UTME 2020 Mathematics | Objective

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Question 1
The first term of a geometrical progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8.
A. \( \frac{8}{5} \)
B. \( \frac{8}{3} \)
C. \( \frac{72}{25} \)
D. \( \frac{56}{9} \)
Question 2
Given that \( \log_a 2 \) = 0.693 and \( \log_a 3 \) = 1.097, find \( \log_a 13.5 \).
A. 1.404
B. 1.790
C. 2.598
D. 2.790
Question 3
Factorize completely the expression \( abx^2 \) + 6y - 3ax - 2byx.
A. (ax - 2y)(bx - 3)
B. (bx + 3)(2y - ax)
C. (bx + 3)(ax - 2y)
D. (ax - 2y)(ax - b)
Question 4
Find the value of \( (0.006)^{3} + (0.0004)^{3} \) in standard form
A. \( 2.8 \times 10^{-9} \)
B. \( 2.8 \times 10^{-7} \)
C. \( 2.8 \times 10^{-5} \)
D. \( 2.8 \times 10^{-6} \)
Question 5
The sum of two numbers is twice their difference. If the difference of the numbers is p, find the larger of the two numbers.
A. \( \frac{P}{2} \)
B. \( \frac{3P}{2} \)
C. \( \frac{5P}{2} \)
D. 3P
Question 6
Simplify \( \log_2 96 - 2\log_2 6 \)
A. \( 2 - \log_2 3 \)
B. \( 3 - \log_2 3 \)
C. \( \log_2 3 - 3 \)
D. \( \log_2 3 - 2 \)
Question 7
Simplify \( \frac{x^2 -1}{ x^2 + 2x^2 - x - 2} \)
A. \( \frac{1}{x-1} \)
B. \( \frac{x-1}{x+1} \)
C. \( \frac{x-1}{x+2} \)
D. \( \frac{1}{x-2} \)
Question 8
What is the value of r if the distance between the points (4,2) and (1, r) is 3 units?
A. 1
B. 2
C. 3
D. 4
Question 9
Factorize \( 9p^{2} \)-\( q^{2} \)+6qr - \( 9r^{2} \).
A. (3p-3q+r)(3p-q-3r)
B. (6p-3q-3r)(3p-q-4r)
C. (3p-q+3r)(3P-q-3r).
D. (3q-p+3r)(3q-p+3r)
Question 10
The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term.
A. 175
B. 85
C. 64
D. 45
Question 11
If \( (1P03)_4 = 115_{10} \) find P.
A. 2
B. 3
C. 4
D. 5
Question 12
Find T in terms of K, Q and S if S=\(2r\sqrt{\pi(QT+K)}\)
A. \( \frac{S^2}{2\pi r^2 Q} - \frac{K}{Q} \)
B. \( \frac{S^2}{2\pi r^2 Q} - K \)
C. \( \frac{S^2}{4\pi r^2 Q} - \frac{K}{Q} \)
D. \( \frac{S^2}{2\pi r^2 Q} \)
Question 13
Make R the subject of the formula if T = \(\sqrt{\frac{KR^2 + M}{3}} \)
A. \( \displaystyle \sqrt{\frac{3T - K}{M}} \)
B. \( \displaystyle \sqrt{\frac{3T + M}{K}} \)
C. \( \displaystyle \sqrt{\frac{3T + K}{M}} \)
D. \( \displaystyle \sqrt{\frac{3T - M}{K}} \)
Question 14
If m * n = \( \frac{n}{m} \) - \( \frac{m}{n} \) for m, n \( \in \) R, evaluate -3 * 4.
A. \( \frac{-25}{12} \)
B. \( \frac{-7}{12} \)
C. \( \frac{7}{12} \)
D. \( \frac{25}{12} \)
Question 15
If x+1 is a factor of \( x^{2} \)+\( 3x^{2} \)+kx+4, find the value of k.
A. 6
B. -6
C. 8
D. -8

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