2000 - JAMB Mathematics Past Questions and Answers - page 3
21
An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.
A
2/3 cm
B
2 cm
C
1 cm
D
3 cm
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22
3y = 4x - 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.
A
-4/3
B
-3/4
C
3/4
D
4/3
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23
if P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is
A
A straight line
B
a circle
C
the bisector of angle PXQ
D
the perpendicular bisector of PQ
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24
In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.
A
8
B
6
C
4
D
3
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25
A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 \(\leq\) x \(\leq\) 2, at which point(s) will they meet?
A
(1,1) only
B
(1,1) and (1,2)
C
(0,0) and (1,1)
D
(√2,√2) only
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26
Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
A
π
B
π/2
C
-π/2
D
-π
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27
If y = 2x - sin2x, find dy/dx when x = π/4
A
π
B
-π
C
π/2
D
-π/2
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28
A bowl is designed by revolving completely the area enclosed by y = x2 - 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?
A
7π cubic units
B
15π/2 cubic units
C
8π cubic units
D
17π/2 cubic units
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29
If the volume of a hemisphere is increasing at a steady rate of 18π m/s, at what rate is its radius changing when its is 6m?
A
2.30m/s
B
2.00 m/s
C
0.25 m/s
D
0.20 m/s
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30
X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.
A
0.30
B
0.50
C
0.57
D
1.80
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