JAMB Mathematics Past Questions & Answers - Page 50

246.

If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.

A.

x = -4

B.

x = 2

C.

x = -2

D.

x = 4

Correct answer is A

\(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\)

\((5^2)^{(1 - x)} \times 5^{(x + 2)} \div (5^{-3})^x = (5^4)^{-1}\)

\(5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}\)

\(5^{(2 - 2x) + (x + 2) - (-3x)} = 5^{-4}\)

Equating bases, we have

\(2 - 2x + x + 2 + 3x = -4\)

\(4 + 2x = -4 \implies 2x = -4 - 4\)

\(2x = -8\)

\(x = -4\)

247.

Express \((0.0439 \div 3.62)\) as a fraction.

A.

\(\frac{21}{100}\)

B.

\(\frac{21}{1000}\)

C.

\(\frac{12}{1000}\)

D.

\(\frac{12}{100}\)

Correct answer is C

\((0.0439 \div 3.62)\)

= 0.01213

\(\approxeq\) 0.012

= \(\frac{12}{1000}\)

248.

If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).

A.

\(\frac{\pi h}{3} (2R + r)\)

B.

\(2R + r + \frac{\pi h}{3}\)

C.

\(\frac{\pi h}{3} (2R^2 + r + 2r)\)

D.

\(\frac{2R^2}{3} \pi h\)

Correct answer is A

\(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\)

\(V = \frac{\pi R^2 h}{3} + \frac{\pi Rr h}{3} + \frac{\pi r^2 h}{3}\)

\(\frac{\mathrm d V}{\mathrm d R} = \frac{2 \pi R h}{3} + \frac{\pi r h}{3}\)

= \(\frac{\pi}{3} (2R + r)\)

249.

A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?

A.

43.7% loss

B.

13.2% gain

C.

13.2% loss

D.

43.7% gain

Correct answer is C

Cost price of the car = N 1,250.00

Selling price = N 1,085.00

Loss = N (1250 - 1085)

= N 165.00

% loss = \(\frac{165}{1250} \times 100%\)

= 13.2% loss

250.

Each of the interior angles of a regular polygon is 140°. Calculate the sum of all the interior angles of the polygon.

A.

1080°

B.

1260°

C.

2160°

D.

1800°

Correct answer is B

Since each interior angle = 140°;

Each exterior angle = 180° - 140° = 40°

Number of sides of the polygon = \(\frac{360°}{40°}\)

= 9 

Sum of angles in the polygon = 140° x 9

= 1260°