data set is normally distributed, what is the probability that a randomly selected value will be between 20 and 30?

A. 0.25

Correct B. 0.5

C. 0.75

D. 0.9

Correct Answer: B

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Question 21 View Details

Find the value of x in the equation $\log_{10} x^2 \$$= 4 ).$

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22 View Details

Solve the inequality $x^2 - 4x + 4 > 0$.

Correct A. $x > 2$

B. $x < 2$

C. $x > 0$

D. $x < 0$

Correct Answer: A

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Question 23 View Details

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

Correct A. \cos 2x

B. \sin 2x

C. \cos x

D. \sin x

Correct Answer: A

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Question 24 View Details

Solve the equation $$1x = \sqrt{3}$.

A. $\frac{\pi}{3}$\)

Correct B. $\frac{2\pi}{3}$\)

C. $\frac{4\pi}{3}$\)

D. $\frac{5\pi}{3}$\)

Correct Answer: B

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Question 25 View Details

Find the value of x in the equation $2^x = 16$.

A. 4

Correct B. 8

C. 12

D. 16

Correct Answer: B

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