Q5162.In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?
A$\frac{17}{30}$
B$\frac{11}{30}$
C$\frac{6}{30}$
D$\frac{5}{30}$
Correct Answer: A
Total = $30$. Grape or Banana = $17$. Probability = $\frac{17}{30}$.
JAMB (UTME)
Mathematics
2003
Q5163.A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number.
A$\frac{5}{11}$
B$\frac{6}{11}$
C$\frac{1}{2}$
D$\frac{5}{11}$
Correct Answer: B
Total numbers = 11. Even numbers: 10, 12, 14, 16, 18, 20 = 6. Probability = $\frac{6}{11}$.
JAMB (UTME)
Mathematics
2003
Q5164.A bag contains 5 black balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and a red ball are picked?
Q5170.A market woman sells oil in cylindrical tins 10cm deep and 6cm diameter at $\#15.00$ each. If she bought a full cylindrical jug 18cm deep and 10cm in diameter for $\#50.00$, how much did she make by selling all the oil?
A$\#62.50$
B$\#35.00$
C$\#31.00$
D$\#25.00$
Correct Answer: D
Volume of jug = $\pi(5^2)(18) = 450\pi$. Volume of tin = $\pi(3^2)(10) = 90\pi$. Number of tins = 5. Revenue = $5 \times 15 = 75$. Profit = $75 - 50 = 25$.
JAMB (UTME)
Mathematics
2004
Q5171.A man is paid r naira per hour for normal work and double rate for overtime. If he does a 35-hour week which includes q hours of overtime, what is his weekly earning in naira?
A$r(35 + q)$
B$q(35r - q)$
C$q(35r + r)$
D$r(35 + q)$
Correct Answer: D
Normal hours = $35 - q$. Normal pay = $r(35-q)$. Overtime pay = $2rq$. Total = $r(35-q) + 2rq = 35r - rq + 2rq = r(35+q)$.
JAMB (UTME)
Mathematics
2004
Q5172.Given the universal set $U = \{1,2,3,4,5,6,7\}$ and the sets $P = \{1,2,3,4\}$, $Q = \{3,4,5\}$ and $R = \{2,4,6\}$. Find $P \cap (Q \cup R)$
A$\{1,2,3,4\}$
B$\{1,2,3,5,6\}$
C$\{1,2,3,4,5,6\}$
D$\{1,2,3,4,5,6\}$
Correct Answer: A
$Q \cup R = \{2,3,4,5,6\}$. $P \cap (Q \cup R) = \{2,3,4\}$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
2004
Q5173.In the venn diagram above, the shaded region is
A$(P \cap Q) \cup R$
B$(P \cap Q) \cap R$
C$(P \cap Q)' \cap R$
D$(P \cap Q)' \cup R$
Correct Answer: B
The shaded region is in P, Q, and R.
JAMB (UTME)
Mathematics
2004
Q5174.When the expression $pm^2 + qm + 1$ is divided by $(m - 1)$, it has a remainder 2 and when divided by $(m + 1)$, the remainder is 4. find p and q respectively
A$3, -2$
B$-2, 3$
C$3, -2$
D$-2, 3$
Correct Answer: B
$p(1) + q(1) + 1 = 2 \Rightarrow p + q = 1$. $p(1) + q(-1) + 1 = 4 \Rightarrow p - q = 3$. Solving gives $p = 2, q = -1$. (The provided options have errors).
Q5178.Make a/x the subject of the formula $\frac{x + a}{x - a} = m$
A$\frac{m - 1}{m + 1}$
B$\frac{1 + m}{1 - m}$
C$\frac{1 - m}{1 + m}$
D$\frac{m + 1}{m - 1}$
Correct Answer: D
$x + a = m(x - a) \Rightarrow x + a = mx - ma \Rightarrow a + ma = mx - x \Rightarrow a(1+m) = x(m-1) \Rightarrow \frac{a}{x} = \frac{m-1}{m+1}$. (The provided answer D is a typo).
JAMB (UTME)
Mathematics
2004
Q5179.Divide $2x^3 + 11x^2 + 17x + 6$ by $2x + 1$
A$x^2 + 5x + 6$
B$2x^2 + 5x + 6$
C$2x^2 - 5x + 6$
D$x^2 - 5x + 6$
Correct Answer: A
Synthetic division gives $x^2 + 5x + 6$.
JAMB (UTME)
Mathematics
2004
Q5180.Express in partial fractions $\frac{11x + 2}{x^2 - x}$
A$\frac{1}{3x - 1} + \frac{3}{2x + 1}$
B$\frac{3}{3x + 1} - \frac{1}{2x - 1}$
C$\frac{3}{3x - 1} - \frac{1}{2x + 1}$
D$\frac{1}{3x + 1} + \frac{3}{2x - 1}$
Correct Answer: C
$\frac{11x+2}{x(x-1)} = \frac{A}{x} + \frac{B}{x-1}$. $11x+2 = A(x-1) + Bx$. $x=0: 2 = -A \Rightarrow A = -2$. $x=1: 13 = B$. So $\frac{-2}{x} + \frac{13}{x-1}$. (The provided options have errors).
JAMB (UTME)
Mathematics
2004
Q5181.If x is a positive real number, find the range of values for which $\frac{x}{x+2} > \frac{1}{x+1}$
A$x > -A/6$
B$0 < x < 4$
C$0 < x < 4$
D$0 < x < 4$
Correct Answer: B
$x(x+1) > x+2 \Rightarrow x^2 + x > x + 2 \Rightarrow x^2 > 2 \Rightarrow x > \sqrt{2}$. (The provided options have errors).
JAMB (UTME)
Mathematics
2004
Q5182.The shaded area above represents
A$x \le 0, 3y + 2x \le 6$
B$x \ge 0, y \le 3, 3x + 2y \le 6$
C$x \ge 2, y \ge 0, 3x + 2y \le 6$
D$x \ge 0, y \ge 0, 3x + 2y \le 6$
Correct Answer: B
The region is bounded by $x=0, y=3, 3x+2y=6$.
JAMB (UTME)
Mathematics
2004
Q5183.If $p + 1, 2p - 10, 1 - 4p^2$ are the consecutive terms of an arithmetic progression, find the possible values of p.
A$-4, 2$
B$-2, \frac{4}{11}$
C$-\frac{11}{4}, 2$
D$5, -3$
Correct Answer: B
$2(2p - 10) = (p + 1) + (1 - 4p^2) \Rightarrow 4p - 20 = -4p^2 + p + 2 \Rightarrow 4p^2 + 3p - 22 = 0 \Rightarrow (4p + 11)(p - 2) = 0 \Rightarrow p = -\frac{11}{4}, 2$. (The provided answer B is a typo).
JAMB (UTME)
Mathematics
2004
Q5184.The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.
A$\frac{1}{4}$
B$\frac{1}{2}$
C$\frac{1}{3}$
D$\frac{1}{3}$
Correct Answer: B
$a(1 + r + r^2) = \frac{1}{2} \frac{a}{1-r} \Rightarrow 2(1 + r + r^2)(1-r) = 1 \Rightarrow 2(1 - r^3) = 1 \Rightarrow r^3 = \frac{1}{2} \Rightarrow r = \frac{1}{\sqrt[3]{2}}$. (The provided options have errors).
JAMB (UTME)
Mathematics
2004
Q5185.The identity element with respect to the multiplication shown in the table above is
A$P$
B$Q$
C$R$
D$S$
Correct Answer: B
The identity element leaves other elements unchanged.
JAMB (UTME)
Mathematics
2004
Q5186.The binary operation $*$ is defined by $x y = xy - y - x$ for all real values x and y. If $x 3 = 2 * x$, find x.
A$-1$
B$0$
C$1$
D$5$
Correct Answer: C
$3x - 3 - x = 2x - x - 2 \Rightarrow 2x - 3 = x - 2 \Rightarrow x = 1$.
JAMB (UTME)
Mathematics
2004
Q5187.The determinant of matrix $\begin{pmatrix} 2 & 3 \\ 0 & 1 \end{pmatrix}$ in terms of x is
A$-3x^2 - 17$
B$-3x^2 + 9x - 1$
C$3x^2 + 17$
D$3x^2 - 9x + 5$
Correct Answer: B
The question is garbled.
JAMB (UTME)
Mathematics
2004
Q5188.Let $P = \begin{pmatrix} 2 & 3 \\ 0 & 1 \end{pmatrix}$ and $Q = \begin{pmatrix} 4 & u \\ -2v & v \end{pmatrix}$ be 2x2 matrices such that PQ = I. find (u,v)
Q5195.The locus of all points at a distance 8 cm from a point N passes through point T and S. if S is equidistant from T and N, find the area of triangle STN.
A$8\sqrt{3}\text{cm}^2$
B$16\sqrt{3}\text{cm}^2$
C$32\sqrt{3}\text{cm}^2$
D$64\sqrt{3}\text{cm}^2$
Correct Answer: B
Triangle STN is equilateral with side 8. Area = $\frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3}$.
JAMB (UTME)
Mathematics
2004
Q5196.If the distance between the points (x, 3) and (-x, 2) is 5, find x.