Correct Answer: B. 5.50

Explanation

Mean \(\bar{x}\) = \(\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10} \)

= \(\frac{55}{10} = 5.50\)

Correct Answer: C. 35

Explanation

?(E?G) = ?(E) + ?(G) - ?(E?G)

80 = 65 + 50 - ?(F?G)

??(E?G) = 115 - 80 = 35

Explanation

(a) \(P(Good) = \frac{18}{24} = \frac{3}{4}\)

\(P(Bad) = \frac{6}{24} = \frac{1}{4}\)

P(2 are good and 1 bad) = \(\frac{3}{4} \times \frac{3}{4} \times \frac{1}{4}\)

= \(\frac{9}{64}\)

(b) P(the 3 are bad) = \(\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}\)

= \(\frac{1}{64}\)

(c) P(the 3 are good) = \(\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4}\)

= \(\frac{27}{64}\)

Correct Answer: D. 2.82

Explanation

f(20\(^o\)) = cos 20\(^o\) = 0.9397

g(0.9397) = 3(0.9397)

= 2.82

Correct Answer: A. 13 metres

Explanation

\(v^{2} = u^{2} + 2as\)

\(v^{2} = u^{2} - 2gs\)

\(0 = 10^{2} - 2(10)s \implies -100 = -20s\)

\(s = 5 m + 8 m = 13m\) (8m is the height from where it was thrown)

Correct Answer: C. 5/22

Explanation

(a) \(\log (\frac{35 \times 49}{40 \div 56})\)

Given \(\log 5 = 0.6990 , \log 7 = 0.8451 , \log 8 = 0.9031\)

\(\log (\frac{35 \times 49}{40 \div 56} = \log (\frac{(7 \times 5) \times 7^{2}}{(8 \times 5) \div (8 \times 7)}\)

= \(\log (\frac{7^{3} \times 5}{5 \div 7}\)

= \(\log 7^{3} + \log 5 - (\log 5 - \log 7)\)

= \(3 \log 7 + \log 5 - \log 5 + \log 7\)

= \(4 \log 7\)

= \(4 \times 0.8471\)

= \(3.3804\)

(b) (i) Since there are 60 more adults than children, then the number of adults = x + 60

\(\therefore D 5(x + 60) + D x(2) = D 1280\)

\(5x + 300 + 2x = 1280\)

\(7x + 300 = 1280 \implies 7x = 1280 - 300 = 980\)

\(x = \frac{980}{7} = 140\)

There were 140 children.

(ii) Ratio of children to adults = \(x : x + 60\)

= \(140 : (140 + 60)\)

= \(140 : 200\)

= \(7 : 10\)

(iii) Total number of persons at the show : 140 + 200 = 340 persons.

Total amount gotten = D 1280

Average paid per person = \( D \frac{1280}{340}\)

= \(D \frac{64}{17}\)

= D 3.765

(iv) Percentage profit

Profit : D (1280 - 720) = D 560

% profit : \(\frac{560}{720} \times 100% = \frac{700}{9} %\)

= \(77.78%\)

Correct Answer: D. 32

Explanation

( 1- 2x)\(^4\) = 1 + px + qx\(^2\) - 32x\(^3\) + 16\(^4\)

compared with: 1 - 8x + 24x\(^2\) - 32x\(^3\) + 16\(^4\)

q = 24 and p = -8

(q - p) = 24 - [-8] = 32

Explanation

(a) \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = \sqrt{3 \times 3} + \sqrt{3 \times 2} - 5\sqrt{2 \times 3} - 5\sqrt{2 \times 2}\)

= \(3 + \sqrt{6} - 5\sqrt{6} - 5(2)\)

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

\(\therefore\) a = -7 and b = -4.

(b) \(\frac{2^{1 - y} \times 2^{y - 1}}{2^{y + 2}} = 8^{2 - 3y}\)

\(\frac{2^{1 - y + y - 1}}{2^{y + 2}} = (2^{3})^{2 - 3y}\)

\(2^{0 - (y + 2)} = 2^{6 - 9y} \implies 2^{- y - 2} = 2^{6 - 9y}\)

\(- y - 2 = 6 - 9y \implies - y + 9y = 6 + 2\)

\(8y = 8 \implies y = 1\).

Correct Answer: D. 6