1) If \(a^2 + b^2 = 25\), \(x^2 + y^2 = 17\), and \(ax + by = 8\), then what is the value of \(ay - bx\)?

• (a) 33
• (b) 25
• (c) 21
• (d) 19

2) If \(2 = x + \frac{1}{1 + \frac{1}{5 + \frac{1}{2}}}\), then the value of \(x\) is:

• (a) \(\frac{14}{13}\)
• (b) 1
• (c) \(\frac{15}{13}\)
• (d) \(\frac{13}{15}\)

3) The value of \[ \left(a^{2/3} + 2a^{1/2} + 3a^{1/3} + 2a^{1/6} + 1\right) \left(a^{1/3} - 2a^{1/6} + 1\right) - a^{1/2}\left(a^{1/2} - 2\right), \text{ when } a = 7, \text{ is:} \]

• (a) 7
• (b) 0
• (c) 1
• (d) \(\sqrt{7}\)

4) If \(a\) is a natural number, then \(7a^2 + 7a\) is always divisible by:

• (a) 7 and 14 both
• (b) 7 only
• (c) 14 only
• (d) 21 only

5) \((ax + by)\) is a factor of:

• (a) \(a^2x^2 + 2ab - b^2y^2\)
• (b) \(a^2x^2 + 2abxy + b^2y^2\)
• (c) \(a^2x^3 + 2abx + b^2y^2x\)
• (d) \(a^2x^2 + 2ab + b^2y^2\)

6) If \(x = \sqrt[3]{5} + 2\), then the value of \(x^3 - 6x^2 + 12x - 12\) is:

• (a) 0
• (b) 2
• (c) 1
• (d) -1

7) If \(x^3 + 2x^2 - ax - b\) is divisible by \(x^2 - 1\), then values of \(a\) and \(b\) are:

• (a) a = -1, b = 2
• (b) a = 1, b = -2
• (c) a = 1, b = 2
• (d) a = 2, b = 2

8) If \(a + b + c + d = 2\), then maximum value of \((1 + a)(1 + b)(1 + c)(1 + d)\) is:

• (a) 91/9
• (b) 81/16
• (c) 63/22
• (d) 54/13

9) If \(x^{2a} = y^{2b} = z^{2c} \neq 0\), and \(x^2 = yz\), then value of \(\frac{ab + bc + ca}{bc}\) is:

• (a) 3
• (b) 3ac
• (c) 3bc
• (d) 3ab

10) The coefficient of \(x^2\) in \((2x + y)^3\) is:

• (a) 12y^2
• (b) 12
• (c) 12y
• (d) 8

11) If \((2x + 3y + 4)(2x + 3y - 5)\) is equivalent to \(ax^2 + by^2 + 2hxy+2gx+2fy+c\), then value of \(\frac{(g + f - c)}{abh}\) is:

• (a) 35/432
• (b) 19/108
• (c) 19/316
• (d) 37/216

12) \((4x^3y - 6x^2y^2 + 4xy^3 - y^4)\) can be expressed as:

• (a) \((x - y)^4 - x^4\)
• (b) \((x + y)^4 - y^4\)
• (c) \((x + y)^4 - x^4\)
• (d) \(x^4 - (x - y)^4\)

13) The value of \(\frac{1}{\sqrt{7 - 4\sqrt{3}}}\) is closest to:

• (a) 4.1
• (b) 4.2
• (c) 1.2
• (d) 3.7

14) If \(x = 5.51, y = 5.52, z = 5.57\), then value of \((x^3 + y^3 + z^3 - 3xyz)\) is:

• (a) 5.146
• (b) 51.46
• (c) 0.05146
• (d) 0.5146

15) If \(\sqrt{86 - 60\sqrt{2}} = a - b\sqrt{2}\), then value of \(\sqrt{a^2 + b^2}\), correct to 1 decimal place is:

• (a) 8.4
• (b) 8.2
• (c) 7.8
• (d) 7.2