# Mathematics 2011 | Study Mode

Question 41
A
6!
B
7!
C
5!
D
8!
##### Explanation
ELATION
Since there are 7 letters. The first letter can be arranged in 7 ways, , the second letter in 6 ways, the third letter in 5 ways, the 4th letter in four ways, the 3rd letter in three ways, the 2nd letter in 2 ways and the last in one way.

therefore, 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways

Question 42
A
24
B
60
C
12
D
120
##### Explanation
The first person will sit down and the remaining will join.

i.e. (n - 1)!

= (5 - 1)! = 4!

= 24 ways

Question 43
A
$$\frac{2}{3}$$
B
$$\frac{1}{3}$$
C
$$\frac{2}{9}$$
D
$$\frac{7}{9}$$
##### Explanation
Prime numbers = (43,47,53,59)

N = (43, 44, 45,..., 60)

The universal set contains 18 numbers.

The prime numbers between 43 and 60 are 4

Probability of picking a prime number = $$\frac{4}{18}$$

= $$\frac{2}{9}$$

Question 44
A
sec2 $$\theta$$
B
tan $$\theta$$ cosec $$\theta$$
C
cosec $$\theta$$sec $$\theta$$
D
cosec2$$\theta$$
##### Explanation
$$\frac {\sin\theta}{\cos\theta}$$

$$\frac{\cos \theta {\frac{d(\sin \theta)}{d \theta}} - \sin \theta {\frac{d(\cos \theta)}{d \theta}}}{\cos^2 \theta}$$

$$\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta}$$

$$\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta}$$

Recall that sin2 $$\theta$$ + cos2 $$\theta$$ = 1

$$\frac{1}{\cos^2\theta}$$ = sec2 $$\theta$$

Question 45
A
{a, b, d, e}
B
{b, d}
C
{a, e}
D
{c}

Question 46
A
30%
B
25%
C
35%
D
20%
##### Explanation
$$\frac{70}{360} \times 36 = \frac{70}{10}$$

= 7

Question 47
A
180
B
135
C
210
D
105