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
√5
√6
√7
√2
Correct answer is B
\(\begin{array}{c|c}Class Interval & 3 - 3 & 6 - 8 & 9 - 11 \\ x & 4 & 7 & 10 \\ f & 2 & 2 & 2 \\ f - x & 8 & 14 & 20 \\ |x - \bar{x}|^2 & 9 & 0 & 9 \\ |x - \bar{x}|^2 & 18 0 & 18 \end{array}\)
\(\bar{x}\) = \(\frac {\sum fx}{\sum f}\)
= \(\frac {8 + 14 + 20}{2 + 2 + 2}\)
= \(\frac{42}{6}\)
\(\bar{x}\) = 7
S.D = \(\sqrt\frac{\sum f(x - \bar{x})^2}{\sum f}\)
= \(\sqrt\frac{18 + 0 + 18}{6}\)
= \(\sqrt\frac{36}{6}\)
= \(\sqrt {6}\)
(8,5)
(3, 5)
(5 , 8)
(5 , 3)
Correct answer is B
Median = \(\frac{\sum fx}{\sum f}\)
\(\begin{array}{c|c}
No & 0 & 1 & 2 & 3 & 4 & 5 \\ F & 1 & 4 & 3 & 8 & 2 & 5 \\ fx & 0 & 4 & 6 & 24 & 8 & 25 \end{array}\)
\(\sum fx\) = 0 + 4 + 6 + 24 + 8 + 25 = 67
\(\sum f\) = 23
Median = \(\frac{\sum fx}{\sum f}\) = \(\frac{67}{23}\) = 2.913
= \(\approx\) 3
Range = 5 - 0 = 5
(3, 5)
The sum of four consecutive integers is 34. Find the least of these numbers
7
6
8
5
Correct answer is A
Let the numbers be a, a + 1, a + 2, a + 3
a + a + 1 + a + 2 + a + 3 = 34
4a = 34 - 6
4a = 28
a = \(\frac{28}{4}\)
= 7
The least of these numbers is a = 7