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POST UTME UNILAG 2019 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $$12x \$ = $\frac{1}{2}$\) ) given that ( 0 leq x leq 2pi ).

Correct A. $\frac{\pi}{6}$\)

B. $\frac{\pi}{4}$\)

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

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

Correct Answer: A

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Question 2 View Details

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

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

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

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

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

Correct Answer: A

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Question 3 View Details

Solve the matrix equation $egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 11 \end{bmatrix}$.

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

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

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

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 4 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 1$ with initial term $a_1 = 3$. Find the value of $a_{10}$.

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 5 View Details

A circle has equation $x - 2 \$^2 + $y - 3)^\(2 = 4$ ). Find the equation of the \\\$(()^(2$ = 4\)\tangent line at the point ( (4, 7) ).

Correct A. $y = x + 1$

B. $y = x - 1$

C. $y = -x + 7$

D. $y = x - 7$

Correct Answer: A

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Question 6 View Details

Find the area under the curve $y = 2x\^2 + 3x - 1$ from $x = 0$ to $x = 2$.

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 7 View Details

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

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

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

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

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

Correct Answer: A

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Question 8 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 9 View Details

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

A. $x =$$\frac{\pi}{2}$\)

Correct B. $x =$$\frac{\pi}{4}$\)

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

D. $x =$$\frac{5\pi}{4}$\)

Correct Answer: B

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Question 10 View Details

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

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = 2x - 3$

D. $y = 2x + 3$

Correct Answer: A

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Question 11 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 12 View Details

Solve the differential equation $\frac{dy}{dx}$\) = $\frac{x^2 + 1}{y^2}$\)\) with the initial condition y(0) = 1.

Correct A. $y =$$\sqrt{x^2 + 1}$\)

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

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

D. $y =$$\frac{x^2 + 1}{x^3}$\)\)

Correct Answer: A

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Question 13 View Details

Find the area of the triangle formed by the points (0, 0), (3, 0), and (0, 4).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 14 View Details

A vector ($\vec{a}$\) has a magnitude of 5 units and makes an angle of 60\$(vec{a}\circ with the positive x-axis. Find the x and y components of \(\vec{a}$.

Correct A. $\vec{a} = 2$.5 \hat{i} + 4.33 \hat{j}

B. $\vec{a} = 4$.33 \hat{i} + 2.5 \hat{j}

C. $\vec{a} = 2$.5 \hat{i} - 4.33 \hat{j}

D. $\vec{a} = 4$.33 \hat{i} - 2.5 \hat{j}

Correct Answer: A

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Question 15 View Details

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

Correct A. x < -2 or $x > 0$

B. x > -2 or $x < 0$

C. $x < 0$ or $x > 2$

D. $x > 0$ or $x < 2$

Correct Answer: A

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Question 16 View Details

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

Correct A. -2

B. 4

C. 6

D. 8

Correct Answer: A

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Question 17 View Details

A histogram of exam scores is shown below. What is the mean score?

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 18 View Details

Solve for x in the equation [ \$\sin^2$ x + \$\cos^2$ $x = 1$ ].

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

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

C. $x =$$\frac{\pi}{6}$\)

D. $x =$$\frac{\pi}{3}$\)

Correct Answer: A

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Question 19 View Details

Find the volume of the solid formed by revolving the region bounded by the curve [ $y = x\^2$ ] about the x-axis.

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

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

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

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

Correct Answer: A

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Question 20 View Details

A vector [ $\vec{a} = 2\hat{i} + 3\hat{j} \] is given$. Find the magnitude of the vector.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 21 View Details

A circle has a diameter of 10 cm. Find the area of the circle in terms of π.

A. 50π

Correct B. 25π

C. 75π

D. 100π

Correct Answer: B

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Question 22 View Details

A histogram is constructed from the following data: 2, 4, 5, 6, 8, 9, 10. Find the mean and median of the data.

Correct A. 5.5, 6

B. 6, 5.5

C. 6.5, 6

D. 7, 6

Correct Answer: A

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Question 23 View Details

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

A. 32π

B. 64π

Correct C. 128π

D. 256π

Correct Answer: C

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Question 24 View Details

A 3x3 matrix is given by A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. Find the determinant of the matrix.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 25 View Details

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

Correct A. $x - 3$^2 + $y - 4$^$2 = 4$

B. $x - 4$^2 + $y - 5$^$2 = 9$

C. $x - 5$^2 + $y - 6$^$2 = 16$

D. $x - 6$^2 + $y - 7$^$2 = 25$

Correct Answer: A

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