POST UTME LAUTECH 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 2
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 1950
B. 2050
C. 2150
D. 2250
Question 3
A circle has a radius of 5 cm. Find the area of the circle u\sing the formula \( A = pi r^2 \).
A. ( 50pi ) cm^2
B. ( 25pi ) cm^2
C. ( 75pi ) cm^2
D. ( 100pi ) cm^2
Question 4
Find the equation of the circle with centre \( -2, 3 \) 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 5
If $f(x) = \frac{1}{x+1}$, find $f^{-1}(x)$.
A. x = \frac{1}{1-x}
B. x = \frac{1}{x-1}
C. x = \frac{1}{x+1}
D. x = \frac{1}{x-1}
Question 6
A binary operation ( odot ) is defined as \( a odot b = ab + 2 \). Find the value of ( 3 odot 4 ).
A. ( 14 )
B. ( 16 )
C. ( 18 )
D. ( 20 )
Question 7
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. \( \frac{1}{2} \)
B. \( \frac{2}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{4}{5} \)
Question 8
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)
Question 9
A histogram of exam scores is shown below. What is the mean of the scores?
A. 60
B. 70
C. 80
D. 90
Question 10
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )
D. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{1}{2} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 12
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. (2, 2)
B. (3, 1)
C. (4, 0)
D. \( 5, -1 \)
Question 13
A population of bacteria is growing at a rate of ( 20% ) per hour. If the initial population is ( 1000 ), find the population after ( 3 ) hours.
A. ( 1000(1.2)^3 )
B. ( 1000(1.2)^2 )
C. ( 1000(1.2)^1 )
D. ( 1000(1.2)^0 )
Question 14
Solve the system of equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = -1 \)
D. \( x = -1, y = 1 \)
Question 15
A vector ( mathbf{a} ) is given by \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \). Find the magnitude of ( mathbf{a} ).
A. \( \sqrt{13} \)
B. \( \sqrt{15} \)
C. \( \sqrt{17} \)
D. \( \sqrt{19} \)

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