JAMB Mathematics Past Questions & Answers - Page 163

811.

x is directly proportional to y and inversely proportional to z. If x = 9 when y = 24 and z = 8, what is the value of x when y = 5 and z = 6?

A.

\(\frac{5}{6}\)

B.

11

C.

3\(\frac{3}{5}\)

D.

2\(\frac{1}{2}\)

E.

1\(\frac{1}{5}\)

Correct answer is D

x \(\alpha\) y = x \(\alpha\) \(\frac{1}{z}\)

x \(\alpha\) \(\frac{1}{z}\)

x = k \(\frac{y}{z}\)

k = \(\frac{xz}{y}\) = \(\frac{9 \times 8}{24}\)

= 3

x = \(\frac{xz}{y}\)

= \(\frac{3 \times 5}{6}\)

= \(\frac{15}{6}\)

= \(\frac{5}{2}\)

= 2\(\frac{1}{2}\)

812.

The annul profits of a transport business were divided between the partners A and B in the ratio 3 : 5. If B received N3000 more than A, the total profit was

A.

N5000

B.

N1800

C.

N12000

D.

N24000

E.

N8000

Correct answer is C

A : B = 3 : 5

Total ratio = 3 + 5 = 8

Let rept, the total profit, A receives \(\frac{3x}{8}\)

\(\frac{5x}{8}\) - \(\frac{3}{x}\) = 3000

\(\frac{5x}{8}\) - \(\frac{3x}{8}\) = 3000

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

= 3000

2x = 2400

x = 1200

N12,000

813.

In base ten, the number 101101 (base 2) equals

A.

15

B.

4

C.

45

D.

32

E.

90

Correct answer is C

(101101)2 \(\begin{array}{c|c} 2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^o\\ \hline 1 & 0 & 1 & 1 & 0 & 1\end{array}\)

= 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 2o

= 32 + 0 + 8 + 4 + 0 + 1

= (45)10

814.

After getting a rise of 15%, a man's new monthly salary is N345. How much per month did he earn before the increase?

A.

N330

B.

N396.75

C.

N300

D.

N293.25

E.

N360

Correct answer is C

Let x represent his monthly salary before increase 15% of

x = 345

% profit = (100 + 15)%

= 115%

\(\frac{115}{100}\)x = 345

115x = 34500

x = N300.00

815.

In \(\bigtriangleup\)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS

A.

4cm

B.

32cm

C.

\(\frac{30}{7}\)

D.

\(\frac{40}{7}\)

E.

4.8cm

Correct answer is E

Cos Q = \(\frac{r^2 + p^2 - q^2}{2rp}\)

= \(\frac{10^2 + 8^2 - 6^2}{2(10)(8)}\)

= \(\frac{164 - 36}{160}\)

= \(\frac{128}{160}\)

= 0.8

Q = Cos-1 o.8

= 37o x rep. from rt< RSQ, Let RS = x

\(\frac{x}{sin 37^o}\) = \(\frac{8}{sin 90^o}\)

but sin 90o = 1

x = 8 sin 37o

x = 4.8cm