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POST UTME BELLS UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Given that $\sin^2 x + \cos^2 x = 1$, find the value of ($1x$ when 1x = \$($1x) when \frac{3}{5}$.

A. 0.6

Correct B. 0.8

C. 1.2

D. 1.5

Correct Answer: B

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Question 2 View Details

Solve for ( x ) in the equation $2x^2 + 5x - 3 = 0$.

Correct A. 1.5

B. -2

C. 3

D. -1

Correct Answer: A

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Question 3 View Details

Find the determinant of the matrix $\begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 4 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 red?

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 5 View Details

Find the value of ( x ) in the equation $x^2 + 4x + 4 = 0$.

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 6 View Details

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix}$. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. $4/5$

B. $3/5$

C. $5/4$

D. $2/3$

Correct Answer: A

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Question 7 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3 or 5?

A. $1/3$

Correct B. $1/2$

C. $2/3$

D. $5/6$

Correct Answer: B

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Question 8 View Details

The equation of a circle is $x^2 + y^2 = 16$. Find the equation of the line passing through the point ( (4, 0) ) that is \tangent to the circle.

Correct A. $y = 4x + 16$

B. $y = 4x - 16$

C. $y = 4x + 4$

D. $y = 4x - 4$

Correct Answer: A

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Question 9 View Details

Simplify the expression $\frac{\log_2 x - \log_2 3}{\log_2 x + \log_2 3}$.

Correct A. $1/3$

B. $1/2$

C. $2/3$

D. $3/4$

Correct Answer: A

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Question 10 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 11 View Details

A random variable X has a probability distribution given by P$X = 1 = 0.3$, P$X = 2 = 0.4$, and P$X = 3 = 0.3$. Find the expected value of X.

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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Question 12 View Details

Solve the equation $\sin^2(x) + \cos^2(x) = 1$ for x.

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

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

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

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

Correct Answer: A

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Question 13 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 greater than 85?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6915

Correct Answer: D

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Question 14 View Details

Find the vector $\vec{a} \times \vec{b}) given that \(\vec{a} = \\() given that (\begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}$ and $\vec{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}$.

Correct A. \begin{pmatrix} -1 \ 8 \ -5 \end{pmatrix}

B. \begin{pmatrix} 1 \ -8 \ 5 \end{pmatrix}

C. \begin{pmatrix} -1 \ -8 \ 5 \end{pmatrix}

D. \begin{pmatrix} 1 \ 8 \ -5 \end{pmatrix}

Correct Answer: A

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Question 15 View Details

Solve the equation $x^2 + 5x + 6 = 0$ using the quadratic formula.

Correct A. \begin{pmatrix} -2 \ 3 \end{pmatrix}

B. \begin{pmatrix} -3 \ 2 \end{pmatrix}

C. \begin{pmatrix} 2 \ -3 \end{pmatrix}

D. \begin{pmatrix} 3 \ -2 \end{pmatrix}

Correct Answer: A

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Question 16 View Details

Find the derivative of the function ( f(x) = $\frac{x^2 + 2x - 3}{x^2 - 4}$\)\) ) using the quotient rule.

A. $\frac{x^2 - 4$ 2x + 2 - $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

B. $\frac{x^2 - 4$ 2x + 2 + $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

Correct C. $\frac{x^2 - 4$ 2x + 2 - $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

D. $\frac{x^2 - 4$ 2x + 2 + $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

Correct Answer: C

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Question 17 View Details

Solve the system of linear equations using matrices:

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 3 \ 4 \end{bmatrix}

C. \begin{bmatrix} 5 \ 6 \end{bmatrix}

D. \begin{bmatrix} 7 \ 8 \end{bmatrix}

Correct Answer: A

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Question 18 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19 View Details

A particle moves in a straight line with a velocity of 5 $(m/s$\). If the acceleration is 2 $m/s\\((m/s). If the acceleration is 2 \^2$, find the distance traveled in 3 seconds.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 20 View Details

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

A. 62

Correct B. 64

C. 66

D. 68

Correct Answer: B

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Question 21 View Details

Find the equation of the circle passing through the points (2,3), (4,5), and $-1,2$.

Correct A. $x^2 + y^2 - 4x + 10y + 25 = 0$

B. $x^2 + y^2 + 4x - 10y - 25 = 0$

C. $x^2 + y^2 - 2x - 6y + 9 = 0$

D. $x^2 + y^2 + 2x + 6y - 9 = 0$

Correct Answer: A

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Question 22 View Details

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

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -\frac{3}{2}$ or $x > 1$

C. $x < -1$ or $x < \frac{3}{2}$

D. $x < -\frac{3}{2}$ or $x > 1$

Correct Answer: A

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Question 23 View Details

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

Correct A. ( 10 )

B. ( 20 )

C. ( 30 )

D. ( 40 )

Correct Answer: A

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Question 24 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $\frac{1}{6}$

B. $\frac{1}{3}$

C. $\frac{2}{3}$

Correct D. $\frac{5}{6}$

Correct Answer: D

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Question 25 View Details

The mean of five numbers is 20. If one of the numbers is 15, what is the sum of the other four numbers?

Correct A. ( 80 )

B. ( 90 )

C. ( 100 )

D. ( 110 )

Correct Answer: A

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