Mathematics 2009 | Study Mode

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Question 71
A
7 cm
B
9 cm
C
12 cm
D
24 cm
Explanation
132 = 52 + b2

169 = 25 + b2

b2 = 144

b = \(\sqrt{144}\)

= 12 cm

Correct option: C
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Question 72
A
7.00cm
B
3.50cm
C
3.00cm
D
1.75cm
Explanation
Surface area of a sphere = 4\(\pi\)r2

4\(\pi\)r2 = 154 cm2

\(\pi\)r2 = \(\frac{154}{4}\)

= 38.5

\(\pi\)r2 = 38.5

r2 = 38.5 + \(\frac{22}{7}\) \(\to\) r2 = 38.5 x \(\frac{7}{22}\)

r2 12.25 \(\to\) r = \(\sqrt{12.25}\)

= 3.5 cm

Correct option: B
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Question 73
A
x + y = 0
B
x - y = 0
C
x + y + k = 0
D
x - y - k = 0
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: D
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Question 74
A
A circle of radius 4 cm and with centre O
B
The perpendicular bisector of the chords
C
a straight line passing through centre O
D
A circle of radius 6 cm and with centre O
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: C
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Question 75
A
-2
B
-1
C
1
D
2
Explanation
\(\frac{y_1 - y_o}{x_1 - x_o}\) = m

\(\frac{4 - p}{p + 1}\) = \(\frac{2}{3}\)

2p + 2 = 12 - 3p

5p = 10

p = \(\frac{10}{5}\)

= 2

Correct option: D
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Question 76
A
1
B
2
C
3
D
4
Explanation
Applying the formula

(x - a)2 + (y - b)2 = r2

(4 - 1)2 + (2 - r)2 = (3)2

(3)2 + (2 - r)2 = (3)2

9 + ( 4 - 4r + r2) = 9

13 - 4r + r2 = 9

r2 - 4r + 13 - 9 = 0

(r2 - 2r) - (2r + 4) = 0

r(r - 2) -2(r - 2) = 0

(r - 2) (r - 2)

r = 2 or -2

Correct option: B
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Question 77
A
\(\frac{2 + \sqrt{6}}{4}\)
B
\(\frac{ \sqrt{2} + \sqrt{3}}{4}\)
C
\(\frac{ \sqrt{2} + \sqrt{3}}{6}\)
D
\(\frac{ \sqrt{2} - \sqrt{3}}{2}\)
Explanation
sin 45o - cos 30o

\(\frac{1}{\sqrt{2}}\) - \(\frac{\sqrt{3}}{2}\)

= \(\frac{2 - \sqrt{2} \times \sqrt{3}}{2\sqrt{2}})\)

= \(\frac{2 - \sqrt{6} \times \sqrt{2}}{2\sqrt{2} \sqrt{2}}\)

= \(\frac{2\sqrt{2} - \sqrt{12}}{4}\)


= \(\frac{2\sqrt{2} - 2\sqrt{3}}{4}\)

= \(\frac{2(\sqrt{2} - \sqrt{3})}{4}\)

= \(\frac{\sqrt{2} - \sqrt{3}}{2}\)

Correct option: D
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Question 78
A
753m
B
1003m
C
2003m
D
100m
Explanation
Tan 60o = \(\frac{300}{x}\)

x Tan 60o = 300

x3 = 300

x = \(\frac{300}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)

x = \(\frac{300\sqrt{3}}{3}\) x 100\(\sqrt{3}\)

Correct option: B
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Question 79
A
6 sin 8x
B
-24 sin 4x
C
12 sin 4x
D
-12 sin 4x
Explanation
If y = 3 cos 4x, \(\frac{dy}{dx}\) equals

\(\frac{dy}{dx}\) = 3(4 - sin 4x)

= -12 sin 4x

Correct option: D
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Question 80
A
0 units per sec.
B
15 units per seconds
C
22 units per seconds
D
26 units per seconds
Explanation
s = (2 + 3t)(5t - 4), find \(\frac{dy}{dx}\) when t = \(\frac{4}{5}\) sec

= 10t - 8 + 15t2 - 12t

\(\frac{ds}{dt}\) = 15t2 - 2t - 8

= 30t - 2 ; t = \(\frac{4}{5}\)

= 30t - 2

= 30 x \(\frac{4}{5}\) - 2 \(\to\) 24 - 2

= 22 sec

Correct option: C

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