A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M
15
12
10
9
Correct answer is D
Average speed = \(\frac{Distance}{Time}\)
\(\frac{400km}{hr} = \frac{60km}{Time}\)
Time = \(\frac{60km}{400 km/hr}\)
= \(\frac{60hr}{400}\)
M = \(\frac{60hr}{400} \times \frac{60min}{1hr}\)
= 9 minutes
Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)
\(\frac{2}{3}\)
\(\frac{1}{2} \log 2\)
\(\frac{3}{2}\)
\(\log 2\)
Correct answer is C
\(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{\frac{1}{2} \log 2^3}{\log 2}\)
= \(\frac{3}{2} \frac{\log 2}{\log 2}\)
= \(\frac{3}{2}\)
If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>?
x varies directly as y
x varies inversely as y
x is partly constant and partly varies as y
x vries jointly as 45 and directly as y
Correct answer is C
No explanation has been provided for this answer.
If \(2^n = 128\), find the value of \(2^{n - 1})(5^{n - 2})\)
5(106)
2(106)
5(105)
2(105)
Correct answer is D
2n = 128
2n = 27
n = 7
(2n - 1)(5n - 2) = (2n - 2.2)(5n - 2) put n = 7
(2n - 1)(5n - 2) = 2(2n - 2 x 5n - 2)
= 2(2 x 5)n - 2
= 2(10n - 2) put n = 7
(2n-1)(5n-2) = 2(105)
If cos (x + 25)o = sin 45o, find the value of x
20
30
45
60
Correct answer is A
cos(x + 25o) = sin 45o
using cos \(\theta\) = sin(90 - \(\theta\))
cos(x + 25o) = cos(90 - 45)
cos(x + 25o) = cos 45
x + 25 = 45
x = 45 - 25
x = 20o