- The cost of fencing around a circular field is Rs 8580 at the rate of Rs 15 per foot . What is the area of the circular field ?
23450260262235121485NoneOption B

Solution:

Fencing = 8580/15=572= Circumference of a circle field

2πr = 572

2*22/7*r = 572

r=91

Area = 22/7 *91 * 91 = 26026 sq meter.

- Water flows into a tank which is 200m long and 150m wide, through a pipe of cross-section 0.3m * 0.2m at 20 km/hour. Then the time (in hours) for the water level in the tank to reach 8m is
180hrs135hrs200 hrs160hrsNoneOption C

Solution:

speed of water = 20 km/hour

= 20000 m/hour

Area of base = 0.3m × 0.2m

= 0.06 sq. meter

Volume of water flows in 1 hour = area of base× speed of water in 1 hour

= 0.06 × 20000

= 1200 cubic meter

Volume of tank up to 8 m height = 200 × 150 ×

= 240000 cubic meter

Time to reach the water 8 m high = 240000/1200

= 200 hrs.

- The outer circumference of a circular track is 220 m. The track is 14 m wide everywhere. Calculate the cost of levelling the track at the rate of 50 paisa/square meter ?
Rs965Rs1100Rs890Rs1232NoneOption D

Solution:

Let outer radius = R

Inner radius = r = R – 14

2 * 22/7 *r = 220

R = 220/(2*22) * 7 = 35m

r = 35 – 14 = 21 m.

Area of track = 22/7 (R^{2 }– r^{2 })

= 22/7{35^{2 }–21^{2 }} = 2464 m^{2 }

Cost of levelling the track = 2464×0.50 = Rs. 1232.

- A cone and sphere have the same radius of 12 cm. Find the height of the cone if the cone and sphere have the same volume.
32cm44cm36cm49cmNoneOption E

Solution:

Volume of the cone=1/3πr^{2}h

=1/3*π*12^{2}*h==>48 πh

Volume of the sphere=4/3 π r^{3}

=4/3* π*12^{3}==>2304 π

Both are equal then

2304 π=48 πh

h= 2304/48=48cm.

- Two cones have their heights in the ratio 4:3 and the radii of their bases in the ratio 3:4. Find the ratio of their volumes.
2:14:53:41:2NoneOption C

Solution:

V1/V2=r1^{2}h/ r2^{2}h

=9*4/(16*3)

=3/4.

- A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
1520120013201300NoneOption B

Solution:

2(15+12)*h=2(15*12)

54h =180*2

h=360/54=20/3

Volume= 15*12*20/3=1200cubic meter.

- The curved surface area of a cylindrical pillar is 264 m
^{2 }and its volume is 924 m^{3 }. Find its height.6m9m10m8mNoneOption A

Solution:

Volume/curved surface area=πr^{2 }h/2πrh==> r/2=924/264*2=7m.

Then Area 264=2*22/7*7*h

h= 6m.

- The cost of the paint is Rs.24.50 per kg. If 1kg of paint covers 12sq.ft, how much will it cost to paint outside of a cube having 10 feet each side.
Rs965Rs1225Rs1100Rs1350NoneOption B

Solution:

Surface area of a cube= 6 * (10 * 10) = 600 sq.ft

Quantity of paint required=(600/12)=50kg

Cost of painting= 24.5*50 = Rs.1225.

- Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 cm
^{2}. The circumference of each plate is:63cm44cm52cm36cmNoneOption B

Solution:

Side of square paper=√784=28cm

Radius of each circular plate=1/4*28=7cm.

Circuference of each circular plate=2*22/7*7=44cm.

- A metallic sheet is of rectangular shape with dimensions 32 m x 18 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 4 m, the volume of the box (in m
^{3}) is:840 m^{3}720 m^{3}960 m^{3}760 m^{3}NoneOption C

Solution:

l = (32 – 8)m = 24 m,

b = (18 -8)m = 10 m,

h = 4 m.

Then Volume of the box = (24 *10 * 4) m^{3}= 960 m^{3}.