1

The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?

A

39cm ≤ P ≤41cm

B

38cm ≤ P < 42cm

C

38.5 ≤ P ≤ 41.5cm

D

38.5 ≤ P ≤ 40cm

CORRECT OPTION:
b

If the side = 10 cm, correct to the nearest whole number, then

The side ranges from 9.5 cm to 10.5 cm. (9.5 \(\leq\) s < 10.5)

Perimeter of a rhombus = 4 x side

\(\therefore\) 4 x 9.5 \(\leq\) perimeter < 4 x 10.5

= 38 cm \(\leq\) P < 42 cm

2

Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.

A

0

B

\(2log_7 2\)

C

\(3log_7 2\)

D

\(4log_7 2\)

CORRECT OPTION:
d

log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4

= log\(_7\) (8/2 x 4)

= log\(_7\) 16

= 4 log\(_7\) 2

3

If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.

A

-2

B

-1

C

1

D

2

CORRECT OPTION:
b

\(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\

2K\sqrt{7}+3\sqrt{7}-\sqrt{7}=0\

2K\sqrt{7}=-2\sqrt{7}\

K=\frac{-2\sqrt{7}}{2\sqrt{7}}\

K=-1\)

4

From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number

A

\(\frac{1}{5}\)

B

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

C

\(\frac{3}{5}\)

D

\(\frac{4}{5}\)

CORRECT OPTION:
b

\(A = {3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}}\)

n(A) = 5

Let the rational nos = R

n(R) = 2 (3, \(\sqrt{9}\))

P(R) = 2/5

5

*The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below*

Find the value of K

A

15^{o}

B

30^{o}

C

60^{o}

D

90^{o}

CORRECT OPTION:
b

Total angle in a circle = 360°

\(\therefore\) 105 + 75 + 2k + k + 3k = 360°

6k = 360 - 180 = 180

k = 180/6 = 30°

6

*The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below*

If he sends \(2\frac{1}{2}\) hours week on science, find the total number of hours he studies in a week

A

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

B

5 hours

C

8 hours

D

12 hours

CORRECT OPTION:
d

Let x represent the total number of hours spent per week

\(∴ \frac{75}{360} \times x = \frac{5}{2}\

∴ x = \frac{360 \times 5}{725 \times 2}=12 hours\)

7

A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

A

\(\frac{2}{11}\)

B

\(\frac{4}{11}\)

C

\(\frac{5}{11}\)

D

\(\frac{11}{13}\)

CORRECT OPTION:
a

Let the number of people that speak both English and French = x

Then (7 - x) + x + (6 - x) = 11

13 - x = 11 \(\implies\) x = 2.

\(\therefore\) P(picking a person that speaks both languages) = 2/11

8

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

A

5

B

6

C

8

D

9

CORRECT OPTION:
b

Let the exterior angle = d

Note: Exterior angle + Interior angle = 180°

\(\implies\) d + 2d = 180°

3d = 180° \(\implies\) d = 60°

Recall, exterior angle = \(\frac{360}{\text{no of sides}}\)

\(\therefore \text{No of sides} = \frac{360}{60}\)

= 6 sides

9

Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite

A

I and II only

B

II and III only

C

I and III only

D

I, II, and III

CORRECT OPTION:
c

Isosceles triangle and Kite shapes have 1 line of symmetry each while the rhombus has 2 lines of symmetry.

10

In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ

A

50^{o}

B

62^{o}

C

112^{o}

D

115^{o}

CORRECT OPTION:
d

In triangle RXY, < RXY = < RYX (base angles of an isosceles triangle)

\(\implies\) 180° - 62° = 2 < RYX

118° = 2 < RYX \(\implies\) < RYX = 59°

In triangle RYZ, < RZY = 62° (base angles of an isosceles triangle)

\(\therefore\) < RYZ = 180° - (62° + 62°)

= 180° - 124° = 56°

\(\therefore\) < XYZ = 56° + 59°

= 115°

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