Find r, if 6r7\(_8\) = 511\(_9\)
3
2
6
5
Correct answer is A
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
Find the derivative of \(\frac {\sin\theta}{\cos\theta}\)
sec2 \(\theta\)
tan \(\theta\) cosec \(\theta\)
cosec \(\theta\)sec \(\theta\)
cosec2\(\theta\)
Correct answer is A
\(\frac {\sin\theta}{\cos\theta}\)
\(\frac{\cos \theta {\frac{d(\sin \theta)}{d \theta}} - \sin \theta {\frac{d(\cos \theta)}{d \theta}}}{\cos^2 \theta}\)
\(\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta}\)
\(\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta}\)
Recall that sin2 \(\theta\) + cos2 \(\theta\) = 1
\(\frac{1}{\cos^2\theta}\) = sec2 \(\theta\)
\(\frac{2}{3}\)
\(\frac{1}{3}\)
\(\frac{2}{9}\)
\(\frac{7}{9}\)
Correct answer is C
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 = \(\frac{4}{18}\)
= \(\frac{2}{9}\)
In how many ways can five people sit round a circular table?
24
60
12
120
Correct answer is A
The first person will sit down and the remaining will join. i.e. (n - 1)! = (5 - 1)! = 4! = 24 ways
In how many was can the letters of the word ELATION be arranged?
6!
7!
5!
8!
Correct answer is B
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