Aptitude - Mensuration Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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The slope of the line Joining A (-4. 6) and B (5, 3) is

  

  

  

  

The radii of two cylinders are in the ratio 2 : 3 and heights 5 : 3. Calculate ratio of their volumes

  

  

  

  

What is the minimum length of a string with which one can surround a triangle of area 36√3 cm?

  

  

  

  

A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is

  

  

  

  

What is the slope of the line given by the equation 3w - 7 = 6 - 2y?

  

  

  

  

  

Spheres A and B have their radii 40 cm and 10 cm respectively. The ratio of the surface area of A to the surface area of B is

  

  

  

  

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

  

  

  

  

The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will It cover in 5 revolutions use (π=22/ 7)

  

  

  

  

  

How many spherical bullets can be made out of lead cylindrical 15 cm high and with base radius 3 cm, each bullet being 5 mm in diameter

  

  

  

  

Where defined, {y2 – 3/3} {8/2y + 3} =

  

  

  

  

  

What is the sum of the total surface areas of all the cubes formed when a cuboid of size  5.2 m x 13 m x 39 m is cut completely into the least possible number of cubes, all of which are identical?

  

  

  

  

A circular park has a path of uniform width around it. The difference between outer and inner circumference of the circular path is 132m. Its width is:

  

  

  

  

The points of intersection of the circle x2 +y2=34 and line y=5

  

  

  

  

The length of a ladder is exactly equal to the height of the wall it is resting against. Iflower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m awayfrom the wall, the upper end of the ladder coincides with the top of the wall. Then,the height of the wall is:

  

  

  

  

Milind takes as much time in running 15 metres as a car takes in covering 40 metres. What will be the distance covered by Milind during the time the car covers 2 km?

  

  

  

  

The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 800 per sq. metre

  

  

  

  

A rectangular tank measuring 5m x 4.5 m x 2.1 m is dug in the centre of the field measuring 13.5.m x 2.5. The earth dug out is spread evenly over the remaining portion of afield. How much is the level of the field raised ?

  

  

  

  

  

Within a square ground with one side 20 m , there is a square path that is 4 m in breadth. What is the area of the park without the path

  

  

  

  

A rectangular plot 15 m x10 m, has a path of grass outside it. If the area of grassy pathway is 54 m2, find the width of the path.

  

  

  

  

  

The ratio between the length and the perimeter of a rectangular plot is 1 : 3. What is the ratio between the length and breadth of the plot?

  

  

  

  

The circumference of a circle is 100 cm. The side of a square inscribed in the circle is:

  

  

  

  

A circular garden has a circumference of 440m. There is a 7m border inside the garden along its periphery. The area of the border is

  

  

  

  

Triangle ABC is right angled at A and has a perimeter of 136. A circle is drawn from A point X on AB such that it is tangent to BC and AC.The radius of the circle is 17 . If BX=m/n where m and n are relatively prime.Then m + n =?

  

  

  

  

  

The curved surface area of a cylinder pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height

  

  

  

  

If the side of a square is increased by 3 cm., the area increases by 33 cm. The side of the square is

  

  

  

  

How many plants will be there in a circular bed whose outer edge measure 30 cms, allowing 4 cm2 for each plant ?

  

  

  

  

  

The length of a rectangle is 18 cm and its breadth is 10 cm. When the length is increased to 25 cm, what will be the breadth of the rectangle if the area remains the same?

  

  

  

  

Three circles touch each other externally. If xy = 15,yz = 10, xz = 21 Find the radius of each circle

  

  

  

  

If the perimeter of a rectangle and a square, each is equal to 80 cm and the difference of their areas is 100sq.cm. The sides of the rectangle are

  

  

  

  

The height of the Qutub Minar is 230 metres. It is planned that a stairway from ground to the topof the Minar would be made by arranging cube shaped boulders in a step like fashion. A man firstplaces a boulder on the ground. He then steps on to it, and then throws one boulder down such thatit touches the side of the previous bolder, and then places one over the new one. He then climbsonto the last boulder thus placed and continues to do the same to create steps right to the top, witheach of his step being 1 metre. If each boulder measures 1 cubic metre, how many boulders arerequired in all ?

  

  

  

  

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