1

A square was given. Inside the square there are white tiles and black tiles. Black tiles was among the diagonal of the square and dimensions of both white as well as black tiles is 1 cm x 1 cm. If there are 81 black tiles in the square. Then find the no of white tiles in it.

View Solution
#### Answer : Option**
B**

#### Explanation:

In a square, number of squares on the diagonal is equal to the tiles on a single row.

If there are even number of square on a side, then total squares on the diagonal is 2n - 1, otherwise 2n.

As the total tiles on the diagonal are given as 81,

then number of tiles on a side = 2n -1 = 81 so n = 41.

So number of white tiles = 41^{2 }– 81 = 1681 – 81 = 1600

2

A largest cone is formed at the base of cube of side measuring 7 cm. What is the ratio of volume of cone to volume of cube?

View Solution
#### Answer : Option**
C**

#### Explanation:

As the Cone is inside a Cube of side 7 cm, then it looks like given below

Volume of cube = side x side x side = 7 x 7 x 7

Volume of cone = $\frac{1}{3}\left[{\mathrm{\pi R}}^{2}\mathrm{H}\right]$ = $\frac{1}{3}\left(\mathrm{\pi}{\left(\frac{7}{2}\right)}^{2}\times 7\right)$

Ratio is $\frac{1}{3}\left(\mathrm{\pi}{\left(\frac{7}{2}\right)}^{2}\times 7\right)$ : 7 x 7 x 7

$\frac{\mathrm{\pi}}{12}$

3

What is the maximum volume of a right circular cone, which can be cut from a solid cuboid having a dimensions 12 x 10 x 15?

View Solution
#### Answer : Option**
C**

#### Explanation:

Since base circle will be in 2-Dimensional and so radius will be 5 in 10 x 12 plane and height will be 15 for the volume to be maximum.

So max possible volume is $\frac{1}{3}\mathrm{\pi}\times 5\times 5\times 15$ = 125 π

On the otherside, If you will take base as 15 x 12 plane,then radius = 6 then height can't be 15. ( it is 10 cm)

In 15 x 12 plane, circle is possible with radius = 6. If you will take r = 6 then height will be 10.

Then the maximum volume will be 120 π.( which is less than 125 π).

Hence 125 π is the maximum volume possible

4

Eden park is a cricket field while Jubilee Park is a football field in Mastnagar. In Mastnagar all cricket fields are circular and football fields are rectangular or square. Along the boundary of all the fields there are advertisement displays. In Mastnagar the length of the advertisement displays has to be the same across all playing fields. Area of the Jubilee park is 468 ${\mathrm{m}}^{2}$. The farthest distance between any two points in Jubilee park football field is 10√10 m. find the approximate area of Eden garden?

Video Solution
#### Answer : Option**
B**

#### Explanation:

#### Answer : Option** 2**

#### Explanation:

This explanation is given clearly in the video

5

From a circular sheet of radius of 30 cm, a sector of 10% area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is:

Video Solution
#### Answer : Option**
B**

#### Explanation:

#### Answer : Option** 2**

#### Explanation:

The explanation is given clearly in the video