I only
II only
I and III only
II and III only
Correct answer is B
No explanation has been provided for this answer.
If \(^nC_2\) = 15, find the value of n
8
7
6
5
Correct answer is C
\(^nC_2\) = 15
\(\frac{n!}{(n - 3)! 2!}\) = 15
\(\frac{n(n - 1)(n - 2)!}{(n - 2)!2}\) = 15
n\(^2\) - n = 30
n\(^2\) - n - 30 = 0
(n - 6)(n + 5) = 0
n = 6 or n = -5
Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)
\(\sqrt{2}\) - 1
1 - \(\sqrt{2}\)
\(\frac{\sqrt{2} - 1}{2}\)
\(\frac{1 - \sqrt{2}}{2}\)
Correct answer is A
\(\frac{1}{\sqrt{2} + 1}\) x \(\frac{\sqrt{2} - 1}{\sqrt{2} - 1}\)
= \(\frac{\sqrt{2} - 1}{2 - 1}\)
= \(\frac{\sqrt{2} - 1}{1} = \sqrt{2} - 1\)
Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)
\(\sqrt{3 + 2}\)
\(\sqrt{3 + 1}\)
\(\sqrt{3 - 1}\)
\(\sqrt{3 - 2}\)
Correct answer is D
Tan 75\(^o\) = Tan (45\(^o\) + 30\(^o\))
= \(\frac{\tan 45^o + \tan 30^o}{1 - \tan 45^o \tan 30^o}\)
= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\)
RATIONALIZE THE DENOMINATOR
= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\) X \(\frac{\sqrt{3} + 1}{\sqrt{3} +1}\)
= \(\frac{4 + 2\sqrt{3}}{3 - 1}\)
= \(\frac{2(2 + \sqrt{3})}{2}\)
= 2 + \(\sqrt{3}\)
Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously
p = -6, k = -6
p = -6, k = 6
p = 6, k = 6
p = 6, k = -6
Correct answer is C
\(\frac{P}{2} + \frac{k}{3}\) = 5
\(\frac{3p + 2k}{6}\) = 5
2p + 3k = 30
- 2p - k = 6
\(\overline{\frac{4k}{4} = \frac{24}{4}}\)
k = 6
From 2p - k = 6
2p - 6 = 6
\(\frac{2p}{2} = \frac{12}{2}\)
p = 6