UTME 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In how many ways can a delegation of 3 be chosen from 5 men and 3 women, if at least 1 man and 1 woman must be included?
A. 15
B. 28
C. 30
D. 45
Question 2
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 3
A binary operation \( \otimes \) defined on the set of integers is such that \( m \otimes n = m + n + mn \) for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0.
A. \( \frac{5}{4} \)
B. \( \frac{-5}{4} \)
C. \( \frac{5}{6} \)
D. \( \frac{-5}{6} \)
Question 4
\( \mathbf{P} \) is a point on one side of the straight line \( \mathbf{U V} \) and \( \mathbf{P} \) moves in the same direction as UV. If the straight line ST is one the locus of P and \( \angle D V U S =50^{\circ} \), find \( \angle D U S T \).
A. \( 50^{\circ} \)
B. \( 80^{\circ} \)
C. \( 130^{\circ} \)
D. \( 310^{\circ} \)
Question 5
What is the size of each interior angle of a 12 -sided regular polygon?
A. \( 120^{\circ} \)
B. \( 150^{\circ} \)
C. \( 30^{\circ} \)
D. \( 180^{\circ} \)
Question 6
Simplify \( 3 \frac{1}{3}-(2\frac{1}{3} \times 1\frac{1}{4})+\frac{3}{5} \)
A. \( 2 \frac{11}{60} \)
B. \( 2 \frac{1}{60} \)
C. \( 1 \frac{11}{60} \)
D. \( 1 \frac{1}{60} \)
Question 7
In a right angled triangle, if \( tanq =E \). What is \( \cos q-\sin q \) ?
A. G
B. H
C. F
D. I
Question 8
If Q= \( \begin{pmatrix} 9 & -2 \\ -7 & 4\end{pmatrix} \), then |Q| is
A. -50
B. -22
C. 22
D. 50
Question 9
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 10
The sum of the first n terms of the arithmetic progression 5,11,17,23,29,35,... is
A. n(3n-0.5)
B. n(3n+2)
C. n(3n+2.5)
D. n(3n+5)
Question 11
A chord of a circle of radius 7 cm is 5 cm from the centre of the circle. What is the length of the chord?
A. \( 4 \sqrt{6} \mathrm{~cm}\)
B. \( 3 \sqrt{6} \mathrm{~cm} \)
C. \( 6 \sqrt{6} \mathrm{~cm} \)
D. \( 2 \sqrt{6} \mathrm{~cm} \)
Question 12
The perpendicular bisector of a line \( \mathbf{X Y} \) is the locus of a point.
A. whose distance from X is always twice its distance from Y
B. whose distance from Y is always twice its distance from X
C. which moves on the line XY
D. which is equidistant from the points X and Y
Question 13
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 14
Determine the value of x for which \( (x^{2}-1)>0 \).
A. x<-1 or x>1
B. -1
C. x>0
D. x<-1
Question 15
A man walks \( 100 \text{ m} \) due West from a point X to Y, and then \( 100 \text{ m} \) due North to a point Z. Find the bearing of X from Z.
A. \( 195^\circ \)
B. \( 1350^\circ \)
C. \( 225^\circ \)
D. \( 045^\circ \)

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