- The side of the square exceeds the side of another square by 6cm and the sum of the areas of the two squares is 260cm
^{2}. The dimensions of the squares is6cm and 12cm8cm and 14 cm10cm and 16cm5cm and 11cmNoneOption B

Solution:

Let the side of the square=x cm

Side of another square = x+6 cm

x^{2}+ (x+6)^{2}=260

x^{2}+6x -112=0

x=-14, 8(negative value neglected)

x=8cm.

Another square 8+6=14cm.

- A lawn is in the shape of rectangle of length 30m and width 20m inside the lawn there is a footpath of uniform width 2m bordering the lawn. The area of the path is.
142m
^{2}154m^{2}165m^{2}184m^{2}NoneOption D

Solution:

Area of the outer rectangle=30*20

=600m^{2}.

Width of path is 2m.

Inner length=30-4=26m

Breadth=20-4=16m

Inner rectangle area=26*16

=416m^{2}.

Then Area of the path =600-416

=184m^{2}.

- The diameter of the wheel of a car is 140cm. Then, in order to keep the speed of 66km/hr. How many revolutions per minute must the wheel make?
250180220195NoneOption A

Solution:

Radius of the wheel =70cm=0.7m

Circumference=2*22/7*0.7

=4.4m

Distance to be covered in 1 min =(66*1000)/60

=1100m.

Then no of revolutions per minute=1100/4.4

=250.

- The length and breadth of a rectangular park are in the ratio 7:3. A path, 2.5m wide running all around the outside of the park has an area of 275m
^{2}. The dimensions of the park28m, 12m21m, 9m35m, 15m56m, 24mNoneOption C

Solution:

Area of the park =7x *3x=21x^{2}

Length including the path =7x+5

Breadth including the path =3x+5

Area=(7x+5) * (3x+5)

=21x^{2}+50x+25

Now, 21x^{2}+50x+25-21x^{2}=275

50x=250

x=5.

Then l=7*5=35m

B=3*5=15m.

- Two circle touch externally. The sum of their areas is 169Ï€ and the distance between their centres is 17cm. The radius of the circles are
10cm, 4cm12cm, 5cm15cm, 8cm8cm, 4cmNoneOption B

Solution:

Let the radius of the circles be x, 17-x

Sum of the area = Ï€ x^{2}+ Ï€(17-x)^{2}

Ï€ x^{2}+ Ï€(17-x)^{2}=169Ï€

2Ï€x^{2}-34Ï€x+120Ï€=0

x^{2}-17x+60=0

x=12 or 5.

Radius=12cm, 5cm.

- A metallic sheet is of rectangular shape with dimensions 45cm *32cm from each of its corners a square of 5cm is cut off. An open box is made of the remaining sheet. What is the volume of the box?
3360cm
^{3}2850cm^{3}2560cm^{3}3850cm^{3}NoneOption D

Solution:

L=45cm

B=32cm

Square of side 5cm is cut off from each corner

Then length= 45 â€“(5+5)=35cm

Breadth=32 â€“(5+5)=22cm

And height of the box=5cm.

Volume of the box=35*22*5

=3850cm^{3}.

- The radius and the height of a right circular cone are in the ratio 5:12. If its volume is 314m
^{3}, the slant height and the radius are13m21m18m24mNoneOption A

Solution:

r=5x and h=12x

Volume of the cone=314 =1/3Ï€r^{2}h

1/3*3.14 *5x^{2}*12x=314

314x^{3}=314

x=1.

Then r=5m h=12m

Slant height=âˆš(r^{2}+h^{2})

=âˆš(25+144)

=âˆš169=13m.

- A 8cm cube is cut into 2cm cubes. What is the ratio of surface area of small cubes to that of the large cube?
3:24:34:15:2NoneOption C

Solution:

No of small cubes= Volume of large cube/volume of a small cube

=8^{3}/2^{3}

=64.

Total surface area of large cube=6*8^{2}=384cm^{2}

Total surface area of 1 small cube=6*2^{2}=24cm^{2}

Total surface area of 64 small cube=64*24=1536cm^{2}

Ratio 1536:384

=4:1.

- The area of a rectangle is 72 m
^{2}and its length is 2 times is breadth. What is the perimeter of the rectangle?42m36m30mData InadequateNoneOption B

Solution:

Let the breadth be x

Then

x*2x=72

x = 6 m

then l=12m and b=6m

Perimeter=2(12+6)

=36m.

- The length of a rectangular floor is twice its breadth. If Rs.450 is required to paint the floor at the rate of Rs.1 per square metre, then what would be the length of floor?
28m34m26m30mNoneOption D

Solution:

To paint per square metre for Rs 1.

Then 450m^{2 is the area of the floor. Let the breadth be x. x*2x=450 2x2=450 x2=225 x=15. Length=2*15=30m. }