TOP QUESTIONS AND ANSWERS FOR YOU

Maths

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8th

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February 28, 2022

1. In a building, there are 24 cylindrical pillars. For each pillar, radius is 28 m and height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m2.

David Miller

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Student

Solution:

Maths

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8th

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February 24, 2022

4. **Write 3.61492 x 106 in usual form.**

David Miller

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Student

Solution: 3.61492 x 106

= 3.61492 x 1000000

= 3614920

Maths

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8th

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February 24, 2022

3. **Express 0.00000000837 in standard form.**

David Miller

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Student

0.00000000837

= 0.00000000837 x 109 / 109

= 8.37 ×10-9

Maths

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8th

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February 24, 2022

2. ** Simplify [25 x t-4]/[5-3 x 10 x t-8]**

David Miller

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Student

Solution:

We can write the given expression as;

[52x t-4]/[5-3 x 5 x 2 x t-8]

= [52 x t-4+8]/[5-3+1 x2]

= [52+2 x t4]/[2]

= [54 x t4]/[2]

= [625/2] t4

Maths

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8th

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February 24, 2022

**1.If a new-born bear weighs 4 kg, calculate how many kilograms a five-year-old bear weigh if its weight increases by the power of 2 in 5 years?**

David Miller

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Student

Weight of new-born bear = 4 kg

Rate of weight increase in 5 years = power to 2

Thus, the weight of the 5-year old bear = 42 = 16 kg

Maths

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9th

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February 24, 2022

5. **In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of Δ XYZ, find ∠OZY and ∠YOZ.**

Joslin Smith

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Student

As we know, the sum of the interior angles of the triangle is 180°.

So, ?X +?XYZ + ?XZY = 180°

substituting the values as given in the question we get,

62° + 54° + ?XZY = 180°

Or, ?XZY = 64°

Now, As we know, ZO is the bisector so,

?OZY = ½ ?XZY

? ?OZY = 32°

Similarly, YO is a bisector and so,

?OYZ = ½ ?XYZ

Or, ?OYZ = 27° (As ?XYZ = 54°)

Now, as the sum of the interior angles of the triangle,

?OZY +?OYZ + ?O = 180°

Substituting their respective values we get,

?O = 180° – 32° – 27°

Or, ?O = 121°

Maths

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9th

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February 24, 2022

4. **In the Figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.**

Joslin Smith

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Student

Solution:

First, construct a line XY parallel to PQ.

As we know, the angles on the same side of the transversal are equal to 180°.

So, ?PQR + ?QRX = 180°

Or,?QRX = 180° – 110°

? ?QRX = 70°

Similarly,

?RST + ?SRY = 180°

Or, ?SRY = 180° – 130°

? ?SRY = 50°

Now, for the linear pairs on the line XY-

?QRX + ?QRS + ?SRY = 180°

Substituting their respective values we get,

?QRS = 180° – 70° – 50°

Or, ?QRS = 60°

Maths

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9th

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February 24, 2022

3. **In the Figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE**.

Joslin Smith

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Student

Solution:

Since AB || CD GE is a transversal.

It is given that ?GED = 126°

So, ?GED = ?AGE = 126° (alternate interior angles)

Also,

?GED = ?GEF + ?FED

As

EF ? CD, ?FED = 90°

? ?GED = ?GEF + 90°

Or, ?GEF = 126° – 90° = 36°

Again, ?FGE + ?GED = 180° (Transversal)

Substituting the value of ?GED = 126° we get,

?FGE = 54°

So,

?AGE = 126°

?GEF = 36° and

?FGE = 54°

Maths

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9th

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February 24, 2022

2. **In the Figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = 1/2(∠QOS – ∠POS).**

Joslin Smith

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Student

In the question, it is given that (OR ? PQ) and ?POQ = 180°

So, ?POS + ?ROS + ?ROQ = 180° (Linear pair of angles)

Now, ?POS + ?ROS = 180° – 90° (Since ?POR = ?ROQ = 90°)

? ?POS + ?ROS = 90°

Now, ?QOS = ?ROQ + ?ROS

It is given that ?ROQ = 90°,

? ?QOS = 90° + ?ROS

Or, ?QOS – ?ROS = 90°

As ?POS + ?ROS = 90° and ?QOS – ?ROS = 90°, we get

?POS + ?ROS = ?QOS – ?ROS

=>2 ?ROS + ?POS = ?QOS

Or, ?ROS = ½ (?QOS – ?POS) (Hence proved).

Maths

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9th

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February 24, 2022

**In the Figure, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.**

Joslin Smith

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Student

Solution:

As we know, the sum of the linear pair is always equal to 180°

So,

?POY + a + b = 180°

Substituting the value of ?POY = 90° (as given in the question) we get,

a + b = 90°

Now, it is given that a : b = 2 : 3 so,

Let a be 2x and b be 3x.

? 2x + 3x = 90°

Solving this we get

5x = 90°

So, x = 18°

? a = 2 × 18° = 36°

Similarly, b can be calculated and the value will be

b = 3 × 18° = 54°

From the diagram, b + c also forms a straight angle so,

b + c = 180°

=> c + 54° = 180°

? c = 126°