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 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 area of a rhombus is 150 cm2. The length of one of its diagonals is 10cm. The length of the other diagonal is:

  

  

  

  

In a cyclic quadrilateral ABCD, if AB = 2, BC = 3, CD = 4 and DA = 5, what is the ratio of the lengths of the diagonals?

  

  

  

  

What length of solid cylinder 2 cm in diameter mush be taken to cast into a hollow cylinder of external diameter 12 cm, 0.25 cm thick and 15 cm long?

  

  

  

  

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?

  

  

  

  

In a mile race Akshay can be given a start of 128 metres by Bhairav. If Bhairav can given Chinmay a start of 4 metres in a 100 metres dash, then who out of Akshay and Chinmay will win a race of one and half mile, and what will be the final lead given by the winner to the loser? (One mile is 1600 metres).

  

  

  

  

What is the largest number of pipes of the shape of right circular cylinders with length10 cm and radius 1 cm that can be fitted into a box, all of whose sides are 20 cm in length?

  

  

  

  

Find the slope of the line given by the equation y + 2 = 6/8 (c – 9)?

  

  

  

  

  

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 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?

  

  

  

  

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

  

  

  

  

One side of a parallelogram is 18 cm and its distance from the opposite side is 8 cm. The area of the parallelogram is:

  

  

  

  

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

  

  

  

  

  

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?

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The curved surface area of a right circular cylinder of base radius r is obtained by multiplying its volume by

  

  

  

  

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

  

  

  

  

The number of bricks, each measuring 25 cm x 12.5 cm x 7.5 cm, required to construct a wall 6m long , 5m high and 0.5 m thick, while the mortar occupies 5% of the volume of the wall, is

  

  

  

  

If the area of a circle decreases by 36%, then the radius of a circle decreases by

  

  

  

  

  

Two diagonals of a parallelogram are 72 cm and 30 cm respectively. What is its perimeter?

  

  

  

  

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm. The radius of the square is

  

  

  

  

In the adjoining figure, AC + AB = 5 AD and AC - AD = 8. The area of the rectangle ABCD is:

  

  

  

  

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

  

  

  

  

  

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?

  

  

  

  

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?

  

  

  

  

Angle 'N. of the quadrilateral ABCD is 260 less than angle B. Angle B is twice angle C and angle C is 100 more than the angle D. What would be the measure of angle A?

  

  

  

  

  

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 ?

  

  

  

  

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