Which of the following is nor a measure of central tendency?
Mean
Variance
Median
Mode
Correct answer is B
Variance is a measure of dispersion not central tendency.
Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.
2
3
5
6
Correct answer is B
\(\frac{^{n}P_{r}}{^{n}C_{r}} = \frac{\frac{n!}{(n - r)!}}{\frac{n!}{(n - r)! r!}} = \frac{90}{15} = 6\)
\(\frac{n!}{(n - r)!} \times \frac{(n - r)! r!}{n!} = r! = 6\)
\(r = 3\)
19
21
23
24
Correct answer is B
\(Mean = \frac{sum of items}{total number of items}\)
\(20 = \frac{x}{8} \implies x = 160\)
The sum of the 7 nos = 160 - 17 = 143
Correct mean = \(\frac{143 + 25}{8} = \frac{168}{8} = 21\)
Find the unit vector in the direction of the vector \(-12i + 5j\)
\(\frac{-12i}{13} - \frac{5j}{13}\)
\(\frac{-1i}{13} + \frac{5j}{13}\)
\(\frac{-12i}{13} + \frac{5j}{13}\)
\(\frac{-5i}{13} + \frac{12j}{13}\)
Correct answer is C
\(\hat{n} = \frac{\overrightarrow{n}}{|n|}\)
\(\hat{n} = \frac{-12i + 5j}{\sqrt{(-12)^{2} + (5)^{2}}}\)
= \(\frac{-12i}{13} + \frac{5j}{13}\)
\(5\sqrt{3} - 3\)
\(3 - 5\sqrt{3}\)
\(5 - 3\sqrt{3}\)
\(3\sqrt{3} - 5\)
Correct answer is A
\(F = F \cos \theta i + F \sin \theta j\)
\(10N = 10 \cos 60 i + 10 \sin 60 j\)
\(6N = -6 \cos 330 i - 6 \sin 330 j\)
\(R_{x} = 10 \cos 60 - 6 \cos 330 \)
= \(10 \times \frac{1}{2} - 6 \times \frac{\sqrt{3}}{2}\)
= \(5 - 3\sqrt{3}\)