### Aptitude - Mensuration

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

A.  (5, 6)

B.  (7, 5)

C.  (8,4)

D.  (9, 6)

E.  (7, 5)

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 =?

A.  20

B.  8

C.  22

D.  85

E.  88

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.  200

B.  250

C.  300

D.  330

E.  None of these

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

A.  124

B.  16.72

C.  12.78

D.  56/7

E.  5/4

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.  Rs.12000

B.  Rs.19500

C.  Rs.18000

D.  Rs.16500

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

A.   2r

B.  2/r

C.  2r2

D.  2/r2

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

A.  (0 , -2)

B.  (-1, 5)

C.  (2, 8)

D.  (-6, 4)

E.  (9, 4)

If the perimeter of a rectangle is 90, what is the area of the rectangle?

A.  324

B.  124

C.  965

D.  56

E.  324

The area of the triangle whose vertices are (a, a), (a + 1, a + 1), (a + 2, a) is :

A.  a3

B.  1

C.  2a

D.  21/2

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

A.  0.8

B.  8

C.  65

D.  28

E.  90

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

A.  30*sqrt(26)

B.  30*sqrt(20)

C.  10*sqrt(6)

D.  10*sqrt(2)

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.  3:2

B.  4:1

C.  4:3

D.  7:4

The capacity of a tank of dimensions (8 m x 6 m x 2.5 m) is

A.  120 liters

B.  1200 liters

C.  12000 liters

D.  120000 liters

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

A.  sqrt6 Units

B.  sqrt5 Units

C.  sqrt 13 Units

D.  sqrt10 Units

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

A.  25 cm, 15 cm

B.  28 cm, 12 cm

C.  30 cm, 10 cm

D.  35 cm, 15 cm

The dimensions of a room are 10 m × 7m ×5 m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1 m × 3m, one window is of size 2 m× 1.5 m and the other two windows are of size 1 m × 1.5 m. The cost of painting the walls at Rs. 3 per m2 is

A.  Rs. 474

B.  Rs. 578.50

C.   Rs. 684

D.  Rs. 894

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

A.  1:8

B.   1:4

C.  2:1

D.  4:1

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

A.  5.5

B.  6

C.  2

D.  4

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

A.  3 cm

B.  4 cm

C.  6 cm

D.  12 cm

An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5, the sides are:

A.  10 cm, 50 cm

B.  20 cm, 100 cm

C.   40 cm, 200 cm

D.  None of these

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?

A.  18 cm

B.  16 cm

C.  22 cm

D.  20 cm

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

A.  87

B.  - 2/3

C.  45.741

D.  36

E.  74

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

A.  120 cm2

B.   240 cm2

C.  390 cm2

D.  780 cm2

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

A.  (2, 4 ) ( -2, 4)

B.  (3, 6) (-3, 6)

C.  (3, 5) (3, -5)

D.  (2, 3) (-2, 3)

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

A.  2cm

B.   3 cm

C.  4 cm

D.  6 cm

If the perimeter of a square is 80, what is the area of the square?

A.  235

B.  987

C.  136

D.  148

E.  324

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:

A.  20 cm

B.   21 cm

C.   22 cm

D.  24 cm

What will be the area of a semi-circle whose perimeter is 36cm?

A.   154 cm2

B.  168 cm2

C.  308 cm2

E.  None of these

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

A.  sqrt6 Units

B.  sqrt5 Units

C.  sqrt13 Units

D.  sqrt10 Units

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

A.  456 cm2

B.  466 cm2

C.  476 cm2

D.  486 cm2