JAMB Mathematics Past Questions & Answers - Page 310

6r7$_8$ = 511$_9$

6 x 8$^2$ + r x 8$^1$ + 7 x 8$^0$ = 5 x 9$^2$ + 1 x 9$^1$ + 1 x 9$^0$

6 x 64 + 8r + 7 x 1 = 5 x 81 + 9 + 1 x 1

384 + 8r + 7 = 405 + 9 + 1

8r = 415 - 391

 8r = 24

r = $\frac{24}{8}$

= 3

$\frac {\sin\theta}{\cos\theta}$

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

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

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

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

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

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 = $\frac{4}{18}$

= $\frac{2}{9}$

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

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