Mathematics 2011 | Study Mode

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Question 31
A
\(\frac{2}{3}\)
B
\(\frac{3}{5}\)
C
\(\frac{1}{5}\)
D
\(\frac{4}{5}\)
Explanation
tan\(\theta\) = \(\frac{3}{4}\)

from Pythagoras tippet, the hypotenus is T

i.e. 3, 4, 5.

then sin \(\theta\) = \(\frac{3}{5}\) and cos\(\theta\) = \(\frac{4}{3}\)

cos\(\theta\) - sin\(\theta\)

\(\frac{4}{5}\) - \(\frac{3}{5}\) = \(\frac{1}{5}\)

Correct option: C
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Question 32
A
195o
B
135o
C
225o
D
045o
Explanation
tan\(\theta\) = \(\frac{100}{100}\) = 1

\(\theta\) = tan-1(1) = 45o

The bearing of x from z is N45oE or 135o

Correct option: B
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Question 33
A
12x + 1
B
6x + 5
C
6x + 1
D
12x + 5
Explanation
(2x + 1)(3x + 1) IS

2x + 1 \(\frac{d(3x + 1)}{d}\) + (3x + 1) \(\frac{d(2x + 1)}{d}\)

2x + 1 (3) + (3x + 1) (2)

6x + 3 + 6x + 2 = 12x + 5

Correct option: D
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Question 34
A
33m
B
5
C
2
D
6
Explanation
\(\int^{1}_{0}\)(3 - 2x)dx

[3x - x2]o

[3(1) - (1)2] - [3(0) - (0)2]

(3 - 1) - (0 - 0) = 2 - 0

= 2

Correct option: C
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Question 35
A
\(\frac{3}{4}\) sin 4x + k
B
-\(\frac{1}{4}\) sin 4x + k
C
-\(\frac{3}{4}\) sin 4x + k
D
\(\frac{1}{4}\) sin 4x + k
Explanation
\(\int^{1}_{0}\) cos4 x dx

let u = 4x

\(\frac{dy}{dx}\) = 4

dx = \(\frac{dy}{4}\)

\(\int^{1}_{0}\)cos u. \(\frac{dy}{4}\) = \(\frac{1}{4}\)\(\int\)cos u du

= \(\frac{1}{4}\) sin u + k

= \(\frac{1}{4}\) sin4x + k

Correct option: D
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Question 36
A
7
B
6
C
8
D
5
Explanation
Let the numbers be a, a + 1, a + 2, a + 3

a + a + 1 + a + 2 + a + 3 = 34

4a = 34 - 6

4a = 28

a = \(\frac{28}{4}\)

= 7

The least of these numbers is a = 7

Correct option: A
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Question 37
A
(8,5)
B
(3, 5)
C
(5 , 8)
D
(5 , 3)
Explanation
Median = \(\frac{\sum fx}{\sum f}\)

\(\begin{array}{c|c}
No & 0 & 1 & 2 & 3 & 4 & 5 \\ F & 1 & 4 & 3 & 8 & 2 & 5 \\ fx & 0 & 4 & 6 & 24 & 8 & 25 \end{array}\)

\(\sum fx\) = 0 + 4 + 6 + 24 + 8 + 25 = 67

\(\sum f\) = 23

Median = \(\frac{\sum fx}{\sum f}\) = \(\frac{67}{23}\) = 2.913

= \(\approx\) 3

Range = 5 - 0 = 5

(3, 5)

Correct option: B
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Question 38
A
5
B
6
C
7
D
2
Explanation
\(\begin{array}{c|c}Class Interval & 3 - 3 & 6 - 8 & 9 - 11 \\ x & 4 & 7 & 10 \\ f & 2 & 2 & 2 \\ f - x & 8 & 14 & 20 \\ |x - \bar{x}|^2 & 9 & 0 & 9 \\ |x - \bar{x}|^2 & 18 0 & 18 \end{array}\)

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

= \(\frac {8 + 14 + 20}{2 + 2 + 2}\)

= \(\frac{42}{6}\)

\(\bar{x}\) = 7

S.D = \(\sqrt\frac{\sum f(x - \bar{x})^2}{\sum f}\)

= \(\sqrt\frac{18 + 0 + 18}{6}\)

= \(\sqrt\frac{36}{6}\)

= \(\sqrt {6}\)

Correct option: B
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Question 39
A
6!
B
7!
C
5!
D
8!
Explanation
ELATION
Since there are 7 letters. The first letter can be arranged in 7 ways, , the second letter in 6 ways, the third letter in 5 ways, the 4th letter in four ways, the 3rd letter in three ways, the 2nd letter in 2 ways and the last in one way.

therefore, 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways

Correct option: B
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Question 40
A
24
B
60
C
12
D
120
Explanation
The first person will sit down and the remaining will join.

i.e. (n - 1)!

= (5 - 1)! = 4!

= 24 ways

Correct option: A

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