POST UTME BABCOCK UNIVERSITY 2021 Mathematics | Objective

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Question 1
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. What is the expected value of X?
A. 1.1
B. 1.2
C. 1.3
D. 1.4
Question 2
Let $A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix}$. Find the product $AB$.
A. \begin{pmatrix} 19 & 22 \ 43 & 50 \end{pmatrix}
B. \begin{pmatrix} 23 & 26 \ 47 & 54 \end{pmatrix}
C. \begin{pmatrix} 27 & 30 \ 51 & 58 \end{pmatrix}
D. \begin{pmatrix} 31 & 34 \ 55 & 62 \end{pmatrix}
Question 3
Solve the trigonometric equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \) for x in the interval [0, 2\pi].
A. \frac{\pi}{6}
B. \frac{\pi}{3}
C. \frac{\pi}{2}
D. \frac{5\pi}{6}
Question 4
A set of numbers is defined as follows: $S = \{ x in \mathbb{R} : x^2 - 4x + 3 = 0 \}$. Find the elements of the set $S$.
A. \{1, 3\}
B. \{2, 4\}
C. \{3, 5\}
D. \{4, 6\}
Question 5
Find the value of \( \sin \left\( \arc\cos \frac{3}{5} \right \ \) ).
A. 0.6
B. 0.8
C. 0.4
D. 0.2
Question 6
A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 1$, with initial term $a_1 = 3$. Find the sum of the first five terms of the sequence.
A. 3 + 7 + 15 + 31 + 63
B. 3 + 5 + 11 + 23 + 47
C. 3 + 7 + 13 + 27 + 51
D. 3 + 9 + 17 + 33 + 65
Question 7
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 3x + 1 \).
A. 200x^2 + 300x + 10
B. 100x^2 + 150x + 5
C. 50x^2 + 75x + 2.5
D. 25x^2 + 37.5x + 1.25
Question 8
Solve the equation \[x^2 + 2x - 6 = 0\].
A. \[x = -3, x = 2\]
B. \[x = -2, x = 3\]
C. \[x = 3, x = -2\]
D. \[x = 2, x = -3\]
Question 9
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \) for \( x in mathbb{R} setminus {3, -3} \).
A. \( -infty, -3 \ \) cup (3, infty) )
B. \( -infty, -3 \ \) cup (3, infty) cup {0} )
C. \( -infty, -3 \ \) cup (3, infty) cup {4} )
D. \( -infty, -3 \ \) cup (3, infty) cup {0, 4} )
Question 10
Let X be a random variable with probability density function f(x) = \( egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} \). Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 11
Find the derivative of the function f(x) = x^3 - 2x^2 + x - 1.
A. 3x^2 - 4x + 1
B. 3x^2 - 4x - 1
C. 3x^2 + 4x + 1
D. 3x^2 + 4x - 1
Question 12
In the complex plane, the points $z_1 = 2 + 3i$ and $z_2 = 4 - 5i$ are represented by vectors $mathbf{z}_1$ and $mathbf{z}_2$. Find the magnitude of the vector $mathbf{z}_1 - mathbf{z}_2$.
A. \sqrt{26}
B. \sqrt{29}
C. \sqrt{31}
D. \sqrt{33}
Question 13
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30 cm^3
B. 40 cm^3
C. 50 cm^3
D. 60 cm^3
Question 14
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 15
In the diagram below, what is the value of x?
A. 3
B. 4
C. 5
D. 6

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