Rationalize the expression \(\frac{1}{\sqrt{2} + \sqrt{5}}\)
\(\frac{1}{3}\)(\(\sqrt{5} - \sqrt{2}\)
\(\frac{\sqrt{2}}{3}\) + \(\frac{\sqrt{5}}{5}\)
\(\sqrt{2} - \sqrt{5}\)
5(\(\sqrt{2} - \sqrt{5}\)
\(\frac{1}{3}\)(\(\sqrt{2} - \sqrt{5}\)
Correct answer is A
\(\frac{1}{\sqrt{2} + \sqrt{5}}\)
\(\frac{1}{\sqrt{2} + \sqrt{5}} \times \frac{(\sqrt{2} - \sqrt{5})}{(\sqrt{2} - \sqrt{5})}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{2 - 5}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{-3}\)
= \(\frac{1}{3} (\sqrt{5} - \sqrt{2})\)
120km/hr
60km/hr
670km/hr
40km/hr
Correct answer is B
Speed = \(\frac{distance}{time}\)
let x represent the speed, d represent distance
x = \(\frac{d}{4}\)
d = 4x
2x = \(\frac{600 - d}{3}\)
6x = 600 - d
6x = 600 - 4x
10x = 600
x = \(\frac{600}{10}\)
= 60km/hr
Find the mean of the following 24.57, 25.63, 24.32, 26.01, 25.77
25.12
25.30
25.26
25.50
25.75
Correct answer is C
\(\frac{24.57 + 25.63 + 24.32 + 26.01 + 25.77}{5}\)
mean = \(\frac{126.3}{5}\)
= 25.26
P = 60o and R = 90o
P = 30o and R = 120o
P = 90o and R = 60o
P = 60o and R 60o
P = 45o and R = 105o
Correct answer is A
By using cosine formula, p2 = Q2 + R2 - 2QR cos p
Cos P = \(\frac{Q^2 + R^2 - p^2}{2 QR}\)
= \(\frac{(3)^2 + 2(\sqrt{3})^2 - 3^2}{2\sqrt{3}}\)
= \(\frac{3 + 12 - 9}{12}\)
= \(\frac{6}{12}\)
= \(\frac{1}{2}\)
= 0.5
Cos P = 0.5
p = cos-1 0.5 = 60°
= < P = 60°
If < P = 60° and < Q = 30
< R = 180° - 90°
angle P = 60° and angle R is 90°
25cm
18cm
36cm
29cm
25.5cm
Correct answer is A
Circumference of PRS = \(\frac{\pi}{2}\) = \(\frac{22}{7}\) x \(\frac{7}{1}\) x \(\frac{1}{2}\)
= 11cm
Side PT = 7cm, Side TR = 7cm
Perimeter(PTRS) = 11cm + 7cm + 7cm
= 25cm