Q1. Find the number of lead balls of diameter 1 cm each, that can be made from a sphere of diameter 16 cm

(a) 4096

(b) 512

(c) 1028

(d) 2048

Q2. The area of the base of rectangular tank is 6500 cm2 and the volume of water contained in it is 2.6 cubic metres. The depth of the water in tank is:

(a) 4 m

(b) 6 m

(c) 8 m

(d) 10 m

Q3. A right cylindrical vessel is full with water. How many right cones having the same diameter and height as that of the right cylinder will be needed to store that water? (Take 𝜋 = 22/7)

(a) 4

(b) 2

(c) 3

(d) 5

Q4. The heights of a cone, cylinder and hemisphere are equal. If their radii are in the ratio 2 : 3 : 1, then the ratio of their volumes is

(a) 2 : 9 : 2

(b) 4 : 9 : 1

(c) 4 : 27 : 2

(d) 2 : 3 : 1

Q5. A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. then the height of the cone (in cm) is

(a) 3.6

(b) 4.8

(c) 6.4

(d) 7.2

Directions (6-10): The pie-chart given below, shows the expenditure on various items and savings of a family during the year 2009. Study the pie-chart and answer the questions based on it.

Percentage of money spent on various items and savings by a family during 2009

Q6. If the total income of the family for the year 2009 was Rs. 1,50,000 then the difference between the expenditures on housing and transport was:

(a) Rs. 15,000

(b) Rs. 10,000

(c) Rs. 12,000

(d) Rs. 7,500

**Ans.(a)**

**Sol. Expenditure on housing = 15%**

**Expenditure on transport = 5%**

**Difference = 150000 × (15% – 5%)**

**=150000×10/100= Rs. 15000**

Q7. Maximum expenditure of the family other than on food, was on:

(a) Housing

(b) Clothing

(c) Others

(d) Education of children

**Ans.(c)**

**Sol. Maximum expenditure of the family other than on food was on others (20%).**

Q8. The savings of the family for the year were equal to the expenditure on:

(a) Food

(b) Housing

(c) Education of children

(d) Clothing

**Ans.(b)**

**Sol. The savings of the family for the year were equal to the expenditure on housing.**

Q9. The percentage of the income which was spent on clothing, education of children and transport together is:

(a) 17

(b) 20

(c) 22

(d) 27

**Ans.(d)**

**Sol. Total expenditure = 10% + 12% + 5% = 27%**

Q10. If the total income of the family was Rs. 1,50,000 then the money spent on food was:

(a) Rs. 20,000

(b) Rs. 23,000

(c) Rs. 30,000

(d) Rs. 34,500

**Ans.(d)**

**Sol. Expenditure on food =150000×23/100 = Rs. 34500**

Q11. If sec θ + tan θ =2+√5, then the value of sin θ + cos θ is:

(a) 3/√5

(b) √5

(c) 7/√5

(d) 1/√5

(a) 2

(b) 0

(c) 4

(d) 1

Q13. A room is 5 metres long and 3 metres broad; the doors and windows occupy 10 sq. metres, and the cost of colouring the remaining part of the surface of the walls with paper 25 cm wide, at Rs. 5 per piece of 15 m is Rs. 40. Find the height of the room.

(a) 4 metres

(b) 3.5 metres

(c) 3 metres

(d) 2.5 metres

**Ans.(d)**

**Sol. Length of paper =40/5×15=120 m**

**Area of paper =120×25/100 = 30 sq. m.**

**Area of walls = 30 + 10 = 40 sq. m**

**Now area of walls = 2(5 + 3) × height**

**= (16 × height)sq. m.**

**Height =40/16 = 2.5 metres**

Q14. The length of a room floor exceeds its breadth by 20 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5 m. The area of the floor (in square metres) is:

(a) 280

(b) 325

(c) 300

(d) 420

**Ans.(c)**

**Sol. Let the breadth of floor be x metre**

**∴ Length = {x + 20} metre**

**∴ Area of the floor = (x + 20) x sq. metre**

**In case II,**

**(x + 10) {x + 5} = x {x + 20}**

**⇒ 20x = 15x + 50**

**⇒5x = 50**

**⇒ x = 10 metre**

**⇒ Length of x + 20 = 10 + 20 = 30 metre**

**Area of the floor=30**

**×**

**10=300 square**

metres

metres

Q15. The radii of two circle are 5 cm and 3 cm, the distance between their centres is 24 cm. Then the length of the transverse common tangent is

(a) 16 cm

(b) 15√2 cm

(c) 16 √2 cm

(d) 15 cm