UTME 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A chord is drawn 5 cm away from the centre of a circle of radius 13 cm. Calculate the length of the chord.
A. 7 cm
B. 9 cm
C. 12 cm
D. 24 cm
Question 2
What is the \( n \)-th term of the sequence \( 2,6,12,20 \ldots \) ?
A. 4 n-2
B. 2\left(3^{n-1}\right)
C. n^{2}+n
D. n^{2}+3 n+2
Question 3
Find the sum of the first 21 terms of the progression \( 10,-8,-6 \).
A. 180
B. 10
C. 200
D. 210
Question 4
Find the radius of a sphere whose surface area is \( 154 \mathrm{~cm}^{2} (\pi=22 / 7) \).
A. 7.00 cm
B. 3.50 cm
C. 3.00 cm
D. 1.75 cm
Question 5
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 6
If # 225.00 yields # 27.00 in x years simple interest at the rate of 4% per annum, find x.
A. 3
B. 4
C. 12
D. 17
Question 7
If the hypotenuse of a right-angled isosceles triangles is 2 cm, what is the area of the triangle?
A. 1 / 2 cm²
B. 1 cm²
C. \( \sqrt{2} \) cm²
D. 2 \( \sqrt{2} \) cm²
Question 8
Find all values of \( x \) satisfying the inequality \( -11 \leq 4-3 x \leq 28 \).
A. \( -5 \leq x \leq 8 \)
B. 5
C. \( -8 \leq x \leq 5 \)
D. \( -5 \leq x \leq 8 \)
Question 9
A cylindrical pipe, made of metal, is 3 cm thick if the internal radius of the pipe is 10 cm. Find the volume of metal used in making 3 cm of the pipe.
A. 153 \pi cm³
B. 207 \pi cm³
C. 15300 \pi cm³
D. 20700 \pi cm³
Question 10
If \( x+1 \) is a factor of \( x^{3}+3 x^{2}+k x+4 \), find the value of k.
A. 6
B. -6
C. 8
D. -8
Question 11
Find the length of a side of a rhombus whose diagonals are 6 cm and 8 cm.
A. 8 cm
B. 5 cm
C. 4 cm
D. 3 cm
Question 12
Obtain a maximum value of the function \( f(x) = x^3 - 12x + 11 \).
A. -5
B. -2
C. 2
D. 27
Question 13
If \( \log_{3} y+\log_{3} x^{2}=4 \), then y is
A. \( 4-\log_{3} x^{2} \)
B. \( \frac{4}{\log_{3} x^{2}} \)
C. \( \frac{4}{x} \)
D. +\( \frac{9}{x} \)
Question 14
A student blows a balloon and its volume increases at a rate of \( \pi(20-t^{2}) cm³ \) after t seconds. If the initial volume is 0 cm³, find the volume of the balloon after 2 seconds.
A. 37.00 \pi
B. 37.33 \pi
C. 40.00 \pi
D. 42.67 \pi
Question 15
In the figure, \( \mathrm{YXZ}=30^{\circ} \), \( X Y Z=105^{\circ} \) and \( X Y=8 \mathrm{~cm} \). Calculate YZ.
A. 16 \( \sqrt{2} \) cm
B. 8\( \sqrt{2} \) cm
C. 4\( \sqrt{2} \) cm
D. 22 cm

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