express 62 \(\div\) 3 as a decimal correct to 3 significant figures
20.6
20.667
20.67
20.7
Correct answer is D
\(\frac{62}{3}\) = 20.6666.....
= 20.7 to 3 sig. fig.
Find correct to 3 decimal places (\(\frac{1}{0.05}\) + \(\frac{1}{5.005}\)) - (0.05 x 2.05)
99.998
98.999
89.899
9.998
Correct answer is A
(\(\frac{1}{0.05}\) + \(\frac{1}{5.005}\)) - (0.05 x 2.05)
(\(\frac{1}{0.05}\) x 5.005) - (0.05 x 2.05)
\(\frac{5.005}{0.05}\) - 0.1025
100.1 - 0.1025
= 99.9975
99.998 to 3 decimal place.
If 2257 is the result of subtracting 4577 from 7056 in base n, find n
8
9
10
11
Correct answer is A
\(\begin{array}{c|c} 7056 \\ \text{- 4577} \\\hline 2257 \end{array}\)
By trial and error method
Let the base to 8
i.e. Let n = 8 and it is easily verified that the subtraction holds.
The subtraction does not hold when other values of n are tried
n = 8
Simplify 3\(\frac{1}{3}\) - 1\(\frac{1}{4}\) x \(\frac{2}{3}\) + 1\(\frac{2}{5}\)
2
3
4
5
Correct answer is C
3 - \(\frac{1}{3}\) - (\(\frac{5}{4}\) x \(\frac{2}{3}\)) + 1\(\frac{2}{5}\)
= \(\frac{10}{3}\) - \(\frac{5}{6}\) + \(\frac{7}{5}\)
= \(\frac{100 - 25 + 42}{30}\)
= \(\frac{117}{30}\)
= 3.9
\(\approx\) 4
48
12
10
7
Correct answer is B
Mathematics = \(^{4} C_{3} = 4\)
Physics = \(^{3} C_{2} = 3\)
\(\therefore\) He can choose in 4 x 3 = 12 ways.