Q5102.The expression $ax^2 + bx + c$ equals 5 at $x = 1$ if its derivative is $2x + 1$ what are the values of a, b, c, respectively?
A$1, 3, 1$
B$1, 2, 1$
C$2, 1, 1$
D$1, 1, 3$
Correct Answer: D
$f'(x) = 2ax + b = 2x + 1 \Rightarrow a = 1, b = 1$. $f(1) = 1 + 1 + c = 5 \Rightarrow c = 3$.
JAMB (UTME)
Mathematics
2000
Q5103.X and Y are two events. The probability of X and Y is 0.7 and the probability of X is 0.4. If X and Y are independent, find the probability of Y.
Q5104.If the mean of the numbers $0, x+2, 3x+6$ and $4x+8$ is 4, find their mean deviation.
A$0$
B$2$
C$3$
D$4$
Correct Answer: C
Sum = $8x + 16 = 16 \Rightarrow 8x = 0 \Rightarrow x = 0$. Numbers: $0, 2, 6, 8$. Mean = 4. Deviations: $4, 2, 2, 4$. Sum = 12. Mean deviation = $\frac{12}{4} = 3$.
JAMB (UTME)
Mathematics
2000
Q5105.In how many ways can the word MATHEMATICS be arranged?
A$\frac{11!}{9!2!}$
B$\frac{11!}{9!2!2!}$
C$\frac{11!}{2!2!2!}$
D$\frac{11!}{2!2!}$
Correct Answer: C
MATHEMATICS has 11 letters with M(2), A(2), T(2). Number of arrangements = $\frac{11!}{2!2!2!}$.
JAMB (UTME)
Mathematics
2000
Q5106.A dice is rolled 240 times and the result depicted in the table above. If a pie chart is constructed to represent the data, the angle corresponding to 4 is
A$10^{\circ}$
B$16^{\circ}$
C$40^{\circ}$
D$60^{\circ}$
Correct Answer: D
The question is incomplete.
JAMB (UTME)
Mathematics
2000
Q5107.If $U = \{x : x \text{ is an integer and } 1 \le x \le 20\}$, $E_1 = \{x : x \text{ is a multiple of } 3\}$, $E_2 = \{x : x \text{ is a multiple of } 4\}$. And an integer is picked at random from U, find the probability that it is not in $E_2$.
Q5110.Find the sum of the range and the mode of the set of numbers $10,5,10,9,8,7,7,10,8,10,8,4,6,9,10,9,10,9,7,10,6,5$
A$16$
B$14$
C$12$
D$10$
Correct Answer: A
Range = $10 - 4 = 6$. Mode = 10. Sum = $6 + 10 = 16$.
JAMB (UTME)
Mathematics
2000
Q5111.In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
A$15$
B$28$
C$30$
D$45$
Correct Answer: D
Total ways = $^8C_3 = 56$. All men = $^5C_3 = 10$. All women = $^3C_3 = 1$. Favorable = $56 - 10 - 1 = 45$.
JAMB (UTME)
Mathematics
2000
Q5112.The table above shows the frequency distribution of the ages (in years) of pupils in a certain secondary school. What percentage of the total number of pupils is over 15 years but less than 21 years?
A$35\%$
B$45\%$
C$50\%$
D$60\%$
Correct Answer: B
Total = $6+14+15+10 = 45$. Over 15 and less than 21: $16-18$ (15) + $19-20$ (10) = 25. Percentage = $\frac{25}{45} \times 100 = 55.6\%$. (The provided answer B is a typo).
JAMB (UTME)
Mathematics
2000
Q5113.A number is selected at random between 20 and 30 both numbers inclusive. Find the probability that the number is a prime.
A$\frac{2}{11}$
B$\frac{5}{11}$
C$\frac{6}{11}$
D$\frac{8}{11}$
Correct Answer: A
Total numbers = 11. Primes: 23, 29 = 2. Probability = $\frac{2}{11}$.
JAMB (UTME)
Mathematics
2000
Q5114.Calculate the standard deviation of the following data: $7,8,9,10,11,12,13$.
A$2$
B$4$
C$10$
D$11$
Correct Answer: A
Mean = $10$. Variance = $\frac{9+4+1+0+1+4+9}{7} = \frac{28}{7} = 4$. Standard deviation = $2$.
Q5116.A cinema hall contains a certain number of people. If $22\frac{1}{2}\%$ are children, $47\frac{1}{2}\%$ are men and 84 are women, find the number of men in the hall.
A$133$
B$113$
C$63$
D$84$
Correct Answer: A
Children + Men = $22.5 + 47.5 = 70\%$. Women = $30\% = 84$. Total = $\frac{84}{0.3} = 280$. Men = $47.5\% \times 280 = 133$.
JAMB (UTME)
Mathematics
2003
Q5117.Simplify $213_4 \times 23_4$
A$13211_4$
B$10311_4$
C$10321_4$
D$12231_4$
Correct Answer: C
$213_4 = 39_{10}$, $23_4 = 11_{10}$. Product = $429_{10} = 12231_4$. (The provided answer C is a typo).
JAMB (UTME)
Mathematics
2003
Q5118.A woman buys 270 oranges for $\#1,800.00$ and sells at 5 for $\#40.00$. what is her profit?
Q5123.In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics?
Q5127.The sum of the first n terms of an arithmetic progression is 252. if the first term is $-16$ and the last term is 72, find the number of terms in the series.
Q5130.Find the values of x and y respectively if $3x - 5y + 5 = 0$ and $4x - 7y + 8 = 0$
A$-4, -5$
B$-5, -4$
C$5, 4$
D$4, 5$
Correct Answer: C
$3x - 5y = -5$, $4x - 7y = -8$. Multiply first by 4, second by 3: $12x - 20y = -20$, $12x - 21y = -24$. Subtracting: $y = 4$. $3x - 20 = -5 \Rightarrow 3x = 15 \Rightarrow x = 5$.
JAMB (UTME)
Mathematics
2003
Q5131.If $\begin{pmatrix} x & 2 \end{pmatrix} \begin{pmatrix} 1 & 4 \\ 3x & -5 \end{pmatrix} = 0$ find the value of x
A$-2$
B$-5$
C$2$
D$5$
Correct Answer: C
$x(1) + 2(3x) = 0 \Rightarrow x + 6x = 0 \Rightarrow 7x = 0 \Rightarrow x = 0$. (The provided options have errors).
JAMB (UTME)
Mathematics
2003
Q5132.Find the range of values of x satisfying the inequalities $5 + x \ge 8$ and $13 + 3x \le 7$
A$-6 \le x \le 3$
B$-6 \le x \le -3$
C$3 \le x \le 6$
D$-3 \le x \le 3$
Correct Answer: A
$x \ge 3$ and $3x \le -6 \Rightarrow x \le -2$. No solution. (The question has errors).
JAMB (UTME)
Mathematics
2003
Q5133.x varies directly as the product of U and V and inversely as their sum. If $x = 3$ when $U = 3$ and $V = 1$, what is the value of x if $U = 3$ and $V = 3$?
Q5142.An arc of a circle subtends an angle of $70^{\circ}$ at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.
Volume = $\frac{1}{2} \times 6 \times 5 \times 10 = 150\text{cm}^3$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
2003
Q5144.A cone with the sector angle of $45^{\circ}$ is cut out of a circle of radius r cm. find the base radius of the cone.
A$\frac{r}{16}\text{cm}$
B$\frac{r}{8}\text{cm}$
C$\frac{r}{4}\text{cm}$
D$\frac{r}{2}\text{cm}$
Correct Answer: B
Arc length = $\frac{45}{360} \times 2\pi r = \frac{\pi r}{4}$. Circumference of cone = $2\pi R = \frac{\pi r}{4} \Rightarrow R = \frac{r}{8}$.
JAMB (UTME)
Mathematics
2003
Q5145.A point P moves so that it is equidistant from points L and M. if LM is 16cm, find the distance of P from LM when P is 10cm from L.
A$12\text{cm}$
B$10\text{cm}$
C$8\text{cm}$
D$6\text{cm}$
Correct Answer: D
P is on the perpendicular bisector. Distance from midpoint = $\sqrt{10^2 - 8^2} = \sqrt{100-64} = 6\text{cm}$.
JAMB (UTME)
Mathematics
2003
Q5146.The angle between the positive horizontal axis and a given line is $135^{\circ}$. find the equation of the line if it passes through the point (2, 3).
A$x - y = 1$
B$x + y = 1$
C$x + y = 5$
D$x - y = 5$
Correct Answer: C
Slope = $\tan 135^{\circ} = -1$. $y - 3 = -1(x - 2) \Rightarrow y - 3 = -x + 2 \Rightarrow x + y = 5$.
JAMB (UTME)
Mathematics
2003
Q5147.Find the distance between the point Q(4, 3) and the point common to the lines $2x - y = 4$ and $x + y = 2$
A$\sqrt{10}$
B$\sqrt{5}$
C$\sqrt{26}$
D$\sqrt{13}$
Correct Answer: A
Intersection: $2x - (2-x) = 4 \Rightarrow 3x = 6 \Rightarrow x=2, y=0$. Distance = $\sqrt{(4-2)^2 + (3-0)^2} = \sqrt{4+9} = \sqrt{13}$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
2003
Q5148.The angle of elevation of a building from a measuring instrument placed on the ground is $30^{\circ}$. if the building is 40m high, how far is the instrument from the foot of the building?
Q5150.In the figure above, XYZ is a triangle with $XY = 5\text{cm}$, $XZ = 2\text{cm}$ and $XZ$ is produced to E making the angle $YZE = 150^{\circ}$. if the angle $XYZ = \theta$, calculate the value of $\sin \theta$.
A$\frac{3}{5}$
B$\frac{1}{2}$
C$\frac{2}{5}$
D$\frac{1}{5}$
Correct Answer: B
Angle $YXZ = 150^{\circ}$ (exterior angle). By sine rule: $\frac{2}{\sin \theta} = \frac{5}{\sin 150^{\circ}} = \frac{5}{0.5} = 10$. $\sin \theta = \frac{2}{10} = \frac{1}{5}$. (The provided answer B is a typo).