Year : 
2004
Title : 
Mathematics (Core)
Exam : 
JAMB Exam

Paper 1 | Objectives

21 - 30 of 45 Questions

# Question Ans
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

Detailed Solution

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

Detailed Solution

\(^{3}C_{1} \times ^{9}C_{5}=\frac{3!}{(3-1)!1!}\times \frac{9!}{(9-5)!5!}\\=\frac{3!}{2!1!}\times \frac{9!}{4!5!}\\=\frac{3 \times 2!}{2!\times 1}\times \frac{9\times8\times7\times6\times5!}{4\times3\times2\times1\times5!}\\=3\times9\times2\times7\\=378 \hspace{1mm}ways\)
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

Detailed Solution

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

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

Detailed Solution

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 are the integer values of x which satisfy the inequality -1 < 3 -2x \(\leq\) 5?

A. 0, 1, 2

B. -2, 1, 0 , -1

C. 0, 1, 2

D. -1, 0, 1

Detailed Solution

-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

Detailed Solution

\(a=6, U_4 = 162\\U_4 = ar^{4-1}\\U_4 = ar^3\\162 = 6(r)^3\\r^3 = 27\\r=\sqrt[3]{27}\\r=3\\S_4 = \frac{a(r^{n}-1)}{r-1}\\=\frac{6(3^{3}-1)}{3-1}\\=\frac{6(27-1)}{2}\\=3\times26\\=78\)
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

Detailed Solution

\(P\times Q=\sqrt{PQ}\\4\times(8\times32)=4\times\sqrt{8\times32}\\=4\times\sqrt{256}\\=4\times16\\=\sqrt{4\times16}\\=\sqrt{64}\\=8\)
29.

Find the remainder when 3x3 + 5x2 - 11x + 4 is divided by x + 3

A. -4

B. 4

C. 1

D. -1

Detailed Solution

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

Detailed Solution

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
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

Detailed Solution

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

Detailed Solution

\(^{3}C_{1} \times ^{9}C_{5}=\frac{3!}{(3-1)!1!}\times \frac{9!}{(9-5)!5!}\\=\frac{3!}{2!1!}\times \frac{9!}{4!5!}\\=\frac{3 \times 2!}{2!\times 1}\times \frac{9\times8\times7\times6\times5!}{4\times3\times2\times1\times5!}\\=3\times9\times2\times7\\=378 \hspace{1mm}ways\)
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

Detailed Solution

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

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

Detailed Solution

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 are the integer values of x which satisfy the inequality -1 < 3 -2x \(\leq\) 5?

A. 0, 1, 2

B. -2, 1, 0 , -1

C. 0, 1, 2

D. -1, 0, 1

Detailed Solution

-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

Detailed Solution

\(a=6, U_4 = 162\\U_4 = ar^{4-1}\\U_4 = ar^3\\162 = 6(r)^3\\r^3 = 27\\r=\sqrt[3]{27}\\r=3\\S_4 = \frac{a(r^{n}-1)}{r-1}\\=\frac{6(3^{3}-1)}{3-1}\\=\frac{6(27-1)}{2}\\=3\times26\\=78\)
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

Detailed Solution

\(P\times Q=\sqrt{PQ}\\4\times(8\times32)=4\times\sqrt{8\times32}\\=4\times\sqrt{256}\\=4\times16\\=\sqrt{4\times16}\\=\sqrt{64}\\=8\)
29.

Find the remainder when 3x3 + 5x2 - 11x + 4 is divided by x + 3

A. -4

B. 4

C. 1

D. -1

Detailed Solution

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

Detailed Solution

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