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**SECTION A ****(Questions 1 to 12 carry 1 mark each)**

**Q.1. Which of the following statements is shown by the given number line?**

Ans.

On the given number line, from 8, five steps are moved towards the left.

Thus, the number line represents 8 - 5 = 3.

According to distributive law of multiplication over addition, we have:

12 Ã— (45 + 30) = (12 Ã— 45) + (12 Ã— 30)

267 can be estimated as 270.

132 can be estimated as 130.

Thus the required estimated sum = 270 + 130 = 400

We have 10 = 2 Ã— 5

18 = 2 Ã— 3 Ã— 3

HCF of 10 and 18 is 2.

Thus, 2 is the required number.

To convert into mixed fraction first divide numerator by denominator. The quotient is taken as the whole number part of mixed fraction. Remainder obtained is taken as the numerator and divisor as the denominator of the fractional part of the mixed fraction.

Therefore,

A region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides is called a sector of the circle.

One crore can be written as 1,00,00,000.

One thousand can be written as 1000.

So, 10000 times one thousand would make one crore.

There are 1000 + 1 = 1001 whole numbers upto 1000.

i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ........., 1000

(â€“42) + (â€“35) = â€“42 â€“ 35 = â€“77

Fifth multiple of 18 = 18 Ã— 5 = 90

The English alphabet Z represents an open curve.

**Section B**

**Q.13. ****Evaluate the difference between the place values of two 9's in the number 79520986. Solution. **

Place value of 9 at the Ten Lakhs place = 9000000

Place value of 9 at the hundreds place = 900

Difference = 9000000 â€“ 900 = 8999100

Radius of a circle is a line joining the center of circle to any point on the circle. So, the radii drawn in the given figure are OP, OQ and OR.

The number of vertices in the given shapes:

Anna is 7 feet above sea level.

She jumps 3 feet down and walks another 2 feet down. Total distance travelled downwards = 3 + 2 = 5 feet.

(â€“13) + (â€“19) + (+15) + (â€“10)

= â€“13 â€“ 19 + 15 â€“ 10

= â€“13 â€“ 19 â€“ 10 + 15

= â€“42 + 15

= â€“27

A 9-digit numeral in Indian system = 94,50,27,983

In International system:

945,027,983: Nine hundred forty five million twenty seven thousand nine hundred eighty three.

Given number is 1258.

Its unit digit is 8, which is divisible by 2. So, 1258 is divisible by 2.

Sum of its digits = 1 + 2 + 5 + 8 = 16, which is not divisible by 3.

So, 1258 is not divisible by 3.

Since, 1258 is divisible by 2 but not by 3, it is not divisible by 6.

Starting from zero, a jump of 8 units is made to the right to reach 8. Then, 3 jumps (each of 1 unit i.e. from 8 to 7, 7 to 6, 6 to 5) are taken to the left to reach 5.

So, we conclude that 8 â€“ 3 = 5

(i) â€“9 ___ -15

(ii) â€“10 ___ 10

(iii) 0 ___ 3

(iv) â€“28 ____ 17

Since the sum of all three angles of a triangle is 180

We have, âˆ X + âˆ Y + âˆ Z = 180

Or, âˆ X + 60

Or, âˆ X + 110

Or, âˆ X = 180

Hence, âˆ X = 70

101 Ã— 33 = 3333

101 Ã— 333 = 33633

101 Ã— 3333 = ?

101 Ã— 33333 = ?

Using distributive property of multiplication over addition, we have:

101 Ã— 33 = (100 + 1) Ã— 33 = 3300 + 33 = 3333

101 Ã— 333 = (100 + 1) Ã— 333 = 33300 + 333 = 33633

101 Ã— 3333 = (100 + 1) Ã— 3333 = 333300 + 3333 = 336633

101 Ã— 33333 = (100 + 1) Ã— 33333 = 3333300 + 33333 = 3366633

**SECTION C**

(Questions 25 to 32 carry 3 marks each)

**Q.25. ****Tanvi bought a notebook for Rs and a pen for Rs How much money should she pay to the shopkeeper? Solution. **

Cost of notebook

Cost of pen

LCM of 4 and 5 = (2 Ã— 2 Ã— 5) = 20

Total cost of both the items

The given fractions are

LCM of 3, 6, 9, 12 = (3 x 2 x 3 x 2) = 36

So, we convert each one of given fractions into an equivalent fraction having 36 as denominator.

Now,

Clearly,

The given fractions in ascending order are

Let the numbers be a and b.

Then, a + b = 55 and ab = 5 Ã— 120 = 600

Therefore, the required sum =

a) What are lines p, q, and r called?

b) What is the point at which they meet called? Label it on the figure.

c) How many lines can pass through the labeled point?

LCM of 12 and 16 = (4 Ã— 3 Ã— 4) = 48

So, we convert each one of into an equivalent fraction having 48 as denominator.**Q.30. ****Each corner of a cube is cut off, leaving a triangular face at each corner and an octagonal face in place of each face of the original cube. How many vertices and faces will the new polyhedron have? Solution. **

Each of the 8 vertices of the cube has now been replaced by three vertices of a triangle. So, there are now 24 vertices. The cube had 6 square faces. Now those faces are still there but have become octagons. Additionally, there are now 8 new triangular faces. So, there is a total of 14 faces.

To solve using number line start with -8, move 12 steps right and then back 2 steps as shown below:

So, we reach at 2, therefore (-8 + 12 - 2) = 2

Find a rule that helps her find the number of sticks.

Let the number of triangles be n.

For 1 triangle: Number of sticks = 2 Ã— 1 + 1 = 3 sticks

For 2 triangles: Number of sticks = 2 Ã— 2 + 1 = 5 sticks

âˆ´ Number of sticks used = 2Ã—n + 1

**SECTION D ****(Questions 33 to 37 carry 4 marks each)**

**Q.33. ****The cost of a pen is Rs. and that of a pencil is Rs. Which costs more and by how much? Solution. **

Cost of a pen =

Cost of a pencil =

Now, converting to like fractions

Clearly,

Difference between their cost =

Hence, the cost of pen is more than cost of pencil by Rs.

(i) Î”LMN with âˆ L = 30Â°, âˆ M = 70Â° and âˆ N= 80Â°.

(ii) Î”DEF with âˆ D= 90Â°.

(iii) Î”PQR such that PQ = QR = PR = 5 cm.

(iv) Î”XYZ with âˆ Y= 90Â° and XY = YZ.

16 â€“ [5 â€“ 2 + {7 of 2 - (2 Ã— 2 â€“ 1 + 3)}]

= 16 â€“ [5 â€“ 2 + {7 of 2 - (4 â€“ 1 + 3)}]

= 16 â€“ [5 â€“ 2 + {7 of 2 - 6}

= 16 â€“ [5 â€“ 2 + {8}]

= 16 â€“ 11

= 5

a) Line l contains point A but not B

b) Lines p and q intersect at point o

c) Rays PQ and QR meet to form angle PQR

Adding

LCM of 3, 9 = 9

= 62/9

We also have

LCM of 6, 9 = (2 Ã— 3 Ã— 3) = 18

= 179/18

Thus,

= 55/18

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