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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

The first person will sit down and the remaining will join. i.e. (n - 1)! = (5 - 1)! = 4! = 24 ways

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 = \(\frac{4}{18}\) = \(\frac{2}{9}\)

\(\frac {\sin\theta}{\cos\theta}\) \(\frac{\cos \theta {\frac{d(\sin \theta)}{d \theta}} - \sin \theta {\frac{d(\cos \theta)}{d \theta}}}{\cos^2 \theta}\) \(\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta}\) \(\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta}\) Recall that sin2 \(\theta\) + cos2 \(\theta\) = 1 \(\frac{1}{\cos^2\theta}\) = sec2 \(\theta\)

No expanded working has been attached for this question yet. The verified answer is Option A.

\(\frac{90}{360} \times 100 = \frac{100}{4}\) = 25

45 + 60 + 30 + 45 = 180 students.

Inception; the commencement or starting point of something

Detached: separate or disconnected.

Dwelt; to live in or at a specified place.

Ignominious; deserving or causing public disgrace or shame.

compliments; a polite expression of praise or admiration.

Ensnared; to trap or gain power over (someone) by dishonest or underhand means.

corrugated; (of a material or surface) shaped into a series of parallel ridges and grooves so as to give added rigidity and strength. Folded

Astute; having or showing an ability to accurately assess situations or people and turn this to one's advantage. shrewd; having or showing sharp powers of judgement; astute.