UTME 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
What is the mean deviation of x, 2x, x+1 and 3x, if their mean is 2?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 2
Find the inverse of \( p \) under the binary operation * defined by \( p^{*} q=p+q-p q \), where \( p \) and \( q \) are real numbers and zero is the identity.
A. p
B. p-1
C. \( \frac{p}{p-1} \)
D. \( \frac{p}{p+1} \)
Question 3
Find to infinity, the sum of the sequence \( 1, T,(T)^{2},(T)^{3} \),
A. 10
B. 9
C. %
D. T
Question 4
If the interest on 3150.00 for \( 2\frac{1}{2} \) years is N4.50, find the interest on N250.00 for 6 months at the same rate.
A. N1.50
B. N7.50
C. N15.00
D. N18.00
Question 5
If Q= \( \begin{pmatrix} 9 & -2 \\ -7 & 4\end{pmatrix} \), then |Q| is
A. -50
B. -22
C. 22
D. 50
Question 6
If m*n=n-(m+2) for any real numbers m and n, find the value of 3*(-5).
A. -6
B. -8
C. -10
D. -12
Question 7
The probability of a student passing any examination is \( \frac{2}{3} \). If the student takes three examinations, what is the probability that he will not pass any of them?
A. \( \frac{2}{3} \)
B. \( \frac{4}{9} \)
C. \( \frac{8}{27} \)
D. \( \frac{1}{27} \)
Question 8
A circle of perimeter 28 cm is opened to form a square. What is the maximum possible area of the square?
A. \( 56 \mathrm{~cm}^{2} \)
B. \( 49 \mathrm{~cm}^{2} \)
C. \( 98 \mathrm{~cm}^{2} \)
D. \( 28 \mathrm{~cm}^{2} \)
Question 9
Find the range of values of x for which 3x-7 ≤ 0 and x+5>0
A. -5
B. -5 ≤ x ≤ \( \frac{7}{3} \)
C. -5
D. -5 ≤ x< \( \frac{7}{3} \)
Question 10
The cumulative frequency curve above shows the distribution of the scores of 50 students in an examination. Find the 36th percentile score.
A. 18%
B. 28%
C. 36%
D. 50%
Question 11
The midpoint of \( P(x, y) \) and \( Q(8,6) \) is (5, 8). Find \( x \) and y.
A. (2,10)
B. (2,8)
C. (2,12)
D. (2,6)
Question 12
The pie chart above represents 400 fruits on display in a grocery store. How many apples are in the store?
A. 45
B. 50
C. 60
D. 75
Question 13
A father decided to give \( 20 \% \) of his monthly income to his three children as their monthly allowance. The eldest child got \( 45 \% \) of the allowance and the youngest got \( 25 \% \). How much was the father's monthly income if the second child got N3 000?
A. N3 000
B. N45 000
C. N50 000
D. N60000
Question 14
Find the equation of a line perpendicular to line \( 2 y =5 x+4 \) which passes through (4,2).
A. \( 5y-2 x -18=0 \)
B. \( 5y+2 x-18=0 \)
C. \( 5y-2 x+18=0 \)
D. \( 5y+2 x-2=0 \)
Question 15
In the diagram above, EFGH is a circle centre of O, FH is a diameter and GE is a chord which meets FH at right angle at the point N. If NH = 8cm and EG = 24cm, calculate FH
A. \( 32 \mathrm{~cm} \)
B. \( 26 \mathrm{~cm} \)
C. \( 20 \mathrm{~cm} \)
D. \( 16 \mathrm{~cm} \)

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