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
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 3
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 4
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 5
Solve the quadratic equation x^2 + 4x + 4 = 0.
A. \text{Solution: } x = -2
B. \text{Solution: } x = -1
C. \text{Solution: } x = 0
D. \text{Solution: } x = 1
Question 6
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 7
Find the area under the curve y = x^2 from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 8
Let X be a random variable with probability density function f(x) = \\begin{cases} 2x & 0 < x < 1 \\ 0 & \text{otherwise} \\end{cases}. Find the probability that X is greater than 1/2.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 9
Solve the equation x^3 + 2x^2 - 7x + 12 = 0.
A. x = -3
B. x = -1
C. x = 3
D. x = 4
Question 10
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 11
If \( x^2 + 2x - 3 = 0 \), find the value of ( x ).
A. \( x = -3 \)
B. \( x = 1 \)
C. \( x = -1 \)
D. \( x = 3 \)
Question 12
In the circle with equation \( x - 1 \ \)^2 + \( y - 2 \)^2 = 4 ), find the equation of the \tangent line at the point where it intersects the line \( y = x + 1 \).
A. \( y = -x + 3 \)
B. \( y = x - 3 \)
C. \( y = -x + 1 \)
D. \( y = x + 1 \)
Question 13
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 14
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \frac{16}{15}\pi
B. \frac{32}{15}\pi
C. \frac{64}{15}\pi
D. \frac{128}{15}\pi
Question 15
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000

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