POST UTME CHRISTOPHER UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the geometric series \( 2, 4, 8, 16, \ldots \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 2
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. \( \frac{64}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{16}{3} \)
D. \( \frac{8}{3} \)
Question 3
Find the surface area of the solid formed by rotating the region bounded by y = x^2 and y = 4 - x^2 about the x-axis.
A. 16π
B. 32π
C. 48π
D. 64π
Question 4
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2, & 0 leq y leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that \( X + Y leq 1 \).
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 5
Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].
A. -3
B. 0
C. 3
D. 6
Question 6
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = 2x - 2
D. y = 2x + 2
Question 7
Let \( S = { 1, 2, 3, 4, 5 } \). Find the number of subsets of ( S ) that contain exactly 3 elements.
A. \( 2^3 = 8 \)
B. \( 2^4 = 16 \)
C. \( 2^5 = 32 \)
D. \( 2^6 = 64 \)
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 9
Find the volume of the sphere with radius 5 cm.
A. 500\pi
B. 1000\pi
C. 2000\pi
D. 5000\pi
Question 10
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the vector ( mathbf{a} cdot mathbf{b} ) u\sing the dot product formula.
A. \( 2\( -1 \ \) + 3(4) = 10 )
B. ( 2(4) + 3\( -1 \) = 5 )
C. ( 2(3) + 3\( -1 \) = 3 )
D. \( 2\( -1 \ \) + 3(3) = 5 )
Question 11
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 0
B. -2
C. 2
D. -4
Question 12
A binary operation \( * \) on the set of real numbers is defined as \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).
A. 13
B. 5
C. 7
D. 9
Question 13
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 2
D. y = x - 2
Question 14
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 15
Solve for x in the equation: \( 2^x = 64 \).
A. 5
B. 6
C. 7
D. 8

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