Simplify \(8^{n} \times 2^{2n} \div 4^{3n}\)
\(2^{-n}\)
\(2^{1 - n}\)
\(2^{n}\)
\(2^{n + 1}\)
Correct answer is A
\(8^{n} \times 2^{2n} \div 4^{3n} = 2^{3n} \times 2^{2n} \div 2^{6n}\)
\(2^{2n + 3n - 6n}\)
= \(2^{-n}\)
Which of the following is a singular matrix?
\(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
\(\begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\)
\(\begin{pmatrix} 3 & 8 \\ 5 & 16 \end{pmatrix}\)
\(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\)
Correct answer is A
No explanation has been provided for this answer.
Simplify \(\frac{^{n}P_{4}}{^{n}C_{4}}\)
24
18
12
6
Correct answer is A
\(^{n}P_{4} = \frac{n!}{(n - 4)!}\)
\(^{n}C_{4} = \frac{n!}{(n - 4)! 4!}\)
\(\frac{^{n}P_{4}}{^{n}C_{4}} = \frac{n!}{(n - 4)!} ÷ \frac{n!}{(n - 4)! 4!}\)
= \(4! = 24\)
15
40
70
175
Correct answer is D
From the five(5) men viable for the position of the chairman, one of them must be selected.
This implies; 4 men and 3 women are open for committee membership.
7 C\(_3\) = \(\frac{7!}{3!(7 - 3)!}\) =
\(\frac{7⋅6⋅5⋅4⋅3⋅2⋅1}{3.2.1 \times 4.3.2.1}\)
= 35 \(\times\) 5 = 175
30
20
18
14
Correct answer is B
Let the sum of the men's ages be f, so that
\(\frac{f}{n} = 50 .... (1)\)
Also, \(\frac{f - (55 + 63)}{n - 2} = 50 - 1 = 49 .... (2)\)
From (1), \(f = 50n\)
From (2), \(f - 118 = 49(n - 2) = 49n - 98\)
\(f = 49n - 98 + 118 = 49n + 20\)
\(\therefore f = 50n = 49n + 20\)
\(50n - 49n = n = 20\)