MATHEMATICS (2016) | Study Mode

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Question 21
A
1.36 x 10-4
B
1.36 x 10-3
C
1.36 x 10-1
D
1.36 x 10-2
Explanation
\(\frac{0.026 \times 0.36}{0.69}\) = \(\frac{26 \times 10^-3 \times 36 \times 10^-2}{69 \times 10^-2}\)

= 0.01356 = 1.36 x 10-2

Correct option: D
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Question 22
A
15
B
25
C
30
D
50
Explanation
Let x represent total number of pencils shared
B : S : T
2 : 3 : 5

2+3+5 = 10
\(\frac{2}{10}\) x x = 5
\(\frac{2x}{10}\) = 5
2x = 50
x = 25

Correct option: B
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Question 23
A
18cm
B
(18 + \(\frac{9\pi}{5}\))cm
C
(9 + \(\frac{9\pi}{5}\))cm
D
\(\frac{9\pi}{5}\)cm
Explanation
Perimeter = 2r + \(\frac{\theta}{360}\) x 2\(\pi\)r
2(9) + \(\frac{36}{360}\) x 2 x \(\pi\) x 9 = 18 + \(\frac{9\pi}{5}\)

Correct option: B
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Question 24
A
\(\frac{23}{5}\)
B
-\(\frac{23}{5}\)
C
\(\frac{1}{8}\)
D
\(\frac{21}{7}\)
Explanation
\(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\)

\(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\) = \(\frac{3\sqrt{27} - 3\sqrt{8}^2}{\sqrt{16} \times 2}\)

\(\frac{3 - 4}{4 \times 2}\)
= \(\frac{-1}{8}\)

Correct option: C
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Question 25
A
3
B
5
C
4
D
6
Explanation
Mean = \(\frac{(2 \times 3) + (3 \times 6) + (4 \times 5) + (2 \times 6)}{2 + 3 + 4 + 6}\)

= \(\frac{6 + 18 + 20 + 12}{15}\) = \(\frac{56}{15}\)

= 3.73

Correct option: C
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Question 26
A
3x2 - \(\frac{4}{x}\)
B
2x2 +\(\frac{4}{x^2}\)
C
3x2 + \(\frac{4}{x^2}\)
D
2x2 - \(\frac{4}{x}\)
Explanation
y = \(\frac{2}{3}\)x3 - \(\frac{4}{x}\)

\(\frac{dy}{dx}\) = 2x2 - Lx-2 = 2x2 + \(\frac{4}{x^2}\)

Correct option: B
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Question 27
A
14.09
B
14.1
C
14.12
D
14.11
Explanation
\(\frac{0.8 \times 0.43 \times 0.031}{0.05 \times 0.72 \times 0.021}\) x \(\frac{10}{10}\) = 14.11

Correct option: D
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Question 28
A
6\(\pi\)cm
B
2\(\pi\)cm
C
3\(\pi\)cm
D
9\(\pi\)cm
Explanation
Length or arc = \(\frac{\theta}{360}\) x 2\(\pi\)r

= \(\frac{30}{360}\) x 2 x \(\frac{22}{7}\) x 12

= \(\frac{1}{12}\) x 2 x \(\pi\) x 2 = 2\(\pi\)cm

Correct option: B
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Question 29
A
2
B
-1
C
1
D
-2
Explanation
\(\int\limits_0^\frac{\pi}{2}\) sin xdx = -cosx|\(\frac{\pi}{2}\)

= -(cos\(\frac{\pi}{2}\) - cos0) = -(0-1) = 1

Correct option: C
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Question 30
A
24cm
B
28cm
C
36cm
D
32cm
Explanation
L = \(\frac{\theta}{360}\) x 2\(\pi\)r
16\(\pi\) = \(\frac{80}{360}\) x 2\(\pi\)r

\(\frac{16\pi \times 360}{80 \times 2\pi}\) = r

r = 36cm

Correct option: C

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