POST UTME NILE UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \begin{align*} x+y+z &= 6, \ x+2y+3z &= 11, \ x+3y+6z &= 16. \end{align*}
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
Question 2
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. \boxed{\frac{13}{3}}
B. \frac{11}{3}
C. \frac{15}{3}
D. \frac{17}{3}
Question 3
A circle passes through the points (2, 3), (4, 5), and (6, 7). Find the equation of the circle.
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
Question 4
A histogram has a mean of 25 and a s\tandard deviation of 5. Find the median.
A. 20
B. 25
C. 30
D. 35
Question 5
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 6
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 2\).
A. 4/3
B. 2/3
C. 1/3
D. 1/2
Question 7
A right-angled triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg.
A. 4 cm
B. 5 cm
C. 6 cm
D. 8 cm
Question 8
Find the equation of the circle with center \( -2, 3 \) and radius 4.
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
Question 9
Find the mean and s\tandard deviation of the data set \( \{ 2, 4, 6, 8, 10 \} \ \).
A. \( \bar{x} = 6, \sigma = 2 \)
B. \( \bar{x} = 4, \sigma = 2 \)
C. \( \bar{x} = 8, \sigma = 2 \)
D. \( \bar{x} = 10, \sigma = 2 \)
Question 10
A random sample of 16 students from a population of 100 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.5 cm
C. 4.5 cm
D. 5.5 cm
Question 11
Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).
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
Question 12
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 1023
B. 1024
C. 1025
D. 1026
Question 13
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 0.25
B. 0.375
C. 0.5
D. 0.625
Question 14
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \boxed{x < -3 \text{ or } x > 2}
B. x < -3 \text{ or } x > 1
C. x < -2 \text{ or } x > 2
D. x < -3 \text{ or } x > 1
Question 15
Find the mean deviation about the median of the data: 2, 4, 6, 8, 10.
A. \boxed{4}
B. 3
C. 2
D. 1

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