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POST UTME LASU 2020 Mathematics | Objective

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Question 1 View Details

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

Correct A. $x^2 + y^2 + 6x - 4y - 12 = 0$

B. $x^2 + y^2 - 6x + 4y - 12 = 0$

C. $x^2 + y^2 + 6x + 4y - 12 = 0$

D. $x^2 + y^2 - 6x - 4y - 12 = 0$

Correct Answer: A

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Question 2 View Details

A rectangular block measures 5cm by 3cm by 2cm. Find the volume of the block.

A. $30cm^3$

B. $60cm^3$

Correct C. $90cm^3$

D. $120cm^3$

Correct Answer: C

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Question 3 View Details

Find the area under the curve $y = \frac{1}{x}$ from $x = 1$ to $x = 2$.

Correct A. ( ln(2) - ln(1) )

B. ( ln(2) + ln(1) )

C. ( ln(1) - ln(2) )

D. ( ln(1) + ln(2) )

Correct Answer: A

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Question 4 View Details

Solve the equation $2^x + 2^{-x} = 10$.

A. $x = 2$

B. $x = -2$

Correct C. $x = \log_2 5 \$ )

D. $x = -\log_2 5 \$ )

Correct Answer: C

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Question 5 View Details

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 6 View Details

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

Correct A. $\frac{-2x}{x^2 + 1$ \ ^2}\)\) )

B. $\frac{2x}{x^2 + 1$ \ ^2}\)\) )

C. $\frac{2}{x^2 + 1$ \ ^2}\)\) )

D. $\frac{-2}{x^2 + 1$ \ ^2}\)\) )

Correct Answer: A

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Question 7 View Details

Solve the system of equations using matrices: $egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}$.

Correct A. $x = 2, y = 3$

B. $x = 3, y = 2$

C. $x = 4, y = 5$

D. $x = 5, y = 4$

Correct Answer: A

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Question 8 View Details

Find the volume of the solid formed by rotating the region bounded by $y = x^2$ and $y = 4$ about the x-axis.

A. $\frac{32}{3} \pi$

Correct B. $\frac{64}{3} \pi$

C. $\frac{128}{3} \pi$

D. $\frac{256}{3} \pi$

Correct Answer: B

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Question 9 View Details

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

Correct A. $2$1x$\cos(x \) )

B. $2$1x \$ )

C. $2$1x \$ )

D. $2$1x$\cos(x \) + \$\sin^2(x)$ )

Correct Answer: A

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Question 10 View Details

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

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 11 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. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 12 View Details

Solve for x in the equation $\frac{x}{2} + 3 = 7$.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 13 View Details

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

Correct A. -2

B. 2

C. 4

D. 6

Correct Answer: A

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Question 14 View Details

A histogram is constructed with the following data: 2, 4, 6, 8, 10. What is the class width?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 15 View Details

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

Correct A. $-∞, -2$ ∪ (2, ∞)

B. $-∞, 2$

C. $-2, 2$

D. (2, ∞)

Correct Answer: A

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Question 16 View Details

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

Correct A. $x^2 + y^2 + 2gx + 2fy + c = 0$

B. $x^2 + y^2 + 2gx - 2fy + c = 0$

C. $x^2 + y^2 - 2gx + 2fy + c = 0$

D. $x^2 + y^2 - 2gx - 2fy + c = 0$

Correct Answer: A

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Question 17 View Details

A rectangular water \tank with a length of 4m, a width of 3m, and a height of 2m is filled with water. Find the volume of water in the \tank.

A. $24m^3$

B. $36m^3$

Correct C. $48m^3$

D. $60m^3$

Correct Answer: C

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Question 18 View Details

Solve the equation $x^3 - 6x^2 + 11x - 6 = 0$ using the factor theorem.

A. $x = 1$

B. $x = 2$

Correct C. $x = 3$

D. $x = 4$

Correct Answer: C

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Question 19 View Details

A right-angled triangle has a hypotenuse of length 10cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. ( 5cm )

Correct B. ( 7.5cm )

C. ( 10cm )

D. ( 12.5cm )

Correct Answer: B

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Question 20 View Details

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

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

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

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

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

Correct Answer: A

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Question 21 View Details

In a circle with center O and radius 6, chord AB is 8 units long. If point P is the midpoint of AB, find the area of triangle OAP.

A. 12\sqrt{3}

B. 16\sqrt{3}

Correct C. 20\sqrt{3}

D. 24\sqrt{3}

Correct Answer: C

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Question 22 View Details

Let $A = \begin{bmatrix} 2 & 1 \\ 1 & 2 end{bmatrix}$. Find the determinant of $A^2\\(end{bmatrix}). Find the determinant of$.

A. 0

B. 1

Correct C. 4

D. 9

Correct Answer: C

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Question 23 View Details

A binary operation (\circ\) on the set \$(circ\(mathbb{Z}_4$ is defined by $a \\(mathbb{Z}_4) is defined by \circ b = a^2 + b^2). Find the value of \(1 \circ 2\\(). Find the value of (1$.

A. 0

B. 1

C. 2

Correct D. 3

Correct Answer: D

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Question 24 View Details

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the die shows an even number and the coin lands heads up, what is the probability that the die shows a 4?

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

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

Correct C. $\frac{1}{2}$\)

D. $\frac{2}{3}$\)

Correct Answer: C

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Question 25 View Details

Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 end{bmatrix}$. Find the inverse of $A\\(end{bmatrix}). Find the inverse of$.

Correct A. \begin{bmatrix} 4 & -2 \\ -3 & 1 \end{bmatrix}

B. \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

C. \begin{bmatrix} 2 & -1 \\ -3 & 1 \end{bmatrix}

D. \begin{bmatrix} 1 & -2 \\ 3 & -4 \end{bmatrix}

Correct Answer: A

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