Correct Answer: C. -6

Explanation

\(4p_2 + 4C_2 - 4p_3\)

\(np_r = \frac{n!}{[n-r]!} and nC_r = \frac{n!}{[n-r]!r!} \)

= \(\frac{4!}{[4-2]!} + \frac{4!}{[4-2]!2!} - \frac{4!}{[4-3]!} = \frac{4!}{2!} + \frac{4!}{2!2!} - \frac{4!}{1!}\)

= \(\frac{4*3*2!}{2!} + \frac{4*3*2!}{2!2!} - \frac{4*3*2*1}{1!}\)

12 + 6 - 24 = -6

Correct Answer: A. -6

Explanation

(a)

C\(B\)D = C\(D\)B = \(\frac{180^o - 107^o}{2}\)

= \(\frac{72^o}{2}\) = 36\(^o\)

< ODE = 90\(^o\) + 36 = 126\(^o\)

(b) tan x = \(\sqrt{3}\)

y\(^2\) (\(\sqrt{3}\))\(^2\) - (l)\(^2\)

y\(^2\) 3 + 1, Cos x = \(\frac{1}{2}\)

y = \(\sqrt{4}\) = 2

sin x = \(\frac{\sqrt{3}}{2}\)

\(\frac{(cos x)^2 - sin x}{(sin x)^2 + cos x}\)

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

= \(\frac{\frac{1}{4} - \frac{\sqrt{3}}{2}}{\frac{3}{4} + \frac{1}{2}}\)

= \(\frac{1 - 2\sqrt{3}}{4}\) \(\div\) \(\frac{5}{4}\)

= \(\frac{1 - 2 \sqrt{3}}{4}\) x \(\frac{4}{5}\)

= \(\frac{1 - 2\sqrt{3}}{5}\)

Correct Answer: A. 1/8

Explanation

(1/2)(1/4) = 1/8

Correct Answer: C. \(\frac{1}{2}\)

Explanation

\(\sqrt{2} + \sqrt{32} - 3\sqrt{18} = x\sqrt{8}\)

= \(\sqrt{36 \times 2} + \sqrt{16 \times 2} - 3\sqrt{2 \times 9}\)

= x\(\sqrt{2 \times 4}\)

= 6\(\sqrt{2} + 4\sqrt{2} - 9\sqrt{2} = 2 \times \sqrt{2}\)

\(\sqrt{2} (6 + 4 - 9) = 2x\sqrt{2}\)

\(\sqrt{2} = 2x \sqrt{2}\) divide both sides by \(\sqrt{2}\)

\(\frac{\sqrt{2}}{\sqrt{2}} = \frac{2 \times \sqrt{2}}{\sqrt{2}}\)

1 = 2x

2x = 1

x = \(\frac{1}{2}\)

Correct Answer: A. \(27^0\)

Explanation

Tan\(\theta = \frac{opp}{adj}\)

Tan\(\theta = \frac{56}{110}\)

\(\theta = tan^1(0.5091)\)

therefore, \(\theta\) = 27° ( to the nearest degree)

Correct Answer: B. 12

Correct Answer: C. 6

Explanation

23\(_y\) = 1111\(_{\text{two}}\),

2 x y\(^1\) + 3 x y\(^0\) = 1 x 2\(^3\) + 1 x 2\(^1\) + 1 x 2\(^o\)

2y + 3 = 8 + 4 + 2 + 1

2y + 3 = 15

\(\frac{2y}{2}\)

\(\frac{12}{2}\)

y = 6

Correct Answer: B. 80°

Explanation

< PQS = 50° (PQ = PR)

< PQS = < SPQ = 50° (QS = PS)

In triangle PSQ, < PQS + < QPS + < PSQ = 180°

50° + 50° + < PSQ = 180°

< PSQ = 180° - 100° = 80°

Correct Answer: B. x = 2.12 or − 0.79