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JAMB Mathematics Past Questions & Answers - Page 325

1,621.

If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P $\cap$ Q

{3}

{2,3}

{2,3,5}

{1,2}

View answer & explanation

Correct answer is B

P = {2,3,5}

Q = {2,3,6,9}

P $\cap$ Q = {2,3}

1,622.

Simplify $(\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2$

$2\sqrt{6}$

$4\sqrt{6}$

$8\sqrt{6}$

$16\sqrt{6}$

View answer & explanation

Correct answer is C

$(\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2$

= $[(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]$

= $(\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]$

= $(2\sqrt{6})(4)$

= $8\sqrt{6}$

1,623.

If log₃x² = -8, what is x?

$\frac{1}{3}$

$\frac{1}{9}$

$\frac{1}{27}$

$\frac{1}{81}$

View answer & explanation

Correct answer is D

log₃x² = -8

x² = 3^-8

x = $3^{-8 \times \frac{1}{2}}$

x = 3^-4

x = $\frac{1}{3^4}$

x = $\frac{1}{81}$

1,624.

If 27 $^{x + 2}$ $\div$ 9 $^{x + 1}$ = 3 $^{2x}$ , find x.

View answer & explanation

Correct answer is B

$27^{x + 2} \div 9^{x + 1} = 3^{2x}$

$3^{3(x + 2)} \div 3^{2(x + 1)} = 3^{2x}$

$3^{3x + 6} \div 3^{2x + 2} = 3^{2x}$

$\therefore (3x + 6) - (2x + 2) = 2x$

$x + 4 = 2x \implies x = 4$

1,625.

A man earns N3,500 per month out of which he spends 15% on his children's education. If he spends additional N1,950 on food, how much does he have left?

N525

N1,025

N1,950

N2,975

View answer & explanation

Correct answer is B

Amount spent on children = $\frac{15}{100} \times 3500 = N525$

Amount spent = Amount on children + Additional amount on food

Amount Spent = N525 + N1950 = N2475

Therefore amount left = N3,500 - N2,475 = N1,025