Mathematics 2009 | Study Mode

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Question 61
A
n(3n - 0.5)
B
n(3n + 2)
C
n(3n + 2.5)
D
n(3n + 5)
Explanation
Tn = \(\frac{1}{2}\)n(2a + (n - 1)d)

= \(\frac{1}{2}\)n(2 x 5 + (n - 1) 6

= \(\frac{1}{2}\)n(10 + 6n - 6)

= n\(\frac{1}{2}\)(6n + 4)

= n(3n + 2)

Correct option: B
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Question 62
A
-5 < x < \(\frac{7}{3}\)
B
-5 \(\leq\) x \(\leq\) \(\frac{7}{3}\)
C
-5 < x \(\leq\) \(\frac{7}{3}\)
D
-5 \(\leq\) x < \(\frac{7}{3}\)
Explanation
3x - 7 \(\leq\) 0 ; x + 5 > 0

3x \(\leq\) 7 ; x > -5

= x \(\leq\) \(\frac{7}{3}\)

-5 < x \(\leq\) \(\frac{7}{3}\)

Correct option: C
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Question 63
A
10
B
9
C
\(\frac{10}{9}\)
D
\(\frac{9}{10}\)
Explanation

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Correct option: B
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Question 64
A
-6
B
-8
C
-10
D
-12
Explanation
If m x n = n

= n - (m + 2)

3 \(\ast\) (-5) = -5 - (3 + 2)

= -5 - 5

= -10

Correct option: C
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Question 65
A
\(\frac{-5}{4}\)
B
\(\frac{-5}{6}\)
C
o
D
5
Explanation

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


Correct option: D
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Question 66
A
-50
B
-22
C
22
D
50
Explanation
If Q = \(\begin{pmatrix} 9 & -2 \\ -7 & 4 \end{pmatrix}\), then |Q| is

= 9 x 4 - (-2) x (-7)

= 36 - 14

= 22

Correct option: C
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Question 67
A
-5
B
-2
C
2
D
5
Explanation
If p = \(\begin{pmatrix} x + 3 & x + 2 \\ x + 1 & x - 1 \end{pmatrix}\) evaluate x if |p| = -10

|P| = (x + 3)(x - 1) - (x + 2)(x + 1)

x2 + 2x - 3 - (x2 + 3x + 2)

x2 + 2x - 3 - x2 - 3x - 2

-x - 5 = -10

-x = -10 + 5

x = 5

Correct option: D
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Question 68
A
15o
B
30o
C
45o
D
60o
Explanation
x \(\leq\) 90o (acute angle)

x2 = 3x

3x = 90o

x = \(\frac{90^o}{3}\) = 30o

Correct option: B
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Question 69
A
12
B
10
C
9
D
8
Explanation
x + 150o = 180o (sum of angle on straight line)

x = 180o - 150o , x = 30o

number of sides (n) = \(\frac{360}{3}\)

= 12

Correct option: A
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Question 70
A
\(\frac{1}{\sqrt{2}}\) cm2
B
1 cm2
C
\(\sqrt{2}\)cm2
D
2\(sqrt{2}\)cm2
Explanation
sin45o = \(\frac{y}{2}\)

y = 2 sin45o

y = 2 (\(\frac{1}{\sqrt{2}}\))

y = \(\frac{2}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)

y = \(\frac{2\sqrt{2}}{2}\)

y = \(\sqrt{2}\)

Since it is an isosceles triangle

x = \(\sqrt{2}\)

Area of \(\Delta\) = \(\frac{1}{2}\)bh

= \(\frac{1}{2}\) x \(\sqrt{2}\) x \(\sqrt{2}\)

= \(\frac{1}{2}\) x 2

= 1 cm2

Correct option: B

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