JAMB Mathematics Past Questions & Answers - Page 201

1,001.

p varies directly as the square of q and inversely as r. If p = 36, when q = 36, when q = 3 and r = 4, find p when q = 5 and r = 2

A.

72

B.

100

C.

90

D.

200

E.

125

Correct answer is D

P \(\alpha\) \(\frac{q^2}{r}\)

P = \(\frac{kq^2}{r}\)

k = \(\frac{pr}{q^2}\)

= \(\frac{36 x 4}{(3)^2}\)

p = \(\frac{16q^2}{r}\)

= \(\frac{16 \times 25}{2}\)

= 200

1,002.

Simplify \(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\)

A.

1

B.

6

C.

\(\frac{1}{27}\)

D.

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

Correct answer is C

\(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\) = \(\frac{3^n - 3^{n - 1}}{3^3(3^n - 3^{n - 1})}\)

= \(\frac{3^n - 3^{n - 1}}{27(3^n - 3^{n - 1})}\)

= \(\frac{1}{27}\)

1,003.

Rationalize \(\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}\)

A.

-2\(\sqrt{35}\)

B.

4\(\sqrt{7}\) - 6\(\sqrt{5}\)

C.

-\(\sqrt{35}\)

D.

4\(\sqrt{7}\) - 8\(\sqrt{5}\)

E.

\(\sqrt{35}\)

Correct answer is C

\(\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}\) = \(\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}\) x \(\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}\)

= \(\frac{(5 \times 7) + (5 \sqrt{7} \times 5) - (7 \times \sqrt{5} \times 7) (-7 \times 5)}{(\sqrt{7})^2}\)

= \(\frac{5 \sqrt{35} - 7\sqrt{35}}{2}\)

= \(\frac{-2\sqrt{35}}{2}\)

= - \(\sqrt{35}\)

1,004.

A trader in country where their currency 'MONI'(M) is in base five bought 1035 oranges at M145 each. If he sold the oranges at M245 each, what will be his gain?

A.

1035

B.

10305

C.

1025

D.

20025

E.

30325

Correct answer is B

Total cost of 1035 oranges at N145 each

= 1035 x 145

= 20025

Total selling price at N245 each

= (103)5 x 245

= 30325

Hence his gain = 30325 - 20025

= 10305

1,005.

A variable point p(x, y) traces a graph in a two-dimensional plane. (0, 3) is one position of P. If x increases by 1 unit, y increases by 4 units. The equation of the graph is

A.

-3 = \(\frac{y + 4}{x + 1}\)

B.

4y = -3 + x

C.

\(\frac{y}{x}\) = \(\frac{-3}{4}\)

D.

4x = y + 3

Correct answer is D

P(x, y), P(0, 3) If x increases by 1 unit and y by 4 units, then ratio of x : y = 1 : 4

\(\frac{x}{1}\) = \(\frac{y}{4}\)

y = 4x

Hence the sign of the graph is y + 3 = 4x