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JAMB Mathematics Past Questions & Answers - Page 196

976.

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

100

200

125

View answer & explanation

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

977.

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

$\frac{1}{27}$

$\frac{4}{3}$

View answer & explanation

Correct answer is C

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

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

= $\frac{1}{27}$

978.

Rationalize $\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}$

-2 $\sqrt{35}$

4 $\sqrt{7}$ - 6 $\sqrt{5}$

- $\sqrt{35}$

4 $\sqrt{7}$ - 8 $\sqrt{5}$

$\sqrt{35}$

View answer & explanation

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 $\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}$

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

= $\frac{5 \sqrt{35} - 7\sqrt{35}}{2}$

= $\frac{-2\sqrt{35}}{2}$

= - $\sqrt{35}$

979.

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?

103₅

1030₅

102₅

2002₅

3032₅

View answer & explanation

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

980.

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

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

4y = -3 + x

$\frac{y}{x}$ = $\frac{-3}{4}$

4x = y + 3

View answer & explanation

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