Mathematics 2008 | Study Mode

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Question 81
A
2t
B
2t - 1
C
\(\frac{2}{3}\)t + 1
D
2t - \(\frac{1}{3}\)
Explanation
\(\frac{t + 2t - 1 + t - 2 + 2t - 1 + 4t + 2t + 2}{6}\)

= \(\frac{12t - 2}{6}\)

= \(\frac {12t}{6}\) - \(\frac{2}{6}\)

= 2t - \(\frac{1}{3}\)

Correct option: D
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Question 82
A
o
B
1
C
2
D
4
Explanation
0, 0, 1, 1, 2, 4, 4, 4, 4

median = 2

Correct option: C
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Question 83
A
3x + 3
B
3x + 1
C
2x + 5
D
2x + 1
Explanation
Range = H - L

= 4x - (x - 1)

= 4x - x + 1

= 3x + 1

Correct option: B
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Question 84
A
1
B
2
C
5
D
7
Explanation
\(\begin{array}{c|c} x & f & fx & x - \bar{x} & f(x - \bar{x}) \\ \hline 2 & 1 & 2 & -3 & -3 & 3\\ 4 & 1 & 4 & -1 & 1 & 1\\ 5 & 1 & 5 & 0 & 0 & 0 \\9 & 1 & 9 & 4 & 4 & 4 \\ \hline & 4 & 20 & & & 8 \end{array}\)

x = \(\frac{\sum fx}{\sum fx}\)

= \(\frac{20}{4}\)

= 5

MD = \(\frac{\sum f(x - \bar{x})}{\sum f}\)

= \(\frac{8}{4}\)

= 2

Correct option: B
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Question 85
A
\(\frac{10!}{2!2!3!}\)
B
\(\frac{10!}{2!3!}\)
C
\(\frac{10!}{2!2!}\)
D
\(\frac{10!}{3!2!2!}\)
Explanation
Acceptance

\(\frac{10!}{3!2!2!}\)

Correct option: D
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Question 86
A
218
B
216
C
215
D
210
Explanation
\(^{10}C_{6}\)

\(\frac{10!}{(n - r)!r!}\)

n = 10, r = 6

= \(\frac{10!}{(10 - 6)!6!}\)

= \(\frac{10!}{4!6!}\)

= \(\frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1}\)

= 5 x 3 x 2 x 7

= 210

Correct option: D
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Question 87
A
\(\frac{1}{11}\)
B
\(\frac{2}{11}\)
C
\(\frac{3}{11}\)
D
\(\frac{4}{11}\)
Explanation
Obstruction

if a T is picked

p = \(\frac{2}{11}\)

Correct option: B
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Question 88
A
\(\frac{3}{10}\)
B
\(\frac{1}{5}\)
C
\(\frac{1}{6}\)
D
\(\frac{1}{10}\)
Explanation
\(\begin{array}{c|c}Number & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Frequency & 12 & 18 & x & 30 & 2x & 45\end{array}\)

12 + 18 + x + 30 + 2x + 45 = 150

3x + 105 = 150

3x = 150 - 105

3x = 45

x = \(\frac{45}{3}\)

x = 15

probability of 5 = \(\frac{30}{150}\)

= \(\frac{1}{5}\)

Correct option: B
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Question 89
A
100o
B
80o
C
50o
D
30o
Explanation
50 + 30 + y = 180

80 + y = 180

y = 100

180 + x = 180o

x = 180o - 100o

x = 80o

Correct option: B
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Question 90
A
90o
B
53o
C
36o
D
26o
Explanation
74 + x + x = 180

2x = 180 - 74

2x = 103

x = 53

Correct option: B

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