Mathematics 2011 | Study Mode

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Question 21
A
-6 
B
C
-12 
D
12 
Explanation.
Share Answer \(\begin{vmatrix} 2 & 3 \\ 5 & 3x \end{vmatrix}\) = \(\begin{vmatrix} 4 & 1 \\ 3 & 2x \end{vmatrix}\)

(2 x 3x) - (5 x 3) = (4 x 2x) - (3 x 1)

6x - 15 = 8x - 3

6x - 8x = 15 - 3

-2x = 12

x = \(\frac{12}{-2}\)

= -6

Correct Option:
A
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Question 22
A
25 
B
45 
C
15 
D
55 
Explanation.
Share Answer \(\begin{vmatrix} 4 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix}\)

4 \(\begin{vmatrix} 3 & -1 \\ 1 & 3 \end{vmatrix}\) -2 \(\begin{vmatrix} 2 & -1 \\ -1 & 3\end{vmatrix}\) -1 \(\begin{vmatrix} 2 & 3 \\ -1 & 1 \end{vmatrix}\)

4[(3 x 3) - (-1 x 1)] -2 [(2x 3) - (-1 x -1)] -1 [(2 x 1) - (-1 x 3)]

= 4[9 + 1] -2 [6 - 1] -1 [2 + 3]

= 4(10) - 2(5) - 1(5)

= 40 - 10 - 5

= 25

Correct Option:
A
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Question 23
A
\(\frac{1}{5}\) \(\begin{vmatrix} 2 & 1 \\ 3 & 4\end{vmatrix}\) 
B
\(\frac{1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2\end{vmatrix}\) 
C
\(\frac{1}{5}\) \(\begin{vmatrix} 2 & -1 \\ -3 & 4\end{vmatrix}\) 
D
\(\frac{1}{5}\) \(\begin{vmatrix} 4 & 3 \\ 1 & 2\end{vmatrix}\) 
Explanation.
Share Answer N = [2 3]

N-1 = \(\frac{adj N}{|N|}\)

adj N = \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)

|N| = (2 x4) - (1 x 3)

= 8 - 3

=5

N-1 = \(\frac {1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)

Correct Option:
B
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Question 24
A
120o 
B
150o 
C
30o 
D
180o 
Explanation.
Share Answer Interior angle = (n - 2)180

but, n = 12

= (12 -2)180

= 10 x 180

= 1800

let each interior angle = x

x = \(\frac{(n - 2)180}{n}\)

x = \(\frac{1800}{12}\)

= 150o

Correct Option:
B
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Question 25
A
56cm2 
B
49cm2 
C
98cm2 
D
28cm2 
Explanation.
Share Answer Perimeter of circle = Perimeter of square

28cm = 4L

L = \(\frac{28}{4}\) = 7cm

Area of square = L2

= 72

= 49cm2

Correct Option:
B
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Question 26
A
46 cm 
B
36 cm 
C
66 cm 
D
26 cm 
Explanation.
Share Answer From Pythagoras theorem

|OA|2 = |AN|2 + |ON|2

72 = |AN|2 + (5)2

49 = |AN|2 + 25

|AN|2 = 49 - 25 = 24

|AN| = \(\sqrt {24}\)

= \(\sqrt {4 \times 6}\)

= 26 cm

|AN| = |NB| (A line drawn from the centre of a circle to a chord, divides the chord into two equal parts)

|AN| + |NB| = |AB|

26 + 26 = |AB|

|AB| = 46 cm

Correct Option:
A
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Question 27
A
48 cm3 
B
33 cm3 
C
60 cm3 
D
27 cm3 
Explanation.
Share Answer Volume of cube = L3

33 = 27cm3

volume of rectangular tank = L x B X h

= 3 x 4 x 5

= 60cm3

volume of H2O the tank can now hold

= volume of rectangular tank - volume of cube

= 60 - 27

= 33cm3

Correct Option:
B
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Question 28
A
whose distance from X is always twice its distance from Y 
B
whose distance from Y is always twice its distance from X. 
C
which moves on the line XY 
D
which is equidistant from the points X and y 
Explanation.
Share Answer

No official Explanation yet!


Correct Option:
D
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Question 29
A
(2, 10) 
B
(2, 8) 
C
(2, 12) 
D
(2, 6) 
Explanation.
Share Answer P(x, y) Q(8, 6)

midpoint = (5, 8)

x + 8 = 5

\(\frac{y + 6}{2}\) = 8

x + 8 = 10

x = 10 - 8 = 2

y + 6 = 16

y + 16 - 6 = 10

therefore, P(2, 10)

Correct Option:
A
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Question 30
A
5y - 2x -18 = 0 
B
5y + 2x - 18 = 0 
C
5y - 2x + 18 = 0 
D
5y + 2x - 2 = 0 
Explanation.
Share Answer 2y = 5x + 4 (4, 2)

y = \(\frac{5x}{2}\) + 4 comparing with

y = mx + e

m = \(\frac{5}{2}\)

Since they are perpendicular

m1m2 = -1

m2 = \(\frac{-1}{m_1}\) = -1

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

The equator of the line is thus

y = mn + c (4, 2)

2 = -\(\frac{2}{5}\)(4) + c

\(\frac{2}{1}\) + \(\frac{8}{5}\) = c

c = \(\frac{18}{5}\)

\(\frac{10 + 5}{5}\) = c

y = -\(\frac{2}{5}\)x + \(\frac{18}{5}\)

5y = -2x + 18

or 5y + 2x - 18 = 0

Correct Option:
B
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