Question 1 :
A rectangular glass container $30$ cm by $20$ cm by $50$ cm is $\displaystyle \frac{4}{5}$ filled with water. Some of the water is poured into $2$ identical tins to their brims. $14$ L of water is then left in the glass container. Find the height of each tin if each has $25$ cm square base.

Question 2 :
The base of a triangle lies along the line $x = a$ and is of length $a$. If the area of the triangle is $a^{2}$, the vertex lies of the line.<br/>

Question 3 :
A,B and C are points in the xy plane such that A(1,2); B (5,6) and AC=3BC. Then

Question 5 :
A rhombus has diagonals of length $a$ and ($a$+$\sqrt a$) units. If the area of the rhombus is $12$, then $a$ equals to

Question 6 :
The dimension of a rectangular court is such that if the length were increased by $2$ metres and the breadth diminished by the same, its area would be diminished by $12$ square metres, and if the length were increased by $2$ metres and its breadth increased by the same. Its area would be increased by $44$ square metres. Find the length.

Question 7 :
A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures $17$ inches across and requires$ 1.6$ bags of concrete in order to fill it to ground level. What is the depth of the hole? Round your answer to the nearest inch. (One bag of concrete, when mixed with the appropriate amount of water, makes $1800 &#160;{in.}^{3}$ of material).

Question 8 :
When freezing water increase its volume by $\dfrac {1}{11}$. By what part of its volume will ice decrease when melts and turns back into water?

Question 9 :
If circle R, of area 4 square inches, radius of circle S is twice of circle R, then the area&#160;of circle S, in square inches, is

Question 10 :
If the sum of the lengths of the diagonals of a rhombus of side $4 cm$ is $10 cm$. What is its area?

Question 11 :
The magnitude of the volume of a closed right circular cylinder of unit height divided by the magnitude of the total surface area of the cylinder ($r$ being the radius of the cylinder) is equal to

Question 12 :
If the side of a rhombus is $20$ meters and its shorter diagonal is three fourth of its longer diagonal, then the area of the rhombus must be

Question 13 :
The surface area of a sphere of radius $5\space cm$ is five times the area of the curved surface of a cone of radius $4\space cm$. Find the height of the cone.

Question 14 :
A parallelogram has sides $30 m, 70 m$ and one of its diagonals is $80 m$ long. Its area will be

Question 15 :
The number of solid spheres, each of diameter $6$cm that could be moulded to form a solid metal cylinder of height $45$cm and diameter $4$cm, is _______.

Question 16 :
A sheet is in the form of a rhombus whose diagonals are $10 m$ and $8 m$. The cost of painting both of its surface at the rate of $Rs. 70$ per&#160;$\displaystyle m^{2}$ is

Question 17 :
A plastic box $1.5m$ long, $1.25m$ wide and $65cm$ deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine:The area of the sheet required for making the box.

Question 18 :
A ceiling has a shape of rhombus whose diagonals lengths are $10$cm &amp; $20$ cm. How many such tiles are required to cover ceiling of area&#160;$\displaystyle 1000{ m }^{ 2 }$.

Question 19 :
Each side of a square is 5 cm. The perimeterof the equilateral triangle formed on the diagonalof the square would be-

Question 20 :
The area of a parallelogram formed by the lines $ax \pm by \pm c= 0$ is