POST UTME CHRISTOPHER UNIVERSITY 2019 Mathematics | Objective

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Question 1
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 72\pi cm^3
D. 96\pi cm^3
Question 2
Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].
A. -120
B. 120
C. 0
D. -60
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 8 )
B. ( 16 )
C. ( 32 )
D. ( 64 )
Question 4
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.
A. 0
B. 1
C. -1
D. 2
Question 5
A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.
A. \( pi \times 4^2 \times 10 \)
B. \( pi \times 4^2 \times 5 \)
C. \( pi \times 4^2 \times 10^2 \)
D. \( pi \times 4^2 \times 10^3 \)
Question 6
Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).
A. ( 6 )
B. ( 12 )
C. ( 18 )
D. ( 24 )
Question 7
Solve the inequality \( \frac{2x-3}{x+1} > 0 \).
A. x<-1 or x>\frac{3}{2}
B. x<-1 or x>\frac{1}{2}
C. x<-1 or x<\frac{3}{2}
D. x<-1 or x>\frac{1}{2}
Question 8
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3
Question 9
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \[ -\frac{2x}{\( x^2 + 1 \)^2} \]
B. \[ \frac{2x}{\( x^2 + 1 \)^2} \]
C. \[ -\frac{2}{\( x^2 + 1 \)^2} \]
D. \[ \frac{2}{\( x^2 + 1 \)^2} \]
Question 10
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. \frac{32\pi}{3}
B. \frac{64\pi}{3}
C. \frac{128\pi}{3}
D. \frac{256\pi}{3}
Question 11
Find the area under the curve y = x^2 - 4x + 3 from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 12
Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 4x + 3} \geq 0.
A. \( -\infty, -1 \) \cup \( 1, \infty \)
B. \( -\infty, -1 \) \cup [1, \infty)
C. \( -\infty, -1 \) \cup (1, \infty]
D. \( -\infty, -1 \) \cup [1, \infty]
Question 13
Find the sum of the first 10 terms of the geometric series \[ 2 + 6 + 18 + \cdots \].
A. 1023
B. 1024
C. 1025
D. 1026
Question 14
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A and B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 15
Solve for ( x ) in the equation \( 2^x = 16 \).
A. ( 2 )
B. ( 4 )
C. ( 8 )
D. ( 16 )

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