POST UTME ESUT 2021 Mathematics | Objective

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Question 1
Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 2
Solve the inequality $|x^2-4x+3| \geq 2$.
A. x \in \( -\infty, -1] \cup [3, \infty \)
B. x \in \( -\infty, 1] \cup [3, \infty \)
C. x \in \( -\infty, -1] \cup [1, \infty \)
D. x \in \( -\infty, 1] \cup [2, \infty \)
Question 3
Determine 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^2}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2x^2}{\( x^2 + 1 \ \)^2} )
Question 4
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. ( 15 )
B. ( 25 )
C. ( 35 )
D. ( 45 )
Question 5
Solve for x in the equation \frac{x}{x+1} + \frac{x}{x-1} = 1.
A. x = 0
B. x = -1
C. x = 1
D. x = -1/2
Question 6
Find the volume of the solid formed by revolving the region bounded by $y=x^2$ and $y=4$ about the x-axis.
A. \frac{256\pi}{15}
B. \frac{256\pi}{3}
C. \frac{256\pi}{5}
D. \frac{256\pi}{7}
Question 7
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)
B. \( 0, \frac{pi}{2}, \frac{3pi}{2} \)
C. ( 0, pi, 2pi )
D. \( \frac{pi}{2}, \frac{3pi}{2}, 2pi \)
Question 8
A binary operation $\circ$ is defined as $a \circ b = a^2 + b^2$. Find the value of $2 \circ 3$.
A. 13
B. 17
C. 19
D. 21
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
C. \( x < -\frac{1}{2} \) or \( x < \frac{3}{2} \)
D. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 10
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. ( 8 )
C. ( 12 )
D. ( 16 )
Question 11
A sequence is defined recursively as \( a_n = 2a_{n-1} + 1 \) with \( a_1 = 3 \). Find the value of \( a_{10} \).
A. ( 1023 )
B. ( 1024 )
C. ( 1025 )
D. ( 1026 )
Question 12
Find the equation of the line pas\sing through the points $A(2, 3)$ and $B(4, 5)$.
A. y = x + 1
B. y = x - 1
C. y = x + 2
D. y = x - 2
Question 13
A set of numbers is defined as \( S = { 1, 2, 3, 4, 5 } \). Find the number of subsets of S.
A. \( 2^5 \)
B. \( 2^3 \)
C. \( 2^2 \)
D. \( 2^1 \)
Question 14
Find the matrix $X$ such that $AX = B$, where $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$, $B = \begin{bmatrix} 7 \ 10 \end{bmatrix}$, and $X = \begin{bmatrix} x_1 \ x_2 \end{bmatrix}$.
A. X = \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. X = \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. X = \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. X = \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 15
A set ( S ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( S ) that contain exactly two elements.
A. ( 10 )
B. ( 12 )
C. ( 15 )
D. ( 20 )

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