POST UTME IMS U 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
A. 72
B. 80
C. 90
D. 96
Question 2
Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 3
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 2/5
C. 3/8
D. 1/3
Question 4
Find the vector \( \mathbf{v} \) such that \( \mathbf{v} \cdot \mathbf{i} = 3 \) and \( \mathbf{v} \cdot \mathbf{j} = 4 \).
A. \begin{pmatrix} 3 \ 4 \end{pmatrix}
B. \begin{pmatrix} 4 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ -4 \end{pmatrix}
D. \begin{pmatrix} -3 \ 4 \end{pmatrix}
Question 5
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. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 6
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 7
In a certain number base, the value of the digit 5 is represented as \( overline{1011}_5 \). What is the decimal equivalent of this number?
A. 21
B. 25
C. 31
D. 35
Question 8
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. ( 15 )
B. ( 20 )
C. ( 25 )
D. ( 30 )
Question 9
Solve for ( x ) in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. 2
B. 3
C. 4
D. 5
Question 10
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 11
Solve for x in the equation [ x^2 + 4x + 4 = 0 ].
A. -2
B. -1
C. 1
D. 2
Question 12
Find the equation of the circle with center \( -2, 3 \ \) ) and radius 4.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 13
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \) for x in the interval \( [0, 2 \pi] \).
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 14
A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If a new score of 90 is added to the set, what is the new mean?
A. 76
B. 77
C. 78
D. 79
Question 15
A particle moves along the curve \( y = x^2 \) with a velocity of 2 m/s. Find the acceleration at the point where \( x = 2 \).
A. 4 m/s²
B. 8 m/s²
C. 12 m/s²
D. 16 m/s²

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