POST UTME UNILAG 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone.
A. ( 288pi ) cm^3
B. ( 288pi ) m^3
C. ( 288pi ) in^3
D. ( 288pi ) ft^3
Question 2
If ( f(x) = \frac{1}{x^2 + 1} ), find \( f\( -x \ \) ).
A. \( f\( -x \ \) = \frac{1}{x^2 - 1} )
B. \( f\( -x \ \) = \frac{1}{x^2 + 1} )
C. \( f\( -x \ \) = \frac{-1}{x^2 + 1} )
D. \( f\( -x \ \) = \frac{1}{x^2 - 1} )
Question 3
Find the area under the curve y = x^2 from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 4
Find the sum of the first 10 terms of the geometric series ( 2, 6, 18, ldots ).
A. ( 10494 )
B. ( 10494.5 )
C. ( 10494.9 )
D. ( 10495 )
Question 5
In the diagram below, the graph of \( y = \frac{1}{2} \sin 2x \) is shown. What is the amplitude of the graph?
A. 1
B. 0.5
C. 2
D. 0.25
Question 6
A right circular cone has a height of 12 cm and a base radius of 4 cm. Find the volume of the cone.
A. 192\pi
B. 384\pi
C. 576\pi
D. 768\pi
Question 7
Find the value of \sin 2x if \sin x = \frac{3}{5}.
A. \frac{12}{25}
B. \frac{24}{25}
C. \frac{36}{25}
D. \frac{48}{25}
Question 8
A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the mean becomes 12. Find the sum of the original 5 numbers.
A. ( 40 )
B. ( 45 )
C. ( 50 )
D. ( 55 )
Question 9
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 10
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 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, -3 \) \cup \( 3, \infty \)
Question 12
Let A and B be two events such that P(A) = 1/4 and P(B) = 1/2. Find P\( A \cap B \) if A and B are indep\endent.
A. 1/8
B. 1/4
C. 1/2
D. 3/4
Question 13
Solve the differential equation \\frac{dy}{dx} = \\frac{y}{x} u\sing the chain rule.
A. y = x^2
B. y = x^3
C. y = x^2 + 1
D. y = x^3 + 1
Question 14
Solve the matrix equation \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 10 \end{bmatrix}.
A. \text{Solution: } x = 1, y = 2
B. \text{Solution: } x = 2, y = 1
C. \text{Solution: } x = 3, y = 4
D. \text{Solution: } x = 4, y = 3
Question 15
Solve the equation x^3 + 2x^2 - 7x + 12 = 0.
A. x = -3
B. x = -1
C. x = 3
D. x = 4

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