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POST UTME SUMMIT UNIVERSITY 2023 Mathematics | Objective

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Question 1 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. 24π $cm^3$

Correct B. 48π $cm^3$

C. 96π $cm^3$

D. 192π $cm^3$

Correct Answer: B

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Question 2 View Details

A random variable X has a probability distribution given by P$X = 1 = 1/4$, P$X = 2 = 1/2$, P$X = 3 = 1/4$. Find the probability that X is greater than 2.

A. $1/2$

Correct B. $3/4$

C. $1/4$

D. 0

Correct Answer: B

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Question 3 View Details

Solve the matrix equation (AX = B\), where A = egin{bmatrix} 1 & 2 \ 3 & 4 \\$((AX = B)$, where A = egin{bmatrix} 1 & 2 \end{bmatrix},$X =$egin{bmatrix} x \ y \end{bmatrix}, and B = egin{bmatrix} 5 \ 6 \end{bmatrix}.

Correct A. $X =$egin{bmatrix} 1 \ 2 \end{bmatrix}

B. $X =$egin{bmatrix} 2 \ 1 \end{bmatrix}

C. $X =$egin{bmatrix} 3 \ 4 \end{bmatrix}

D. $X =$egin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 4 View Details

A histogram of the heights of 100 students is shown below. If the mean height is 170 cm, find the standard deviation.

A. 10 cm

Correct B. 15 cm

C. 20 cm

D. 25 cm

Correct Answer: B

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Question 5 View Details

Find the surface area of the sphere with radius 5 cm.

A. 100π $cm^2$

B. 200π $cm^2$

Correct C. 300π $cm^2$

D. 400π $cm^2$

Correct Answer: C

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Question 6 View Details

A random variable X follows a binomial distribution with parameters $n = 10$ and $p = 0.4$. Find the probability that X is greater than 6.

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 7 View Details

Find the equation of the circle passing through the points (2, 3), (4, 5), and (6, 7).

Correct A. $x - 4$^2 + $y - 5$^$2 = 9$\)

B. $x - 3$^2 + $y - 4$^$2 = 16$\)

C. $x - 5$^2 + $y - 6$^$2 = 25$\)

D. $x - 6$^2 + $y - 7$^$2 = 36$\)

Correct Answer: A

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Question 8 View Details

Solve the inequality $2x^2 + 5x - 3 \geq 0$.

Correct A. x \leq -1 \text{ or } x \geq $\frac{3}{2}$\)

B. x \leq -2 \text{ or } x \geq 1

C. x \leq -3 \text{ or } x \geq 2

D. x \leq -4 \text{ or } x \geq 3

Correct Answer: A

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Question 9 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 10 View Details

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

Correct A. $f'(x) = \frac{-2x}{x^2 + 1 ^2}$

B. $f'(x) = \frac{2x}{x^2 + 1 ^2}$

C. $f'(x) = \frac{x}{x^2 + 1 ^2}$

D. $f'(x) = \frac{1}{x^2 + 1 ^2}$

Correct Answer: A

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Question 11 View Details

Find the value of $\lim_{x\to\infty} \left \frac{$1x^2 + 1 \}{x}\right)$.

Correct A. 0

B. 1

C. \infty

D. undefined

Correct Answer: A

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Question 12 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

A. $1/6$

Correct B. $1/3$

C. $2/3$

D. $5/6$

Correct Answer: B

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Question 13 View Details

Solve the equation ($\sqrt{x + 5}\\() - 3 = 2$\) for \$(sqrt{x + 5} - 3 = 2\(x$.

Correct A. -16

B. -8

C. 4

D. 16

Correct Answer: A

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Question 14 View Details

A vector $\mathbf{a}$ has magnitude 5 and direction $\theta = \frac{\pi}{3}). Find the magnitude of the vector \(\mathbf{a} + \\(). Find the magnitude of the vector (\mathbf{b}), where \(\mathbf{b}\\(), where ($ is a vector with magnitude 3 and direction $\theta = \frac{\pi}{6}$.

A. 4

B. 5

Correct C. 6

D. 8

Correct Answer: C

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Question 15 View Details

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

A. $1/3$

B. $1/2$

Correct C. $2/3$

D. 1

Correct Answer: C

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Question 16 View Details

Let X be a random variable with probability density function (pdf) ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the expected value of X.

Correct A. $1/3$

B. $1/2$

C. $2/3$

D. 1

Correct Answer: A

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Question 17 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.9544

Correct B. 0.9772

C. 0.9987

D. 0.9999

Correct Answer: B

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Question 18 View Details

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

Correct A. -2x/$x^2 + 1$^2

B. 2x/$x^2 + 1$^2

C. -1/$x^2 + 1$^2

D. 1/$x^2 + 1$^2

Correct Answer: A

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Question 19 View Details

Solve the system of equations using matrices: $egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}$.

Correct A. [1, 2]

B. [2, 1]

C. [3, -1]

D. [-1, 3]

Correct Answer: A

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Question 20 View Details

Find the sum of the first 10 terms of the geometric series $2 + 6 + 18 + cdots$.

Correct A. 1048576

B. 1048575

C. 1048574

D. 1048573

Correct Answer: A

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Question 21 View Details

In a set of consecutive integers, the sum of the first and last term is 56. If the sum of the second and second last term is 34, find the sum of the first and second term.

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 22 View Details

Find the equation of the circle with center at $-2, 3$ and passing through the point (1, 2).

Correct A. \left$x + 2 \right$^2 + \left$y - 3 \right$^$2 = 5$

B. \left$x + 2 \right$^2 + \left$y - 3 \right$^$2 = 10$

C. \left$x + 2 \right$^2 + \left$y - 3 \right$^$2 = 15$

D. \left$x + 2 \right$^2 + \left$y - 3 \right$^$2 = 20$

Correct Answer: A

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Question 23 View Details

Solve the inequality $\frac{x - 2}{x + 1}$\$) > 0.$

Correct A. $x < -1$\text{ or } $x > 2$

B. $x < -1$\text{ or } $x < 2$

C. $x > -1$\text{ or } $x > 2$

D. $x > -1$\text{ or } $x < 2$

Correct Answer: A

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Question 24 View Details

Find the value of x in the matrix equation \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 7 \end{bmatrix}.

A. $x = 2$

B. $x = 3$

Correct C. $x = 4$

D. $x = 5$

Correct Answer: C

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Question 25 View Details

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 300

Correct B. 400

C. 500

D. 600

Correct Answer: B

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