MATHEMATICS (2016) | Study Mode

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Question 31
A

2

B

t

C

-t

D

-2

Explanation

Mean = \(\frac{2 - t + 4 + t + 3 - 2t + 2 + t + t - 1}{5}\)

= \(\frac{10}{5}\) = 2


Correct option: A
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Question 32
A
0.157
B
0.154
C
0.155
D
0.158
Explanation
\(\frac{12.02 \times 20.06}{26.04 \times 60.06}\) = \(\frac{241.1212}{15698.96}\) = 0.154

Correct option: B
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Question 33
A
6x2 + 12x + 1
B
6x2 + 6x + 1
C
6x2 + 6x + 6
D
6x2 + 12x + 6
Explanation
y = 2x3 + 6x2 + 6x + 1

\(\frac{dy}{dx}\) = 6x2 + 12x + 6

Correct option: D
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Question 34
A
3 x 3n-2
B
3 x 3n-1
C
3 x 3n+2
D
3 x 3n+1
Explanation
3,9,27,81,.....
r = \(\frac{9}{8}\) = 3
Tn = arn-1

Tn = 3(3)n-1 = \(\frac{3(3^2)}{3}\)

Correct option: B
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Question 35
A
2
B
\(\frac{1}{3}\)
C
1
D
\(\frac{2}{3}\)
Explanation
1 - (\(\frac{1}{7}\) x 3 \(\frac{1}{2}\)) \(\div\) \(\frac{3}{4}\)

1 - (\(\frac{1}{7}\) x \(\frac{7}{2}\)) x \(\frac{4}{3}\)

1 - \(\frac{1}{2}\) x \(\frac{4}{3}\)

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

Correct option: B
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Question 36
A
720 litres
B
160 litres
C
225 litres
D
960 litres
Explanation
120km \(\to\) 45litres
1km \(\to\) \(\frac{45}{120}\)litres
600km \(\to\) \(\frac{45}{120}\) x 600 = 225litres

Correct option: C
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Question 37
A
9x2 + 4x + 3
B
9x2 - 4x - 3
C
9x2 + 4x - 3
D
9x2 - 4x + 3
Explanation
y = 3x3 + 2x2 + 3x + 1
\(\frac{dy}{dx}\) = 9x2 + 4x + 3

Correct option: A
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Question 38
A
-cosx - 10x + k
B
cosx - \(\frac{5x^3}{3}\) + k
C
-cosx - \(\frac{5x^3}{3}\) + k
D
cosx - 10x + k
Explanation
\(\int\)(sin x - 5x^2) = -cosx - \(\frac{5x^3}{3}\) + k

Correct option: C
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Question 39
A

48

B

108

C

54

D

216

Explanation

N = \(\frac{p}{2}\)(\(\frac{T_1 - T_2}{T_1}\))
12 = \(\frac{p}{2}\)(\(\frac{27 - 24}{27}\))
24 = P(\(\frac{3}{27}\))
P = 24 x 9 = 216


Correct option: D
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Question 40
A
\(\frac{3}{4}\), 1
B
\(\frac{4}{3}\), 1
C
\(\frac{3}{4}\), -1
D
\(\frac{4}{3}\), -1
Explanation
3x - 5y = 9 ------x2
6x - 4y = 12 -----x1
6x - 10y = 18
-6x - 4y = 12
____________
\(\frac{6y}{-6}\) = \(\frac{6}{6}\)

y = -1
in eq (1) 3x - 5y = 9
3x - 5(-1) = 9
3x + 5 = 9
3x = 4
x = \(\frac{4}{3}\)

Correct option: D

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