POST UTME BABCOCK UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \sin \( 2x \ \) ) given that \( \sin \( x \ \) = \frac{3}{5} ) and \( \cos \( x \ \) = \frac{4}{5} ).
A. \frac{24}{25}
B. \frac{24}{25}
C. \frac{24}{25}
D. \frac{24}{25}
Question 2
Find the area under the curve of ( f(x) = \frac{1}{x^2} ) from \( x = 1 \) to \( x = 2 \).
A. 0.5
B. 1
C. 1.5
D. 2
Question 3
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are of different colors?
A. 1/4
B. 1/3
C. 2/5
D. 3/5
Question 4
Evaluate the definite integral \int_0^1 \( 2x + 1 \) dx.
A. 3
B. 2
C. 1
D. 4
Question 5
A histogram of exam scores is shown below. What is the mean score of the exam?
A. 30
B. 40
C. 50
D. 60
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 7
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30
D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30
Question 8
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2
A. 14.67
B. 14.67 m^2
C. 14.67 km^2
D. 14.67 cm^2
Question 9
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 10
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 11
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 12
A circle with center ( C ) and radius ( r ) is shown below. If \( OC = 6 \), find the length of ( AB ).
A. 4
B. 6
C. 8
D. 10
Question 13
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 14
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.
A. 12.5%
B. 15%
C. 17.5%
D. 20%
Question 15
A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. If the dis\tance between the two cities is 240 km, what is the average speed for the round trip?
A. 48
B. 50
C. 52
D. 54

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