Question

a
SUBJECT: MATHEMATICS
1. Find the mean of first ten natural numbers.
2. My younger sister's age today is 3 times what it will be 3 years from now minus 3
times what her age was 3 years ago. Find her present age.
3. Find value of x if 32% of x kg is 400 kg.
4. The cost of a flower vase got increased by 12%. If the current cost is Rs 896, what was
its original cost?
5. Draw an isosceles triangle with each of equal sides of length 3 cm and angle between
them is 45
6. Express as standard form:
a) 76,47,000
b) 8,19,00,000
7. From a circular sheet of radius 4 cm a circle of 3 cm is removed. Find the area of the
remaining sheet.
8. Simplify and express in exponential form:
3 X 72 X11°
21 X 11
9. A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed
outside the park. Find the area of the path.


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Answer 1

1)Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And the mean of three numbers a, b, c is a + b + c3. Hence, the mean of the first 10 natural numbers is 5.5.

2)Let my younger sister be x years old at present.

After 3 years, her age =(x+3)

Before 3 years, her age was =(x−3)

ACQ,

x=3(x+3)−3(x−3)

⇒ x=3(x+3−x+3)

⇒ x=2×6

⇒ 18

Therefore, 18 years is the present age of my younger sister.

3)32% of xkg is 400kg

100

32

​

×x=400⇒x=  

32

400×100

​

=1250

4)The present price Rs. 896. Therefore, the original price of the vase is Rs. 800

5)Step I Firstly, we draw a rough sketch of triangle with given measures marked on it. Step II Draw a line segment AB of length 3 cm. Step III Draw an angle of 45° on point B and produce it to ray Y. Step IV With B as centre, draw an arc of 3 cm which intersects ray BY at C.

6) a)7.647 x (10)3 x (10)3 = 7.647 x (10)6

(b) 8,19,00,000 = 81900000.00 = 819 x 10 s  = 8.19 x(10)2 x (10)5  = 8.19 x(10)7

7)Radius of circular sheet (r₁) = 4 cm

Radius of removed circle (r₂) = 3 cm

Area of remaining sheet = Area of circular sheet – Area of removed circle = πr₁2 - πr₂2

= π (r₁2 - r₂2)

= 3.14 (42 - 32) cm2  

= 3.14 (16 - 9) cm2  

= 3.14 × 7 cm2  

= 21.98 cm2

Thus, the area of the remaining sheet is 21.98 cm2.

idk 8th ques :(

9)Area of park =l×b=45×30=1350 cmsq  

 

Area of park with path is =45+2.5+2.5×30+2.5+2.5=1750 cmsq

 

Therefore,

Area of path = Area of park with path − Area of rectangular park              

=1750−1350=400 cm

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