# Mathematics (2015) | Study Mode

Question 61
A

3(2 + $$\sqrt{5}$$)

B

2(3 + $$\sqrt{5}$$)

C

5(2 + $$\sqrt{3}$$)

D

$$3\sqrt{3}$$ + 1

##### Explanation

5 (2 - $$\sqrt{3}$$)

Using conjugate surds

[5 (2 - $$\sqrt{3}$$)]$$\times$$(2 + $$\sqrt{3}$$) (2 + $$\sqrt{3}$$)]

[5(2+$$\sqrt{3}$$)((2- $$\sqrt{3}$$))2]

[5(2 +$$\sqrt{3}$$) (2)2- ($$\sqrt{3}$$)2]

[5(2 +$$\sqrt{3}$$) (4- 3)]

= 5(2 + $$\sqrt{3}$$)

Question 62
A

(a + b)(a - b)

B

(a - 2 + b)

C

(a + 1)(a - 2 + b)

D

(a + b) 2

##### Explanation

The trinomial = $$a^2 - 4a + 4 \\ a^2 - b^2- 4a + 4 = (a^2 - 4a + 4) - b^2 \\ (a^2 - 2a - 2a + 4) - b^2 \\ [a(a - 2)- 2(a - 2)] - b^2 \\ (a - 2)2 - b^2 \\ (a - 2 + b)(a - 2 - b )$$

Question 63
A
$$\frac{2\sqrt{13}}{13}$$
B
$$\frac{3\sqrt{13}}{13}$$
C
$$\frac{4\sqrt{13}}{13}$$
D
$$\frac{6\sqrt{13}}{13}$$
##### Explanation
tan x = $$\frac{2}{3}$$(given), is illustrated in a right-angled $$\Delta$$

thus m2 = 22 + 32

= 4 + 9 = 13

m = $$\sqrt{13}$$

Hence, 2sin x = 2 x $$\frac{2}{m}$$

2 x$$\frac{2}{\sqrt{13}}$$

= $$\frac{4}{\sqrt{13}}$$

= $$\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}$$

= $$\frac{4\sqrt{13}}{13}$$

Question 64
A

10.5cm

B

5cm

C

10cm

D

12cm

##### Explanation

The area of an ellipse (e) =ab/4

Let a rep. the length of its major axis = 14cm

Let b rep. the length of its minor axis = ?

= 3.142

Area of an ellipse = 132cm2

132 = (14 $$\times$$ b) 4

132 = (3.142 $$\times$$ 14b) 4

3.142 $$\times$$ 14b =132 $$\times$$ 4

b = (1324 $$\times$$ 4) (3.142 $$\times$$ 14)
= 528/43.988

= 12cm

The length of its minor axis (b) = 12cm

Question 65
A

1/2

B

1/3

C

2/5

D

3/4

##### Explanation

Prob.(A outcome) = $$\frac{1}{6}$$, Prob.(B outcome) =

P(A B) = 1/12, Prob.(A $$\cup$$ B)

Prob.(A $$\cup$$ B) = Prob.(A) + Prob.(B) $$\cup$$ Prob.(A B)

1/6 + 1/4 + 1/12

= (2 + 3 ? 1) 12

= 4/12

= 1/3

Prob.(A $$\cup$$ B) = 1/3

Question 66
A

x = 1, y = 1/2

B

x = 2, y = 1/2

C

x =0, y = 1

D

x = 2, y = 1

##### Explanation

$$27^x 81^{(x + 2y)} = 9$$

$$27^x = 9 \times 81^{(x+2y)}$$

$${(3^{3} )}^x =32 \times 3^{4(x + 2y)}$$

$$=3^{(2 + 4x + 8y)}$$

$$3^{3x} = 3^{ (2 + 4x + 8y)}$$

3x = 2 + 4x + 8y

3x - 4x - 8y = 2 ----- (1)

x + 4y = 0 ------- (2)

- 4y = 2

y = (- 2) 4 = -

y = -

Substitute the value of y into equation (2)

i.e x + 4y = 0

x + 4( - 1/2) = 0

x - 2 = 0

x = 2

- x = 2,y = -

Method II

$$27^x 31^{(x + 2y) }= 9$$

3^{3x} $$\times$$ $$3^{( - 4x - 8y)} = 32$$

$$3^{(3x - 8y)} = 32$$

- x - 8y=2 ---- (1)

x + 4y = 0 ----- (2)

- 4 = 2

y= 2/4 =

y =

Substitute the value of y into equation 2

x + 4y=0

x + 4 (- 1) 2) = 0

x - 2 = 0

x = 2

x = 2, y =

Question 67
A

x = 1 twice

B

x = 0 or 1

C

x = 3 or 1

D

x = 2 twice

##### Explanation

-(2x + 2 ) - -x = 1

-(2x + 2) = 1 + -x

Square both sides

-(2x + 2)2 = (1 + -x)2

((2x + 2)2) = 1 + -x + -x+ x

2x + 2 = 1 + 2-x +x

Collect the like term together

2x - x + 2 - 1 = 2 -x
x + 1 = 2-x

Square both sides

(x + 1)2 = (2-x)2

x2 + 2x + 1 = 4x

x2 + 2x - 4x + 1 = 0

(x2- x)(x + 1)= 0

x(x - 1) -1(x - 1)

(x - 1)(x -1)

Either (x - 1) = 0 or (x - 1) = 0

x = 1 or 1

x = 1 twice

Try this quiz in in E-test/CBT Mode
switch to

Question Map