Mathematics 2008 | Study Mode

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Question 61
A
-4 \(\leq\) x \(\leq\) 7
B
-7 \(\leq\) x \(\leq\) 4
C
x \(\geq\) -7
D
-7 \(\leq\) x \(\leq\) 6
Explanation
4x - 7 \(\leq\) 3x

4x - 3x \(\leq\) 7

x \(\leq\) 7

ii. 3x - 4 \(\leq\) 4x

3x - 4x \(\leq\) 4

-x \(\leq\) -4

-4 \(\leq\) x \(\leq\) 7

Correct option: A
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Question 62
A
x \(\leq\) 2, x \(\geq\) 3
B
x \(\leq\) 3, x \(\geq\) 2
C
x \(\leq\) -2, x \(\geq\) -3
D
x \(\leq\) -3,x \(\geq\) 2
Explanation
x2 - 5x + 6 \(\geq\) 0

x2 - 2x - 3x + 6 \(\geq\) 0

x(x - 2) - 3(x - 2) \(\geq\) 0

(x - 2) (x - 3) \(\geq\) 0

x \(\geq\) 2 or \(\geq\) 3

x \(\leq\) 2 \(\geq\)

Correct option: A
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Question 63
A
12
B
4
C
-12
D
-24
Explanation
In = a + (n - 1)d

24 = a + (5 - 1)d

24 = a + 4d.......(i)

96 = a + (11 - 1)d

96 = a + 10d.......(ii)

a = 24 - 4d.......(iii)

96 = 24 - 4d + 10d

96 = 24 + 6d

96 - 24 = 6d

72 = 6d

d = \(\frac{72}{6}\)

d = 12

a = 24 - 4d

a = 24 - 4 x 12

a = 24 - 48

a = -24

Correct option: D
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Question 64
A
commutative and closed on the set of positive integers
B
neither commutative nor closed on the set of positive integers
C
commutative but not closed on the set of positive integers
D
not commutative but closed on the set of positive integers
Explanation
a \(\ast\) b = b \(\ast\) a

x \(\ast\) y = y \(\ast\) x

2x - 3y + 2 \(\neq\) 2y - 3y - 3x + 2

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

= 4 - 9 + 2

= -3

1 \(\ast\) 2 = 2(1) - 3(2) + 2

= 2 - 6 + 2

= 2 - 6 + 2

= -2

Correct option: B
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Question 65
A
1
B
o
C
-\(\frac{1}{2}\)
D
-1
Explanation
m \(\Delta\) n = m + n + mn

m \(\Delta\) e = e \(\Delta\) m = m

m \(\Delta\) e = m

m + e + me = m

e + me = m - m

e + me = 0

e(1 + m) = 0

e = \(\frac{0}{1 + m}\) = 0

Correct option: B
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Question 66
A
-3, -2
B
-5, -3
C
-2, -5
D
-3, -5
Explanation

\(\begin{pmatrix} 1 & 0 \\ -1 & -1\\ 2 & 2 \end{pmatrix}\) + \(\begin{pmatrix} x & 1 \\ -1 & 0\\ y & -2 \end{pmatrix}\) = \(\begin{pmatrix} -2 & 1 \\ -2 & -1\\ -3 & 0 \end{pmatrix}\)

therefore, (x, y) = (-3, -5) respectively


Correct option: D
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Question 67
A
-\(\frac{1}{8}\)
B
\(\frac{3}{8}\)
C
\(\frac{5}{8}\)
D
\(\frac{1}{4}\)
Explanation
-2p + r = 1.......(i)

2p + 3r = 0.......(ii)

r - 1 + 2p ........(iii)

2p + 3(1 + 2p) = 0

2p + 3(1 + 2p) = 0

2p + 3 + 6p = 0

3 - 8p = 0 \(\to\) 8p = 3

p = \(\frac{3}{8}\)

6 = 1 - 2 \(\frac{3}{8}\)

= 1 - \(\frac{6}{8}\)

\(\frac{8 - 6}{8}\) = \(\frac{2}{8}\)

= \(\frac{1}{4}\)

Correct option: D
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Question 68
A
30o
B
45o
C
60o
D
90o
Explanation
Equilateral are equal in sides and angle

180o = 60o + 60o + 60o

\(\theta\) = 60o

Correct option: C
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Question 69
A
44 000 litres
B
4400 litres
C
440 litres
D
44 litres
Explanation
r = 1

h = 14

\(\pi\) = \(\frac{22}{7}\)

A = \(\pi\)r2h

A = \(\frac{22}{7}\) x 12 x 14

A = 44m2

A = 44 x 10 litres

A = 440 litres

Correct option: C
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Question 70
A
(2, 5)
B
(5, 2)
C
(1, 0)
D
(0,1)
Explanation
let (6, 2) be represented as (x1, y1) and (4, 2) be (x2, y2)

p(6, 2) R(4, 2)

m.p = (\(\frac{x_1 + x_2}{2}\)) (\(\frac{y_1 + y_2}{2}\))

= (\(\frac{6 + 4}{2}\) , \(\frac{2 + 2}{2}\))

= (\(\frac{10}{2}\),\(\frac{4}{2}\))

= (5, 2)

Correct option: B

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