POST UTME UNN 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
A. 62
B. 64
C. 66
D. 68
Question 2
Solve for $x$: $\log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 3
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. \( x = 1, 2, 3 \)
B. \( x = 1, 3, 4 \)
C. \( x = 2, 3, 4 \)
D. \( x = 1, 2, 5 \)
Question 4
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.
A. 8
B. 9
C. 10
D. 12
Question 5
A population of 1000 bacteria is growing at a rate of 20% per hour. What is the population after 3 hours?
A. 1600
B. 1800
C. 2000
D. 2200
Question 6
Solve for x in the equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -1
C. 1
D. 2
Question 7
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = π/2
C. x = π
D. x = 2π
Question 8
A random sample of 25 students from a university had a mean height of 175 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. 3.33 cm
C. 4.17 cm
D. 5.00 cm
Question 9
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the 5th term of the sequence.
A. 9
B. 11
C. 13
D. 15
Question 11
Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find \( det \( A + B \ \) ).
A. 20
B. 22
C. 24
D. 26
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{2} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{2} \)
C. \( x < -\frac{5}{2} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{2} \) or \( x < \frac{3}{2} \)
Question 13
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. \boxed{\( x - 1 \)^2 + \( y - 2 \)^2 = 5}
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4
C. \( x + 1 \)^2 + \( y - 2 \)^2 = 9
D. \( x - 1 \)^2 + \( y + 2 \)^2 = 4
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)

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