Mathematics | Study Mode

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Question 31 Mathematics
A
2:3 
B
3:4 
C
3:8 
D
1:2 
Explanation.
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\(\frac{x}{y}\) = \(\frac{1}{4} \div \frac{3}{8}\) = \(\frac{1}{4} \times \frac{8}{3}\) = \(\frac{2}{3}\)

\(\frac{y}{z}\) = \(\frac{1}{3} \div \frac{4}{9}\) = \(\frac{1}{3} \times \frac{9}{4}\) = \(\frac{3}{4}\)

But,

x = \(\frac{2}{5}T_1\), y = \(\frac{3}{5}T_1\)

y = \(\frac{3}{7}T_2\), z = \(\frac{4}{7}T_2\)

Using y = y

\(\frac{3}{5}T_1\) = x = \(\frac{3}{7}T_2\)

\(\frac{T_1}{T_2}\) = \(\frac{3}{7}\) x \(\frac{5}{3}\) = \(\frac{15}{21}\)

\(T_1 = 15\) and \(T_2 = 21\)

Thus , x = \(\frac{2}{5}\) x 15 = 6

y = \(\frac{3}{5}\) x 15 = 9

y = \(\frac{3}{7}\) x 21 = 9

z = \(\frac{4}{7}\) x 21 = 12

Hence; x : z = 6 : 12

= 1 : 2


Correct Option:
D
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Question 32 Mathematics
A
If p is true and q is true 
B
If p is true and q is false 
C
If p is false and q is false 
D
If p is false and q is true 
Explanation.
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From the truth table above, p \(\to\) q would be false if p is true and q is false

Maths-explained-image

Correct Option:
B
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Question 33 Mathematics
A
0.0 
B
0.5 
C
1.0 
D
1.5 
Explanation.
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First arrange the numbers in ascending order of magnitude; 0, 0, 1, 1, 1, 1, 2, 2, 3, 4

Counting from the right, the fifth number is 1

Counting from the left, the fifth number is 1

Hence, median = \(frac{1 + 1}{2}\)

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

= 1


Correct Option:
C
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Question 34 Mathematics
A
B
C
10 
D
12 
Explanation.
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Mean = \(\frac{\sum f x}{\sum f}\)

= \(\frac{350}{10}\)

= 35

= \(\frac{\sum f |d|}{\sum f}\)

= \(\frac{90}{10}\)

= 9


Correct Option:
B
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Question 35 Mathematics
A
63\(^o\) 
B
117\(^o\) 
C
126\(^o\) 
D
234\(^o\) 
Explanation.
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In the diagram,

\(\alpha\) = 180\(^o\) - 177\(^o\) (angles on a straight line)

\(\alpha\) = 63\(^o\)

t = 2 x 63\(^o\) (angle at centre = 2 x angle at circum)

= 126\(^o\)

Maths-explained-image

Correct Option:
C
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Question 36 Mathematics
A
40\(^o\) 
B
65\(^o\) 
C
85\(^o\) 
D
95\(^o\) 
Explanation.
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In the diagram,

a = 50\(^o\) (alternate angles)

b\(_1\) + a 35\(^o\) = 180\(^o\) (sum of angles on a straight line)

i.e; b\(_1\) + 50\(^o\) + 35\(^o\)

= 180v

b\(_1\) + 180\(^o\) - 85\(^o\) = 90\(^o\)

But b\(_2\) = \(b_1\) = 95\(^o\) (angles in alternate segement)

<QST = b\(_2\) = 95\(^o\)

Maths-explained-image

Correct Option:
D
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Question 37 Mathematics
A
Trapezium 
B
Prism 
C
Rectangle 
D
Rhombus 
Explanation.
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No official Explanation yet!


Correct Option:
D
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Question 38 Mathematics
A

110\(^o\)

 
B

135\(^o\)

 
C

165\(^o\)

 
D

225\(^o\)

 
Explanation.
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In the diagram,

Thus, m = 2 x 55\(^o\) (is a bisector of obtuse

m = 110\(^o\)

n = \(\frac{1}{2}\) x 110\(^o\) (angle at centre = 2 x angle at circum)

n = 55\(^o\)

= 165\(^o\)

Maths-explained-image


Correct Option:
C
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Question 39 Mathematics
A

25cm\(^2\)

 
B

24cm\(^2\)

 
C

16cm\(^2\)

 
D

12cm\(^2\)

 
Explanation.
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Area of shaded part = 2 x area of \(\bigtriangleup\)SPQ

= 2 x \(\frac{1}{2}\) 8 x 3 =24cm

Hence, area of the unshaded part of the rectangle = area of rectangle - area of shaded part

= 8 x 6 - 24

= 48 - 24

= 24 cm\(^2\)


Correct Option:
B
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