Algebra, Geometry & Mensuration

If the side of square is decreased by $50\%$, then its new area will be:

The length, breadth and height of the cuboid are in the ratio $2:3:4$ and if the total surface area is $8788\text{ cm}^2$, then find the volume of the cuboid:

The two parallel sides of trapezium are $2.02\text{ meters}$ and $4.04\text{ meters}$ respectively. The perpendicular distance between them is $5\text{ meters}$. The area of the trapezium is:

Evaluate the following expression: $$\frac{(9.6)^3 - 0.343}{(9.6)^2 + 6.72 + 0.49} + \frac{(2.6)^3 - 0.008}{(2.6)^2 + 0.52 + 0.04}$$

Four circular bangles each having radius of $6\text{ cm}$ are placed in such a way that each bangle touches two other bangles. The area of the closed space formed by the four bangles is:

The area of the largest circle that can be drawn inside a rectangle with sides $16\text{ cm}$ by $12\text{ cm}$ is

Find the next number in the series $125, 80, 45, 20, \dots$

A vertical object $20\text{ cm}$ long casts a shadow $7\text{ cm}$ long on the ground. At the same time a pole casts a shadow $30\text{ m}$ long on the ground. Then find the approximate height of the pole?

40 men took a dip in a water tank $30\text{ m}$ long and $20\text{ m}$ broad on a religious day. If the average displacement of water by a man is $4\text{ m}^3$, then the approximate rise in the water level in the tank will be

If $1.5x = 0.04y$, then the value of $\left(\frac{y - x}{y + x}\right)$ is:

The length of the floor of a rectangular hall is 10 m more than its breadth. If 34 carpets of size 6 x 4 m are required to cover the floor of the hall, then find the breadth and length of the hall:

If the perimeter of a circle is 40 meters, find out the radius of the circle:

There are 20 people in a party. If every person shakes hands with every other person, what is the total number of handshakes?

If each edge of a cube is increased by 50%, find the percentage increase in its surface area:

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall in m^3 is: