JAMB Mathematics Past Questions & Answers - Page 86

426.

The curved surface area of a cylinder 5cm high is 110cm2. Find the radius of its base
π = \(\frac{22}{7}\)

A.

2.6cm

B.

3.5cm

C.

3.6cm

D.

7.0cm

Correct answer is B

Curved surface area of cylinder = 2πrh

110 = 2 × \(\frac{22}{7}\) × r × 5

r = \(\frac{110 \times 7}{44 \times 5}\)

= 3.5cm

427.

If U = {x : x is an integer and 1 ≤ x ≤ 20 }
E1 = {x: x is a multiple of 3}
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2

A.

\(\frac{3}{4}\)

B.

\(\frac{3}{10}\)

C.

\(\frac{1}{4}\)

D.

\(\frac{1}{20}\)

Correct answer is A

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

E1 = {3, 6, 9, 12, 15, 18}

E2 = {4, 8, 12, 16, 20}

Probability of E2 = \(\frac{5}{20}\) i.e \(\frac{\text{Total number in}E_2}{\text{Entire number in set}}\)

Probability of set E2 = 1 − \(\frac{5}{20}\)

= \(\frac{15}{20}\)

= \(\frac{3}{4}\)

428.

What is the next number in the series 2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\)...

A.

\(\frac{1}{3}\)

B.

\(\frac{2}{8}\)

C.

\(\frac{3}{7}\)

D.

\(\frac{1}{8}\)

Correct answer is D

2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\).....

There are 4 terms in the series
Therefore the next number will be the 5th term

Tn = ar\(^{n − 1}\) (formular for geometric series)

a = first term = 2

r = common rate = \(\frac{\text{next term}}{\text{previous term}}\) = \(\frac{1}{2}\)

n = number of terms

T5 = 5th term = ?

T5 = ar\(^{5 - 1}\)

= ar\(^4\)

= 2 × (ar\(^{n − 1}\))4

= 2 × \(\frac{1}{16}\)

= \(\frac{1}{8}\)

429.

Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N

A.

{2, 3}

B.

{2, 3, 4}

C.

{3, 4, 6}

D.

{2}

Correct answer is D

T = {evenn numbers from 1 to 12} N = {common factors of 6,8 and 12} Find T ∩ N T = {2, 4, 6, 8, 10, 12} N = {2} T ∩ N = {2} i.e value common to T & N

430.

Given that tan x = \(\frac{2}{3}\), where 0o d" x d" 90o, Find the value of 2sinx.

A.

\(\frac{2\sqrt{13}}{13}\)

B.

\(\frac{3\sqrt{13}}{13}\)

C.

\(\frac{4\sqrt{13}}{13}\)

D.

\(\frac{6\sqrt{13}}{13}\)

Correct answer is C

tan x = \(\frac{2}{3}\)(given), is illustrated in a right-angled \(\Delta\)

thus m2 = 22 + 32

= 4 + 9 = 13

m = \(\sqrt{13}\)

Hence, 2sin x = 2 x \(\frac{2}{m}\)

2 x\(\frac{2}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}\)

= \(\frac{4\sqrt{13}}{13}\)