Mathematics 2011 | Study Mode

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Question 11
A
2X - 1 
B
X + 3 
C
2X + 1 
D
X - 3 
Explanation.
Share Answer X2 + 1 \(\frac{X - 2}{\sqrt{X^3 - 2X^2 + 3n - 3}}\)

= \(\frac {- 6X^3 + n}{-2X^2 + 2X - 3}\)

= \(\frac{(-2X^2 - 2)}{2X - 1}\)

Remainder is 2X - 1

Correct Option:
A
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Question 13
A
-3, -9 
B
9, -3 
C
-9,3 
D
3, -9 
Explanation.
Share Answer -2x -5y = 3

x + 3y = 0

x = -3y

-2 (-3y) - 5y = -3

6y - 5y = 3

y = 3

but, x = -3y

x = -3(3)

x = -9

therefore, x = -9, y = 3

Correct Option:
C
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Question 14
A
20\(\frac{1}{4}\) 
B
27 
C
2\(\frac{1}{4}\) 
D
36 
Explanation.
Share Answer x \(\alpha\sqrt y\)

x = k\(\sqrt y\)

81 = k\(\sqrt9\)

k = \(\frac{81}{3}\)

= 27

therefore, x = 27\(\sqrt y\)

y = 1\(\frac{7}{9}\) = \(\frac{16}{9}\)

x = 27 x \(\sqrt{\frac{16}{9}}\)

= 27 x \(\frac{4}{3}\)

dividing 27 by 3

= 9 x 4

= 36

Correct Option:
D
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Question 15
A
\(\frac{1}{18}\) 
B
\(\frac{1}{12}\) 
C
\(\frac{1}{24}\) 
D
\(\frac{1}{6}\) 
Explanation.
Share Answer T \(\alpha \frac{1}{R^3}\)

T = \(\frac{k}{R^3}\)

k = TR3

= \(\frac{2}{81}\) x 33

= \(\frac{2}{81}\) x 27

dividing 81 by 27

k = \(\frac{2}{2}\)

therefore, T = \(\frac{2}{3}\) x \(\frac{1}{R^3}\)

When R = 2

T = \(\frac{2}{3}\) x \(\frac{1}{2^3}\) = \(\frac{2}{3}\) x \(\frac{1}{8}\)

= \(\frac{1}{12}\)

Correct Option:
B
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Question 16
A
x \(\leq\) 2 
B
x \(\geq\) -1 
C
x \(\geq\) -2 
D
x \(\leq\) -1 
Explanation.
Share Answer -6(x + 3) \(\leq\) 4(x - 2)

-6(x +3) \(\leq\) 4(x - 2)

-6x -18 \(\leq\) 4x - 8

-18 + 8 \(\leq\) 4x +6x

-10x \(\leq\) 10x

10x \(\leq\) -10

x \(\leq\) 1

Correct Option:
B
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Question 17
A
x < -3 or x > 5 
B
-5 < x < 3 
C
x < 3 or x > 5 
D
x > 3 or x < -5 
Explanation.
Share Answer x2 + 2x > 15

x2 + 2x - 15 > 0

(x2 + 5x) - (3x - 15) > 0

x(x + 5) - 3(x + 5) >0

(x - 3)(x + 5) > 0

therefore, x = 3 or -5

then x < -5 or x > 3

i.e. x< 3 or x < -5

Correct Option:
D
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Question 18
A
505 
B
513 
C
433 
D
635 
Explanation.
Share Answer 3, 6, 9,..., 36.

a = 3, d = 3, i = 36, n = 18

Sn = \(\frac{n}{2}\) [2a + (n - 1)d

S18 = \(\frac{18}{2}\) [2 x 3 + (18 - 1)3]

= 9[6 + (17 x 3)]

= 9 [6 + 51] = 9(57)

= 513

Correct Option:
B
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Question 19
A
60 
B
62 
C
54 
D
64 
Explanation.
Share Answer T2 = 4, T4 = 16

Tx = arn-1

T2 = ar2-1 = 4 i.e. ar3 = 16, i.e. ar = 4

T4 = ar4-1

therefore, \(\frac{T_4}{T_r}\) = \(\frac{ar^3}{ar}\) = \(\frac{16}{4}\)

r2 = 4 and r = 2

but ar = 4

a = \(\frac{4}{r}\) = \(\frac{4}{2}\)

a = 2

Sn = \(\frac{a(r^n - 1)}{r - 1}\)

S5 = \(\frac{2(2^5 - 1)}{2 - 1}\)

= \(\frac{2(32 - 1)}{2 - 1}\)

= 2(31)

= 62

Correct Option:
B
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Question 20
A
- \(\frac{1}{2}\) 
B
\(\frac{1}{3}\) 
C
-1 
D
Explanation.
Share Answer N + Y = XY + X + Y

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

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

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

= \(\frac{1}{3}\)

Correct Option:
B
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