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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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 =?

  

  

  

  

  

ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x - y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC?

  

  

  

  

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 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

  

  

  

  

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

  

  

  

  

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?

  

  

  

  

  

The volume of the sphere Q is 3764% less than the volume of sphere P and the volume of sphere R is 1927 % less than that of sphere Q. By what % is the surface area of sphere R less than the surface area of sphere P?

  

  

  

  

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

  

  

  

  

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 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 :

  

  

  

  

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

  

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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?

  

  

  

  

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

  

  

  

  

The radii of two cones are in the ratio 2:1, their volumes are equal. Find the ratio of their heights

  

  

  

  

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

  

  

  

  

  

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. 

  

  

  

  

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

  

  

  

  

What is the distance between the c intercept and the r intercept of the line given by the equation? 2r = 6 - f?  

  

  

  

  

  

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

  

  

  

  

  

The ratio between rhe perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle ?

  

  

  

  

  

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

  

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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