Explanation

(a)

Draw RC produced to E parallel to DE.

\(\therefore < BCR = 52°\) (alternate angles BA//RC)

also < RCD = 48° (alternate angles RC//DE)

\(x° = 360° - (52° + 48°) = 360° - 100° = 260°\) (angles at a point = 360°)

(b) \(y - 2x < 5 ... (i)\)

\(2y + 2x \geq 4 \implies y + x \geq 2 ... (ii)\)

\(y + 2x \leq 10 ... (iii)\)

From (i), if \(y - 2x = 5\), when x = 0, y = 5, when x = 2, y = 9.

From (ii), if \(y + x = 2\). when x = 0, y = 2, when x = 3, y = -1

From (iii), if \(y + 2x = 10\), when x = 0, y = 10, when x = 2, y = 6.

Correct Answer: C. 72°

Explanation

In the diagram,< TUQ + 60^o(corresp. angles)

< QTU = 48^o (alternate angles)

< QU + 60^o + 48^o = 180^o(sum of angles of a \(\Delta\))

< TQU = 180^o - 108^o

= 72^o

Correct Answer: B. 11001

Explanation

4 girls and 5 boys

(a) p(only boys) = \(\frac{^{5}C_{3}}{^{9}C_{3}}\)

= \(\frac{5!}{2!3!} \times \frac{3!6!}{9!}\)

= \(\frac{10 \times 1}{84}\)

= \(\frac{5}{42}\)

(b) p(more girls than boys) = p(3 girls and no boys) or p(2 girls and 1 boy)

Number of ways of selecting = \(^{4}C_{3} \times ^{5}C_{0} + ^{4}C_{2} \times ^{5}C_{1}\)

= \(4 \times 1 + 6 \times 5\)

= 34 ways.

Without restrictions, selection can be made in \(^{9}C_{3}\) ways.

= \(\frac{9!}{6! 3!}\)

= 84 ways.

\(\therefore\) p(more girls than boys) = \(\frac{34}{84}\)

= \(\frac{17}{42}\).

Correct Answer: C. 7.44%

Explanation

%error = \(\frac{1.21 - 1.12}{1.21} \times 100%\)

= \(\frac{9}{121} \times 100%\)

= 7.44%

Correct Answer: A. \(-\frac{5}{3}\)

Explanation

\(8^{x+1}=\frac{1}{4}\\

2^{3(x+1)}=2^{-2}\Rightarrow 3(x+1)=-2\Rightarrow 3x+3=-2\\

3x=-5\Rightarrow x=-\frac{5}{3}\)

Correct Answer: C. 7cm

Explanation

Volume of a cube = (side)³

= (side)³

(side)³ = 343

side = 3\(\sqrt{343}\)

side = 7cm

Explanation

\(\sin 30° = \frac{4}{RT} \implies RT = \frac{4}{\sin 30°}\)

= \(\frac{4}{0.5} = 8m\)

(ii) |RQ| = |XY|

\(\therefore |XY|^{2} = 8^{2} - 4^{2} = 64 - 16 = 48\)

\(|XY| = \sqrt{48} = 4\sqrt{3} m = 6.928m\)

But |PY| = |PX| + |XY|

= 20 + 6.928 = 26.928m \(\approxeq\) 26.9m.

(iii) Let the angle of elevation = \(\theta\)

\(\tan \theta = \frac{TY}{PY} = \frac{7}{26.928}\)

\(\tan \theta = 0.26 \implies \theta = \tan^{-1} (0.26)\)

\(\theta = 14.57° \approxeq 14.6°\) (to 1 decimal place)

Explanation

(i) \(m * n = m + n + 2\)

Let the identity element be e.

Then \(m * e = m + e + 2 = m\)

\(e = -2\)

(ii) Let N be the inverse of n.

Then \(n * N = e\)

\(n * N = n + N + 2 = -2\)

\(n + N = -4 \implies N = -4 - n\)

Correct Answer: C. {x}