The polynomial \(2x^{3} + x^{2} - 3x + p\) has a remainder of 20 when divided by (x - 2). Find the value of constant p.

• A. 8
• B. 6
• C. -6
• D. -8

Two numbers are respectively 35% and 80% more than a third number. The ratio of the two numbers is

• A. 7 : 16
• B. 3 : 4
• C. 16 : 7
• D. 4 : 3

Fifty boxes each of 50 bolts were inspected for the number which were defective. The following was the result

\(\begin{array}{c|c} \text{No. defective per box} & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No. of boxes} & 2 & 7 & 17 & 10 & 8 & 6\end{array}\)

Find the percentage of boxes containing at least 5 defective bolts each

• A. 96
• B. 94
• C. 92
• D. 90

Factorize the expression 2s\(^2\) - 3st - 2t\(^2\)

• A. (2s - t)(s + 2t)
• B. (2s + t)(s - 2t)
• C. (s + t)(2s - 1)
• D. (2s + t)(s -t)

Simplify; 2\(\frac{1}{4} \times 3\frac{1}{2} \div 4 \frac{3}{8}\)

• A. \(\frac{5}{9}\)
• B. 1\(\frac{1}{5}\)
• C. 1\(\frac{1}{4}\)
• D. 1\(\frac{4}{5}\)

A man bought a car for N800 and sold it for N520. Find his loss per cent

• A. 15%
• B. 25%
• C. 35%
• D. 10%

If f(x - 4) = x² + 2x + 3, Find, f(2)

• A. 6
• B. 11
• C. 27
• D. 51

Simplify the expression \(log_{10}18 - log_{10}2.88+log_{10}16\)

• A. 31.12
• B. 3.112
• C. 2
• D. 1

(a)

Curved Surface Area = \(\pi rl\)

\(115.5 = \frac{22}{7} \times r \times 10.5\)

\(115.5 = 33r\)

\(r = \frac{115.5}{33} = 3.5 cm\)

(b)

\(\therefore h^{2} + (3.50)^{2} = (10.5)^{2}\)

\(h^{2} = 10.5^{2} - 3.5^{2}\)

\(h^{2} = 98 \implies h = \sqrt{98}\)

\(h = 9.8994 cm \approxeq 9.90 cm\)

(c) Volume of a cone = \(\frac{1}{3} \pi r^{2} h\)

= \(\frac{1}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 9.90\)

= \(\frac{23.1 \times 11}{2}\)

= \(127.05 cm^{3} \approxeq 127 cm^{3}\)

If the 6th term of an arithmetic progression is 11 and the first term is 1, find the common difference.

• A. 125
• B. 53
• C. -2
• D. 2