Mathematics 2018 | Study Mode

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Question 21
A
5.0 cm 
B
7.0 cm 
C
8.5 cm 
D
12.0 cm 
Explanation.
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Total surface area of hemisphere is

3\(\pi r^2\) = 75\(\pi cm^2\)

\(r^2\) = \(\frac{75 \pi}{3 \pi}\)

\(r^2\) = 25

r = \(\sqrt{25}\)

r = 5cm


Correct Option:
A
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Question 22
A
0 or 5 
B
-5 or 5 
C
-11 or 5 
D
0 or 1 
Explanation.
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The expression \(\frac{x - 5}{x(x - 1)}\) is defined whten

x(x - 5) = 0.38

either x = 0 or x - 5 = 0

Hence, x = 0 or x = 5


Correct Option:
A
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Question 23
A
x = \(\frac{-3}{2}\) or 2 
B
x = -2 or \(\frac{3}{2}\) 
C
x = -3 or 2 
D
x = 3 or -2 
Explanation.
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\(2x^2 - x - 6\) = 0

\(2x^2 - 4x + 3x - 6\) = 0

2x(x - 2) + 3(x - 2) = 0

(2x + 3) (x - 2) = 0

Either; 2x + 3 = 0 or x - 2 = 0

x = \(\frac{-3}{2}\) or x = 2


Correct Option:
A
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Question 24
A
(3x + 2)(1 - x) 
B
(3x + 2)(2x + 1) 
C
3\((x + 2)^2\) 
D
3(x + 1)(1 - x) 
Explanation.
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\((x + 2)^2\) - \((2x + 1)^2\)

= \((x^2 + 4x + 4) - (4x^2 + 4x + 1)\)

= \(x^2 \) + 4x + 4 - 4 \(x^2 \) - 4x - 1

= -3 \(x^2 \) + 3

= 3 - 3 \(x^2 \)

= 3(1 - \(x^2 \))

= 3(1 + x)(1 - x)


Correct Option:
D
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Question 25
A
2\(^n\) x 3(n + 1) 
B
2\(^n\) x 3n 
C
2\(^n\) x 3\(^n\) 
D
2\(^n\) x 3\(^n - 1\) 
Explanation.
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2 x 3, 4 x 6, 8 x 9, 16 x 12,...

2\(^1\) x 3 x 1, 2\(^2\) x 3 x 2, 2\(^3\) x 3 x 3, 2\(^4\) x 3 x 4,.... 2\(^n\) x 3n


Correct Option:
B
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Question 26
A
B
C
D
Explanation.
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3x \(\equiv\) 4(mod 5)

In modulo 5, multiples of 5 that give solution to the given equation are 5, 20, 35, 50,... but 5 will yield the leaast value of x.

Thus; 3x = 4 + 5 = 9

x = \(\frac{9}{3}\)

x = 3


Correct Option:
C
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Question 27
A
B
C
D
Explanation.
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\(Q_1 = \frac{1}{4}\)Nth

\(\frac{1}{4} \times 11^{th}\) no.

= 2\(\frac{3}{4}th\) (\(\cong\) 4)

\(Q_3 = \frac{3}{4}\) Nth

= \(\frac{3}{4}\) x 11th no.

= 8\(\frac{1}{4}\) no. (\(\cong\) 11) (\(\cong\) 11)

Hence, interquartile range

= \(Q_3 = Q_1\)

= 11 - 4

= 7


Correct Option:
B
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Question 28
A
\(\frac{153}{250}\) 
B
\(\frac{68}{111}\) 
C
\(\frac{61}{100}\) 
D
\(\frac{21}{33}\) 
Explanation.
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0.612 = \(\frac{0.612}{1}\) x \(\frac{1000}{1000}\)

= \(\frac{612}{1000}\)

= \(\frac{153}{250}\)


Correct Option:
A
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Question 29
A
27m 
B
13.5 \(\sqrt{3m}\) 
C
13.5 \(\sqrt{2m}\) 
D
9\(\sqrt{3m}\) 
Explanation.
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From the diagram,

tan 30\(^o\) = \(\frac{h}{27}\)

h = 27 tan 30\(^o\)

= 27 x \(\frac{1}{\sqrt{3}}\)

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

= \(\frac{27 \sqrt{3}}{3}\)

= 9\(\sqrt{3m}\)

Maths-explained-image

Correct Option:
D
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Question 30
A
\(\frac{|PN|}{|PR|}\) 
B
\(\frac{|PM|}{|PQ|}\) 
C
\(\frac{|PM|}{|PR|}\) 
D
\(\frac{|PR|}{|PQ|}\) 
Explanation.
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\(\frac{|PN|}{|PQ|}\) = \(\frac{|PM|}{|PR|}\)


Correct Option:
C
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