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Showing 4901–4950 of 10710 questions
Instruction
JAMB Mathematics 1996
JAMB (UTME)
Mathematics
1996
Q4901.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).
Q4913.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
1996
Q4914.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 = $\frac{6}{11}$.
Instruction
JAMB Mathematics 1997
JAMB (UTME)
Mathematics
1997
Q4915.If $(1P03)_4 = 115_{10}$ find P
A$0$
B$1$
C$2$
D$3$
Correct Answer: C
$1(64) + P(16) + 0(4) + 3(1) = 67 + 16P = 115 \Rightarrow 16P = 48 \Rightarrow P = 3$. (The provided answer C is a typo).
JAMB (UTME)
Mathematics
1997
Q4916.Evaluate $64.764^2 - 35.236^2$ correct to 3 significant figures
A$2960$
B$2950$
C$2860$
D$2850$
Correct Answer: A
$(64.764 - 35.236)(64.764 + 35.236) = 29.528 \times 100 = 2952.8$. To 3 s.f. = $2950$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
1997
Q4917.Find the value of $(0.006)^3 + (0.004)^3$ in standard form.
Q4923.If $U = \{S, P, L, E, N, D, O, U, R\}$, $X = \{S, P, E, N, D\}$, $Y = \{P, N, O, U, R\}$. Find $X \cap (Y' \cup Z)$
A$\{P, O, U, R\}$
B$\{S, P, D, R\}$
C$\{P, N, D\}$
D$\{N, D, U\}$
Correct Answer: C
The question is incomplete.
JAMB (UTME)
Mathematics
1997
Q4924.A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students Igbo, while only 9 students speak both languages. How many students neither Hausa nor Igbo?
Let $u = \frac{1}{x}, v = \frac{1}{y}$. $2u - 3v = 2$, $4u + v = 10$. Solving gives $u = 2, v = \frac{2}{3}$. $x = \frac{1}{2}, y = \frac{3}{2}$. (The provided answer C is a typo).
JAMB (UTME)
Mathematics
1997
Q4927.Find the minimum value of $x^2 - 3x + 2$ for all real values of x.
Q4935.Two binary operations $*$ and $\oplus$ are defined as $m n = mn - n - 1$ and $m \oplus n = mn + n - 2$ for all real numbers m, n. find the values of $3 \oplus (4 5)$.
Q4939.Each of the base angles of an isosceles triangle is $58^{\circ}$ and all the vertices of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.
A$64^{\circ}$
B$116^{\circ}$
C$128^{\circ}$
D$148^{\circ}$
Correct Answer: C
Vertex angle = $180 - 2(58) = 64^{\circ}$. Angle at centre = $2 \times 64 = 128^{\circ}$.
JAMB (UTME)
Mathematics
1997
Q4940.From the figure above, FK // GR and FH = GH, $\angle RFK = 34^{\circ}$ and $\angle FGH = 47^{\circ}$, calculate the angle marked x.
Q4941.The figure above shows circles of radii 3cm and 2cm with centres at X and Y respectively. The circles have a transverse common tangent of length 25cm. Calculate XY.
A$630\text{cm}$
B$626\text{cm}$
C$615\text{cm}$
D$600\text{cm}$
Correct Answer: B
$XY = \sqrt{25^2 + (3+2)^2} = \sqrt{625 + 25} = \sqrt{650} \approx 25.5$. (The provided options have errors).
JAMB (UTME)
Mathematics
1997
Q4942.A chord of a circle diameter 42cm subtends an angle of $60^{\circ}$ at the centre of the circle. Find the length of the minor arc.
Q4943.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
1997
Q4945.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
1997
Q4946.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
1997
Q4947.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
1997
Q4948.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
1997
Q4949.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?
