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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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 ?

  

  

  

  

Five-third of the smallest side of a right angled triangle is equal to its largest side. Also the length of the second largest side of triangle is 8 cm. What is the sum of the smallest and the largest sides of that triangle together?

  

  

  

  

  

A powder tin has a square base with side 16 cm and height 28 cm. Another tin has a circular base with diameter 16 cm and height 28 cm. Find the difference in their capacities. 

  

  

  

  

If the area of an equilateral triangle is 24√3 sq. cm, then its perimeter is

  

  

  

  

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

  

  

  

  

  

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 currencies in countries X and Y are denoted by Xs. and Ys. respectively. The exchange rate in 1990 was 1 Xs. = 0.6 Ys. The price level in 2006 in X and Y are 150 and 400 respectively with 1990 as a base of 100. The exchange rate in 2006, based solely on this purchasing power parity consideration, is 1 Xs.=

  

  

  

  

If a wire is bent into the shape of a square, then the area of the square is 81sq.cm. When the wire is bent into a semi-circular shape, then the area of the semi-circle will be:

  

  

  

  

The distance between the points (-9, 5) and (-8, -20) is

  

  

  

  

  

The angle of elevation of a ladder leaning against a wall is 600 and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

  

  

  

  

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 ?

  

  

  

  

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 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 closed wooden box of thickness 0.5 cm and length 21 cm, width 11 cm, and height 6 cm, is panted on the inside. The cost of painting is Rs 70. What is the rate of painting in rupees per sq. cm?

  

  

  

  

XYZ is an equilateral triangle with vertices X (6, -2), Y (2, - 1) and Z (4, -2). If ZA is one of its medians find the length of the median

  

  

  

  

What is the slope of the line given by the equation 2h – 8 = 7 – 2a?

  

  

  

  

  

The cost of cultivating a square field at the rate of Rs. 135 per hectare is Rs. 1215. The cost of putting a fence around it at the rate of 75 paise per metre would be

  

  

  

  

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 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

  

  

  

  

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:

  

  

  

  

The cross-section of a canal is trapezium in shape. The canal is 12m wide at the top and 8 m wide at the bottom. If the area of the cross-section is 840sq.m, the depth of the canal is:

  

  

  

  

Cost of painting the 4 walls of a room 40ft.*15ft. At Rs.5 per square feet is Rs.7500. Find the height of the room?

  

  

  

  

The number of revolutions made by a wheel of diameter 56 cm in covering a distance of 1.1 km is: (use π= 22/7)

  

  

  

  

P ( - 4, b ) and Q ( 2, b + 2 ) are 2 points and the co-ordinates of the middle point of PQ are ( - 2, 2) . The value of b is

  

  

  

  

The area of a triangle is 21 sq. units. If two of its vertices lie on points (5, 3) and (–4, –3), then find the locus of the third vertex.

  

  

  

  

The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2. The height of the mountain is

  

  

  

  

A circular cylinder can hold 61.6 c.c of water. If the height of the cylinder is 40 cm and the outer diameter is 16 mm, then the thickness of the material of the cylinder is

  

  

  

  

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

  

  

  

  

Find the area of the cyclic quadrilateral whose sides are 15,12,10 and 13 cms.

  

  

  

  

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

  

  

  

  

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