Correct Answer: B. 210°

Explanation

\(\pi = 180°\)

\(\frac{7\pi}{6} = \frac{7 \times 180}{6} \)

= \(210°\)

Explanation

(a)(i) \(4x < 2 + 3x ..... (1)\)

\(4x - 3x < 2\)

\(x < 2\)

\(x - 8 < 3x ..... (2)\)

\(-8 < 2x\)

\(x > -4\)

\(x < 2 ; x > -4\).

(ii)

(b) Let the digits of the number be x and y.

\(x + y = 9 .... (1)\)

\((10y + x) - (10x + y) = 45 \)

\(10y - y + x - 10x = 45\)

\(9y - 9x = 45 .... (2)\)

From (1), y = 9 - x. Putting it into (2), we have

\(9(9 - x) - 9x = 45\)

\(81 - 9x - 9x = 45\)

\(36 = 18x \implies x = 2\)

\(\therefore y = 9 - x\)

= \(9 - 2 = 7\)

\(\therefore\) The bill = £27.

Correct Answer: A. 6

Explanation

sum of exterior angles = 360^o

Sum of interior angle = (n - 2) x 180

360 = \(\frac{1}{2}\) x(n - 2) x 180(90^o)

360 = \(\frac{1}{2}\) x(n - 2) x 90^o

\(\frac{360}{90}\) = a - 2

4 = n - 2

n = 4 + 2 = 6

Correct Answer: A. 2

Explanation

\(x^2+y^2+-2x-6y+5 =0\)

When differentiated:

\(x^2+y^2+-2x-6y+5 =0\) → 2x + 2y - 2 - 6 = 0

where x=3 and y=2

2[3] + 2[2] - 8 = 0

6 + 4 - 8 = 2

Explanation

(a) Present ages of a father and his son are in the ratio 10 : 3.

Let the sum of their ages be x.

The son's age = 15 years = \(\frac{3}{13} \times x = 15\)

\(x = \frac{15 \times 13}{3} = 65\)

\(\therefore\) The Father's present age = 65 - 15 = 50 years.

In z years time, the ratio of their ages = 2 : 1

\(\frac{50 + z}{15 + z} = \frac{2}{1}\)

\(\implies 50 + z = 2(15 + z)\)

\(50 + z = 30 + 2z \implies 50 - 30 = 2z - z\)

\(20 = z\)

Therefore, in 20 years' time, the ratio of their age will be 2 : 1.

(b) \(\frac{x + y + z}{3} = 6 \implies x + y + z = 18 .... (1)\)

\(\frac{x + y + z + l + u + v + w}{7} = 9 \implies x + y + z + l + u + v + w = 63 .... (2)\)

Putting (1) into (2), we have

\(18 + l + u + v + w = 63 \)

\(\therefore l + u + v + w = 63 - 18 = 45\)

Mean of l, u, v and w = \(\frac{45}{4} = 11.25\).

Correct Answer: C. 85cm²

Explanation

Area of a sector = θ/360 x πr\(^2\)

= 120/360 x 22/7 x 81/1

= 84.86 cm\(^2\)

\(\approxeq\) 85cm\(^2\) (to the nearest cm)

Correct Answer: D. inverse

Correct Answer: D. 52°

Correct Answer: B. 100.8

Explanation

\(\frac{28 * 360}{100}\)

= 100.8º

Correct Answer: C. 0

Explanation

\(\frac{x + P}{(x-1)(x-3)} = \frac{Q}{x-1} + \frac{2}{x-3}\)

\(\frac{x + P}{(x-1)(x-3)} = \frac{Q(x-3) + 2(x-1)}{(x-1)(x-3)}\)

Comparing LHS and RHS of the equation, we have

\(x + P = Qx - 3Q + 2x -2\)

\(P = -3Q - 2\)

\(Q + 2 = 1 \implies Q = 1 - 2 = -1\)

\(P = -3(-1) - 2 = 3 - 2 = 1\)

\(P + Q = 1 + (-1) = 0\)