POST UTME FUTO 2021 Mathematics | Objective

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Question 1
Let \( A = egin{pmatrix} 2 & 1 \ 3 & 2 \end{pmatrix} \). Find the inverse of ( A ).
A. \( A^{-1} = egin{pmatrix} 2 & -1 \ -3 & 2 \end{pmatrix} \)
B. \( A^{-1} = egin{pmatrix} 1 & -1 \ -3 & 2 \end{pmatrix} \)
C. \( A^{-1} = egin{pmatrix} 2 & 1 \ -3 & 2 \end{pmatrix} \)
D. \( A^{-1} = egin{pmatrix} 1 & 1 \ -3 & 2 \end{pmatrix} \)
Question 2
Find the area under the curve \( y = x^3 - 2x^2 + x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{23}{2}
B. \frac{25}{2}
C. \frac{27}{2}
D. \frac{29}{2}
Question 3
A binary operation \(*\) on the set \( \{0, 1\} \) is defined as follows: \( 0*0 = 0, 0*1 = 1, 1*0 = 1, 1*1 = 0 \). Find the value of \( 1*0 \)*\( 1*1 \).
A. 0
B. 1
C. 10
D. 01
Question 4
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. \( y = 2x - 3 \)
D. \( y = 2x + 3 \)
Question 5
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < -5 \) or \( x > 1 \)
C. \( x < -1 \) or \( x < 5 \)
D. \( x < -5 \) or \( x > 1 \)
Question 6
Solve the equation $\tan^2 x + \tan^2 2x = 2$ for $0 < x < \frac{\pi}{2}$.
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{6}
C. x = \frac{\pi}{3}
D. x = \frac{\pi}{2}
Question 7
Solve the system of linear equations \( egin{cases} x + y + z = 6 \ 2x + 2y + 2z = 12 \end{cases} \).
A. \( x = 2, y = 2, z = 2 \)
B. \( x = 3, y = 2, z = 1 \)
C. \( x = 4, y = 1, z = 1 \)
D. \( x = 5, y = 0, z = 1 \)
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 128
C. 256
D. 512
Question 9
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases} \).
A. \( x = \frac{7}{5}, y = \frac{17}{5} \)
B. \( x = \frac{7}{5}, y = -\frac{17}{5} \)
C. \( x = -\frac{7}{5}, y = \frac{17}{5} \)
D. \( x = -\frac{7}{5}, y = -\frac{17}{5} \)
Question 10
A circle with center $C$ passes through points $A$ and $B$. If $AB = 6$ and $CA = 3$, find the area of the circle.
A. 9\pi
B. 12\pi
C. 18\pi
D. 24\pi
Question 11
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ and $f_Y(y) = 3y^2$ for $0 < x < 1$ and $0 < y < 1$, respectively. Find the probability that $X + Y < 1$.
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{3}{4}
D. \frac{4}{5}
Question 12
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 13
Determine the value of $n$ in the equation $2^n + 5 cdot 2^{n-1} = 33$.
A. 3
B. 4
C. 5
D. 6
Question 14
Find the determinant of the matrix $\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}$.
A. -1
B. 1
C. 2
D. 3
Question 15
Let $A = \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}$. Find the inverse of $A$.
A. \begin{pmatrix} 1 & -1 \ -1 & 1 \end{pmatrix}
B. \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}
C. \begin{pmatrix} 1 & 1 \ 1 & 2 \end{pmatrix}
D. \begin{pmatrix} 2 & -1 \ -1 & 1 \end{pmatrix}

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