- 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

l^{2}=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:
49m
^{2}53m^{2}38m^{2}40m^{2}NoneOption A

Solution:

Area=[2(lb+bh+hl)-lb] =2(bh+hl)+lb

=[2(4*1.25 + 6*1.25) + (6*4)] =25+24

=49m^{2}.

- 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:

√(l^{2}+ b^{2})=√125

lb=50

(l+b)^{2}=l^{2}=+b^{2}=+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*r^{3}

4/3*22/7*r^{3}=21*77*24

r^{3}=(21*77*24*3*7)/(4*22)

=3^{3}* 7^{3}

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 =πr + 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*side^{2}

6*side^{2}=2400

side^{2}=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.