- The ratio between the perimeter and the breadth of a rectangle is 26 : 5. If the area of the rectangle is 1000 sq. cm, what is the length of the rectangle?
45cm35cm40cm30cmNoneOption C
Solution:
2(l+b):b=26:5
10l+10b=26b
10l=16b
b=5/8l
Area lb=1000
l*5/8l=1000
l2=1600
l=40cm.
- A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
49m253m238m240m2NoneOption A
Solution:
Area=[2(lb+bh+hl)-lb] =2(bh+hl)+lb
=[2(4*1.25 + 6*1.25) + (6*4)] =25+24
=49m2.
- The radius of the base of a cylindrical Can is 140cm and its height is 240cm. It is full of Petrol. How many tins, each of size 25 cm × 22 cm × 30 cm can be filled with Petrol from the Can?
896784852926NoneOption A
Solution:
Volume of Can=(22/7)*140*140*240
=22*20*140*240
Volume of a tin=25*22*30
Number of tins=(22*20*140*240)/(25*22*30)
=4*8*28=896.
- The length of a room is 6.5 m and width is 2.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 400 per sq.metre.
Rs7350Rs6100Rs7150Rs6450NoneOption C
Solution:
Area = 6.5 * 2.75
Cost for 1 sq. metre. = Rs. 400
Total cost = 6.5 * 2.75 * 400
=Rs7150.
- The ratio of the radius and height of a cone is 7: 18. Its volume is 924 cm. Its radius and height is
14cm, 36cm21cm, 54cm7cm, 18cm28cm, 72cmNoneOption C
Solution:
Radius:Height=7x:18x
Volume of cone 1/3*22/7*7x*7x*18x=92
22*6*7x=924
x=1.
Then r=7, h=18.
- The diagonal of a rectangle is √125 cm and its area is 50 sq. cm. The perimeter of the rectangle must be:
45cm30cm42cm36cmNoneOption B
Solution:
√(l2 + b2)=√125
lb=50
(l+b)2=l2=+b2=+2lb
=125+(2*50)
=225.
L+b=15
Perimeter=2*15=30cm.
- A rectangular block of metal has dimensions 21 cm*77 cm*24 cm. The block has been melted into a sphere. The radius of the sphere is
28cm21cm32cm18cmNoneOption B
Solution:
Volume of the sphere=4/3*22/7*r3
4/3*22/7*r3=21*77*24
r3=(21*77*24*3*7)/(4*22)
=33 * 73
r=3*7=21cm.
- The perimeter of a square is equal to twice the perimeter of a rectangle of length of 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square?
34.6cm36cm38cm38.5cmNoneOption D
Solution:
Perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm
Perimeter of square is twice the perimeter of rectangle = 2*30= 60cm
Then, side of the square is = 1/4 x 60 = 15cm.
Circumference of the semicircle =Ï€r + 2r
=22/7*15/2 +2*15/2
=23.5+15
=38.5cm.
- Surface area of a cube is 2400 cm 2. Find out the length of its diagonal.
16√3cm20√3cm24√3cm26√3cmNoneOption B
Solution:
Surface area of cube 6*side2
6*side2=2400
side2=2400/6=400
side=20cm.
Diagonal of cube=√3*side=20√3cm.
- The radius of a circular field is equal to the side of a square field. If the difference between the perimeter of the circular field and that of the square field is 48m, what is the side of the square field?
26m31m24m21mNoneOption D
Solution:
Radius of circular field=side of square field
2*22/7a – 4a=48
(44-28)a=(48*7)
16a=48*7
a=21m.
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