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POST UTME NILE UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Determine the probability that a randomly selected student from a class of 30 students will be taller than 1.75m, given that 60% of the students are taller than 1.75m.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 2 View Details

Find the equation of the circle with center $-2, 3$ and radius 4.

Correct A. $x + 2$^2 + $y - 3$^$2 = 16$

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

C. $x + 2$^2 + $y + 3$^$2 = 16$

D. $x - 2$^2 + $y - 3$^$2 = 16$

Correct Answer: A

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Question 3 View Details

Evaluate the definite integral $int_0^1 x^2 dx$.

Correct A. $1/3$

B. $1/2$

C. $2/3$

D. 1

Correct Answer: A

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Question 4 View Details

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

Correct A. $x - 1$, x - 2\)$x - 3 = 0$

B. $x + 1$, x - 2\)$x - 3 = 0$

C. $x - 1$, x + 2\)$x - 3 = 0$

D. $x + 1$, x + 2\)$x - 3 = 0$

Correct Answer: A

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Question 5 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.

Correct A. $4/3$

B. $2/3$

C. $1/3$

D. $1/2$

Correct Answer: A

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Question 6 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 7 View Details

Solve for y in the equation $y = \frac{1}{2} \left x + \frac{1}{x} \right \$ ).

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

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

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

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

Correct Answer: A

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Question 8 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 9 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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Question 10 View Details

A matrix A has the following elements: $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$. Find the determinant of matrix A.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 11 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 2$ from $x = 1$ to $x = 4$.

A. 20

B. 25

Correct C. 30

D. 35

Correct Answer: C

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Question 12 View Details

Solve the inequality ($\frac{x}{x - 2}\(> 0$\) for \$(frac{x}{x - 2} > 0\(x \neq 2$\).

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

B. $x < 2$

C. $x > 2$

D. $x < 0$

Correct Answer: A

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Question 13 View Details

A circle has equation $x - 1 \$^2 + $y - 2)^\(2 = 4$ ). Find the equation of the \\\$(()^(2$ = 4\)\tangent line at the point ( (3, 5) ).

Correct A. $y = -2x + 11$

B. $y = 2x - 7$

C. $y = -x + 6$

D. $y = x - 3$

Correct Answer: A

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Question 14 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the value of ( k ) if the area under the histogram is ( k ) square units.

A. 100

Correct B. 200

C. 300

D. 400

Correct Answer: B

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Question 15 View Details

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

Correct A. $x = -2$

B. $x = 0$

C. $x = -1$

D. $x = 1$

Correct Answer: A

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Question 16 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. 32\pi

B. 64\pi

Correct C. 96\pi

D. 128\pi

Correct Answer: C

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Question 17 View Details

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

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 18 View Details

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

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

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

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

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

Correct Answer: A

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Question 19 View Details

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

Correct A. $$12$

B. $$11$

C. $$13$

D. $$14$

Correct Answer: A

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Question 20 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the median.

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 21 View Details

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 6cm.

A. 100\pi $cm^3$

B. 200\pi $cm^3$

Correct C. 300\pi $cm^3$

D. 400\pi $cm^3$

Correct Answer: C

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Question 22 View Details

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

A. x < -1 or $x > 2$

Correct B. $x < 1$ or $x > 2$

C. $x < 1$ or $x > 3$

D. x < -1 or $x > 3$

Correct Answer: B

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Question 23 View Details

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 24 View Details

Solve the system of equations \begin{align*} x+y+z &= 6, \ x+2y+3z &= 11, \ x+3y+6z &= 16. \end{align*}

Correct A. $x = 1$, $y = 2$, $z = 3$

B. $x = 2$, $y = 3$, $z = 1$

C. $x = 3$, $y = 1$, $z = 2$

D. $x = 1$, $y = 3$, $z = 2$

Correct Answer: A

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Question 25 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. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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