D

Diameter = 1.4 m.
Circumference of the wheel = πd = [latex]\frac {22}{7}[/latex] × 1.4
= 4.4
We have distance traveled in 1 rotation = 4.4 meter
Distance covered in 500 rotations = 4.4 × 500 = 2200 meters

B

We have Volume and radius of cylinder and sphere are same
Let R be the radius of both the figures.
Then Volume of sphere = [latex]\Rightarrow \frac {4 \pi {(R)}^{3}}{3}[/latex]
And Volume of cylinder = [latex]π{R}^{2}h[/latex]
Hence equating both the volumes
[latex]\Rightarrow \frac {4 \pi {(R)}^{3}}{3} = π{R}^{2}h[/latex]
[latex]\Rightarrow \frac {4R}{3} = h[/latex]
[latex]\Rightarrow R = \frac {3h}{4}[/latex]

B

Length of the room = 13m
Breadth of the room = 9m
Area of the room = length × breadth
Area = 13 × 9 = 117 [latex] {m}^{2}[/latex]
Also, we need to cover the entire area with a carpet which is 0.75 m wide.
Hence, length of carpet required = [latex] \frac {Area of room}{width of carpet}[/latex]
= [latex] \frac {117}{0.75}[/latex]
= 156 m
Cost of 1 m carpet = Rs 12.4
Cost of 156m carpet = Rs 12.4 × 156
= Rs 1934.4

A

Area of triangle = [latex] (\frac {\sqrt {3}}{4}){a}^{2} [/latex]
Let number of 1 inch triangle = n
∴ [latex] n × (\frac {\sqrt {3}}{4}) × {1}^{2} = (\frac {\sqrt {3}}{4}) × {3}^{2}[/latex]
[latex]\Rightarrow[/latex] n = 9
Hence Option (A)

D

Diameter = 2.8 m.
Circumference of the wheel = πd = [latex]\frac {22}{7}[/latex] × 2.8
= 8.8
We have distance traveled in 1 rotation = 8.8 meter
Distance covered in 100 rotations = 8.8 × 100 = 880 meter