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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A square of 36 cm x 36 cm is completely divided into a grid of cells of size 3 cm x 2 cm each, where 3cm is the vertical dimension of each cell and 2 cm is the horizontal dimension. What is the total number of squares that can be located in the grid?

  

  

  

  

A rectangle has width a and length b. If the width is decreased by 20% and the length is increases by 10%, then what is the area of the new rectangle in percentage compared to ’ab’ ?

  

  

  

  

The cost of carpeting a room 18 m long with a carpet 75 cm wide at Rs. 4.50 per meter is Rs. 810. The breadth of the room is :

  

  

  

  

The coordinates of a point which divide the join of A (5, 5) and (8, 5) in the ratio 2 : 1 are

  

  

  

  

  

A well 20m in diameter is dug 15m deep and earth is spread all around a width of 5m to form an embankment. Find the height of the embankment.

  

  

  

  

The radius of the wheel of a bus is 70 cms and the bus is 66 km/h, then the r.p.m. (revolutions per minute)of the wheel is

  

  

  

  

  

A flagstraff 17.5 m high casts a shadow of length 40.25 m. The height of the building which casts a shadow of length 28.75 m under similar conditions will be?

  

  

  

  

Water flows at the rate of 10 meters per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

  

  

  

  

The perimeter of a right-angled triangle is 60 cm. Its hypotenuse is 26 cm. The area of the triangle is

  

  

  

  

At what coordinates does the graph of 4c+ 6 = d - 1 intersects the c axis?

  

  

  

  

  

The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?

  

  

  

  

There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is

  

  

  

  

What is the slope of the line given by the equation 4g - 5 = 7 - 2e?

  

  

  

  

  

Find the co-ordinates of the foot of the perpendicular from point (5,7) on the line whose equation is: x + 7y - 10 = 0.

  

  

  

  

A 70 cm long wire is to be cut into two pieces such that one piece will be 2/5 as long as the other. How many centimeters will the shorter piece be ?

  

  

  

  

How many litres of pure acid are there in 8 litres of a 20% solution?

  

  

  

  

What will be the area of a semi-circle of 14 metres diameter?

  

  

  

  

  

A flagstaff 17.5 m high casts a shadow of length 40.25m. The height of the building which casts a shadow of length 28.75 under similar conditions will be:

  

  

  

  

If an arc of 600 on circle I has the same length as an arc of 450 on circle II, what is the ratio of thearea of circle I to that of circle II ?

  

  

  

  

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

  

  

  

  

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

  

  

  

  

if the volume of a cube is 729 cm3, then the surface area of the cube will be

  

  

  

  

The sum of the radius of the base and height of a solid cylinder is 40m. If the total surface area of the cylinder is 1760 m2 its volume is:

  

  

  

  

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

  

  

  

  

What is the least number of square tiles required to pave the floor of a room 15 cm 17 cm long and 9 m 6 cm broad?

  

  

  

  

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

  

  

  

  

  

In two triangles, the ratio of the areas is 4 : 3 and ratio of their heights is 3 : 4. Find the ratio of their bases

  

  

  

  

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 ?

  

  

  

  

  

A tank of capacity 165 liters, has N taps, numbered from 1 to N fitted to it. At the start of the nth minute, where 1≤ n ≤ N, the tap numbered n, which fills the tank at the rate of n liters per mite, is opened. If it takes exactly N minutes to fill the tank in his manner , find N.

  

  

  

  

  

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

  

  

  

  

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