POST UTME IMS U 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A quadratic equation has roots 2 and 3. What is the product of the roots?
A. \( -6 \)
B. \( -5 \)
C. \( -4 \)
D. \( -3 \)
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 3
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8 cm
B. 6 cm
C. 4 cm
D. 2 cm
Question 4
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{4}{5} \)
B. \( \frac{3}{4} \)
C. \( \frac{5}{4} \)
D. \( \frac{4}{3} \)
Question 5
Solve the equation \log_{10} \( x^2 \) = 4.
A. 10
B. 100
C. 1000
D. 10000
Question 6
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. What is the probability that a randomly selected student from this population has a height between 170 cm and 180 cm?
A. 0.308
B. 0.3087
C. 0.309
D. 0.3097
Question 7
Solve the equation \( x^3 + 2x^2 - 7x + 12 = 0 \).
A. \( x = -3 \)
B. \( x = -1 \)
C. \( x = 2 \)
D. \( x = 3 \)
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 = 25 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 49 )
Question 9
A cylindrical \tank with a radius of 5m and height of 10m is filled with water. Find the volume of water in the \tank.
A. \( 785.4 , \text{m}^3 \)
B. \( 1570.8 , \text{m}^3 \)
C. \( 3141.6 , \text{m}^3 \)
D. \( 6283.2 , \text{m}^3 \)
Question 10
Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \( x = \frac{-5 pm \sqrt{109}}{4} \)
B. \( x = \frac{5 pm \sqrt{109}}{4} \)
C. \( x = \frac{-5 pm \sqrt{109}}{2} \)
D. \( x = \frac{5 pm \sqrt{109}}{2} \)
Question 11
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. -1
D. 2
Question 12
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 13
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{4pi}{3} \)
B. \( \frac{5pi}{3} \)
C. \( \frac{2pi}{3} \)
D. \( \frac{pi}{3} \)
Question 14
Let \( S = \{ 1, 2, 3, \ldots, 10 \} \). Find the number of subsets of S that contain exactly 3 elements.
A. \( 120 \ \)
B. \( 126 \ \)
C. \( 132 \ \)
D. \( 140 \ \)
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 12 )
B. ( 20 )
C. ( 30 )
D. ( 40 )

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