POST UTME DELSU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let ( f(x) = \frac{1}{x^2 + 1} ). Find the value of \( int_{-1}^{1} f\( x \ \) , dx ).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{8} \)
D. \( \frac{pi}{16} \)
Question 2
Solve the equation x^3 - 6x^2 + 11x - 6 = 0
A. 1, 2, 3
B. 1, 2, 4
C. 1, 3, 4
D. 2, 3, 4
Question 3
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. ( 4 )
B. ( 6 )
C. ( 8 )
D. ( 10 )
Question 4
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. -2
B. -1
C. 1
D. 2
Question 5
A random variable ( X ) has a probability density function ( f(x) = egin{cases} 2x & 0 < x < 1 \ 0 & \text{otherwise} \end{cases} ). Find \( E\( X^2 \ \) ).
A. 1/3
B. 1/2
C. 2/3
D. 1
Question 6
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 = 32 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 64 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 128 )
Question 7
A histogram of the heights of students in a class is shown below. If the total number of students is 50, find the mean height of the students.
A. ( 170 )
B. ( 175 )
C. ( 180 )
D. ( 185 )
Question 8
A vector ( vec{A} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of ( vec{A} ).
A. x-component: 4, y-component: 3
B. x-component: 3, y-component: 4
C. x-component: 4, y-component: 4
D. x-component: 3, y-component: 3
Question 9
Solve the inequality \( |2x - 1| geq 3 \).
A. \( -∞, -2] ∪ [4, ∞ \)
B. \( -∞, -1] ∪ [2, ∞ \)
C. \( -∞, -3] ∪ [1, ∞ \)
D. \( -∞, -4] ∪ [3, ∞ \)
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. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 9
Question 11
Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 0 \end{cases} \).
A. x = 1, y = 1
B. x = 1, y = 0
C. x = 0, y = 1
D. x = 0, y = 0
Question 12
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
A circle has a radius of 4 cm. Find the area of the circle.
A. 16π cm^2
B. 32π cm^2
C. 64π cm^2
D. 128π cm^2
Question 14
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. Find the expected value of X.
A. 1.1
B. 1.4
C. 1.7
D. 2.1
Question 15
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = 90
C. x = 180
D. x = 270

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