2004 - JAMB Mathematics Past Questions & Answers - page 3

21
A container has 30 gold medals, 22 silver medals and 18 bronze medals. If one medals is selected at the random from the container, what is the probability that it is not a gold medal?
A
9/35
B
11/35
C
4/7
D
3/7
CORRECT OPTION: c
Gold medals = 30
silver medals = 22
Bronze medals = 18/70
P(Gold medals) = 30/70 = 3/7
∴ P(not Gold medal) = 1 - 3/7
= 4/7
22
A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly
A
378 ways
B
462 ways
C
840 ways
D
924 ways
CORRECT OPTION: a
\(^{3}C_{1} \times ^{9}C_{5}=\frac{3!}{(3-1)!1!}\times \frac{9!}{(9-5)!5!}\=\frac{3!}{2!1!}\times \frac{9!}{4!5!}\=\frac{3 \times 2!}{2!\times 1}\times \frac{9\times8\times7\times6\times5!}{4\times3\times2\times1\times5!}\=3\times9\times2\times7\=378 \hspace{1mm}ways\)
23
The weight of 10 pupils in a class are 15 kg, 16 kg, 17 kg, 18 kg, 16 kg, 17 kg, 17 kg, 17 kg, 18 kg, and 16 kg. What is the range of this distribution?
A
4
B
3
C
1
D
2
CORRECT OPTION: b
Range = 18 - 15
= 3
24
I. Rectangular bars of equal width
II. The height of each rectangular bar is proportional to the frequency of the corresponding class interval.
III. Rectangular bars have common sides with no gaps in between
A histogram is described completely by
A
I, II and III
B
I and II
C
II and III
D
I and III
CORRECT OPTION: a
25
y = is inversely proportional to x and y = 4 when x = 1/2. Find x when y = 10.
A
2
B
10
C
1/5
D
1/10
CORRECT OPTION: c
y ∝ 1/x
y = K/x
K = xy
K = (1/2) * 4 ( when y = 4 and x = 1/2)
K = 2
∴y = 2/x
10 = 2/x (when y = 10)
10x = 2
x = 2/10
x = 1/5
26
What is the integral value of x which satisfy the inequality -1 < 3 -2x \(\leq\) 5?
A
-1. 0, 1, 2
B
-2, 1, 0 , -1
C
0, 1, 2
D
-1, 0, 1
CORRECT OPTION: d
-1 < 3 -2x and 3 - 2x \(\leq\) 5
2x < 3 + 1 and -2x \(\leq\) 5 - 3
2x < 4 and -2x \(\leq\) 2
x < 2 and x \(\geq\) 2/-2 = x \(\geq\) -1
If -1 \(\leq\) x < 2
it implies that x = -1, 0, 1
27
Given that the first and forth terms of G.P are 6 and 162 respectively, find the sum of the first three terms of the progression
A
27
B
8
C
78
D
48
CORRECT OPTION: c
\(a=6, U_4 = 162\U_4 = ar^{4-1}\U_4 = ar^3\162 = 6(r)^3\r^3 = 27\r=\sqrt[3]{27}\r=3\S_4 = \frac{a(r^{n}-1)}{r-1}\=\frac{6(3^{3}-1)}{3-1}\=\frac{6(27-1)}{2}\=3\times26\=78\)
28
If the operation * on the set of integers is defined by p * Q = \(\sqrt{pq}\), find the value of 4 * ( 8 * 32).
A
8
B
3
C
16
D
4
CORRECT OPTION: a
\(P\times Q=\sqrt{PQ}\4\times(8\times32)=4\times\sqrt{8\times32}\=4\times\sqrt{256}\=4\times16\=\sqrt{4\times16}\=\sqrt{64}\=8\)
29
Find the remainder when 3x3 + 5x2 - 11x + 4 is divided by x + 3
A
-4
B
4
C
1
D
-1
CORRECT OPTION: c
x = -3
substitute x = -3 in 3x3 + 5x2 - 11x + 4
3(-3)3 + 5(-3)2 - 11(-3) + 4
-81 + 45 + 33 + 4
-81 + 82
= 1
30
The nth term of two sequences are Qn = 3 . 2n - 2 and Um = 3 . 22m - 3. Find the product of Q2 and U2.
A
18
B
12
C
6
D
3
CORRECT OPTION: a
Qn = 3 * 2n - 2
Um = 3 * 22m - 3
Q2 * U2 = (3 * 22 - 2) * (3 * 22(2) - 3)
= 3 * 20 * 3 * 21
= 3 * 1 * 3 * 2
= 18
Pages: