The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.
6
8
14
2
Correct answer is B
Using x = \(\frac{\sum x}{N}\) in each case, we get;
\(\sum_{6}^{i=1} x_i\) = 10 x 7 = 70
\(\sum_{7}^{i=1} x_i\) = 2 + 4 + 8 + 14 + 16 + 18 = 62
Hence the missing number can be obtained from
\(\sum_{6}^{i=1} x_i - \sum_{7}^{i=1} x_i\) = 70 - 62 = 8
So, all the seven numbers are 2, 4, 8, 8, 14, 16, 18
Mode = 8
Find the mean of t + 2, 2t - 4, 3t + 2 and 2t.
t + 1
2t
2t + 1
t
Correct answer is B
\(\sum x\) = (t + 2) + (2t + 4) + (3t + 2) + 2t = 8t
N = 4_
∴ Mean, x = \(\frac{\sum x}{N} = \frac{8t}{4} = 2t\)
= 2t
0.75cm2S-1
0.53cm2S-1
0.35cm2S-1
0.88cm2S-1
Correct answer is D
A = \(\pi\)r2, \(\frac{\delta A}{\delta r}\) = 2πr
So, using \(\frac{\delta A}{\delta t}\) = \(\frac {\delta A}{\delta r}\) x \(\frac {\delta A}{\delta t}\)
= 2\(\pi\)r x 0.02
= 2\(\pi\) x 7 x 0.02
= 2 x \(\frac{22}{7}\) x 0.02
= 0.88cm2s-1
If y = (2x + 2)\(^3\), find \(\frac{\delta y}{\delta x}\)
3(2x +2)2
6(2x +2)
3(2x +2)
6(2x +2)2
Correct answer is D
\(y = (2x + 2)^{3}\)
\(\frac{\mathrm d y}{\mathrm d x} = 3(2x + 2)^{3 - 1} . 2\)
= \(6(2x + 2)^{2}\)
If y = x sin x, find \(\frac{\delta y}{\delta x}\)
sin x - cos x
cos x - x sin x
cos x + x sin x
sin x + x cos x
Correct answer is D
y = x sin x
Where u = x and v = sin x
Then \(\frac{\delta u}{\delta x}\) = 1 and \(\frac{\delta v}{\delta x}\) = cos x
By the chain rule, \(\frac{\delta y}{\delta x} = v\frac{\delta u}{\delta x} + u\frac{\delta v}{\delta x}\)
= (sin x)1 + x cos x
= sin x + x cos x