Correct Answer: C. 55°

Explanation

?SOR = ?ORQ alternate angle.

Also ?OQR = ?OQR (Base angle of isosceles)

?QOR = 108

Correct Answer: D. 65.5°

Explanation

∠PQR (Reflex) = 360° – 68° = 292°

∠PQR = 2∠PQR

292° = 4x + 30°

4x = 292 – 30 = 262

\(x = \frac{262}{4}=65.5°\)

Correct Answer: D. 15

Explanation

First four prime numbers greater than 10 are 11, 13, 17, 19

The average \(= \frac{11+13+17+19}{4}=15\)

Correct Answer: D. x < -4

Explanation

\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\\

\frac{3(x+2)-4(x+1)>6}{12}; 3x + 6

Correct Answer: C. 6.4cm

Explanation

\(\frac{PR}{QR} = \frac{QR}{QY} = \frac{QP}{YR}\) (SSS Congruence)

\(\frac{QR}{4} = \frac{8}{5}\)

\(QR = \frac{4 \times 8}{5}\)

= 6.4 cm

Correct Answer: C. 32

Explanation

\(\sqrt{128} +\sqrt{18}-\sqrt{k}=7\sqrt{2}\\

\sqrt{2\times 64}+\sqrt{9\times 2} - \sqrt{k} = 7\sqrt{2}\\

8\sqrt{2} + 3\sqrt{2} - \sqrt{k} = 7\sqrt{2}; 11\sqrt{2} - \sqrt{k} = 7\sqrt{2}\\

-\sqrt{k}=7\sqrt{2}-11\sqrt{2}; -\sqrt{k} = -4\sqrt{2}; \sqrt{k}=4\sqrt{2}\\

=\sqrt{4^2\times 2} = \sqrt{16\times 2}; \sqrt{k}=\sqrt{32}; k = 32\)

Correct Answer: B. 10111

Explanation

\(23_{five} = X_{ten}; X_{ten} = 2\times 5^1 + 3\times 5^0 = 10 + 3 = 13\\

101_{three}=P_{ten}; P_{ten} = 1\times 3^2 + 0\times 3^1 + 1\times 3^0=9+0+1=10_{ten}\\

Y = 13+10=23_{ten}\);

Converting to base two

\(\begin{matrix}

2 & 23\\

2 & 11 &R1\\

2 & 5 & R1\\

2 & 2 & R1\\

2 & 1 & R0\\

& 0& R1 \uparrow\\

\end{matrix} \\

=y=10111_2\)

Correct Answer: C. 3

Explanation

Median = 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5

Median mark = \(\frac{3+3}{2} = \frac{6}{2} = 3\)

Correct Answer: C. 269.5cm³

Explanation

Volume of a solid cylinder = Base area x height

Base area \(=\pi r^2 =\frac{22}{7} \times \frac{7}{2}\times \frac{7}{2} = \frac{77}{2}\)

Volume of a solid cylinder = \(\frac{77}{2}\times \frac{7}{1} = \frac{539}{2}cm^3\\

=269.5cm^3\)

Explanation

(a) \((\frac{x^{2}}{2} - x + \frac{1}{2})(\frac{1}{x - 1})\)

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

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

\(\therefore (\frac{x^{2}}{2} - x + \frac{1}{2})(\frac{1}{x - 1}) = (\frac{(x - 1)^{2}}{2})(\frac{1}{x - 1})\)

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

(b)

(i) TQ = PR (North of Q)

\(\implies \sin 29 = \frac{PR}{40}\)

\(PR = 40 \sin 29 = 19.39 km\)

(ii) QR = East of Q

\(\frac{QR}{40} = \cos 29\)

\(QR = 40 \cos 29\)

= 34.98km

\(\approxeq\) 35km.

(c) Let the son's share = x.

Each daughter's share = \(\frac{3}{4}x\)

For the three daughters = \(3 \times \frac{3}{4} = \frac{9}{4}\)

\(x + \frac{9}{4}x = 5720 \implies \frac{13}{4}x = 5720\)

\(x = \frac{5720 \times 4}{13} = N1760\)