**Q1. If the length and the perimeter of a rectangle are in the ratio 5:16. Then its length and breadth will be in the ratio **

(a) 5:11

(b) 5:8

(c) 5:4

(d) 5:3

**S1. Ans.(d)**

**Sol. **Let length = 5x

⇒ breadth =(16x – 2 × 5x)/2=3x

∴ Required ratio =5x/3x

= 5: 3

**Q2. ABC is a right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’B’B of the area of the triangle ABC is **

(a) 1: 2

(b) 2: 3

(c) 3: 4

(d) None of the above

**Q3. If the arcs of unit length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is**

(a) 3: 4

(b) 4: 5

(c) 5: 4

(d) 3: 5

**S3. Ans.(c)**

**Sol.** By using result,

R1 θ1=R2 θ2

R1/R2 =θ2/θ1 =(75°)/(60°)=5/4=5:4

**Q4. If the altitude of a triangle is increased by 10% while its area remains same, its corresponding base will have to be decreased by **

(a) 10%

(b) 9%

(c) 100/11%

(d) 100/9%

**Q5. A cuboidal water tank has 216 liters of water. Its depth is 1/3 of its length and breadth is 1/2 of 1/3 of the difference of length and height. The length of the tank is **

(a) 72 dm

(b) 18 dm

(c) 6 dm

(d) 2 dm

**S5. Ans.(b)**

**Sol**. Let l=9x, h=3x, b=x

l×b×h=216×1000

(1 litre = 1000 cm3)

9x×3x×x=216000

27x^3=216000

x^3=8000

x=20

l=180 cm = 18 dm

**Q6. A wooden box measures 20 cm by 12 cm by 10 cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cube cm) is**

(a) 960

(b) 519

(c) 2400

(d) 1120

**S6. Ans.(a) **

**Sol. **

The external dimensions of the box are

l = 20 cm, b = 12 cm, h = 10 cm

External volume of the box = 20 × 12 × 10 = 2400 cm3

Thickness of the wood = 1 cm

Internal length = 20 – 2 = 18 cm

Internal breadth = 12 – 2 = 10 cm

Internal height = 10 – 2 = 8 cm

Internal volume of the box = 18 × 10 × 8 = 1440 cm3

Volume of the wood = (2400 – 1440) cm3

= 960 cm3

**Q7. The area of three adjacent faces of a cuboid are x, y, z square units respectively. If the volume of the cuboid by v cube units, then the correct relation between v, x, y, z is **

**Q8. The area of three consecutive faces of a cuboid are 12 cm2, then the volume (in cm3) of the cuboid is **

(a) 3600

(b) 100

(c) 80

(d) 24 √3

**S8. Ans.(d)**

**Sol. **Let the three sides of the cuboid be l, b and h

⇒ lb = bh = hl = 12

⇒ l^(2 ) b^2 h^2=12×12×12=1728

⇒lbh=√1728=12√12

=24√3 cm^3

**Q9. Three solid iron cubes of edges 4 cm, 5cm and 6 cm are melted together to make a new cube, 62cm3 of the melted material is lost due to improper handing. The area (in cm2) of the whole surface of the newly formed cube is **

(a) 294

(b) 343

(c) 125

(d) 216

**Q10. A low land, 48 m long and 31.5 m broad is raised to 6.5 dm. For this, earth is removed from a cuboidal hole, 27 m long and 18.2 m broad, dug by the side of the land. The depth of the hole will be.**

(a) 3 m

(b) 2 m

(c) 2.2 m

(d) 2.5 m

**S10. Ans.(b) **

**Sol.** According to the question

Let depth of the hole = d

∴ 48 m×31.5×6.5/10 m

=27×18.2×d ( 1 dm =1/10 m )

d = 2m