**Q1. The front wheels of a wagon are 2π feet in circumference and the back wheels are 3π feet in circumference. When the front wheels have made 10 more revolutions than the back wheels, how many feet has the wagon traveled?**

(a) 30 π

(b) 90 π

(c) 60 π

(d) 150 π

Solutions

1. Ans.(c)

Sol.

Suppose the back wheel has made x revolutions.

∴ Front wheel has made (10 + x) revolutions.

⟹3πr=2π(10+x)

⟹πr=2π×10⟹x=20

∴ The wagon has travelled 3πx=60π

**Q2. The length of a rectangle is 3/5 of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. what is the area of the rectangle if the breadth of the rectangle is 8 cm?**

(a) 112.4 cm^2

(b) 104.2 cm^2

(c) 100.8 cm^2

(d) Cannot be determined

2. Ans.(c)

Sol.

Let, the side of the square be a.

∴ Length fo the rectangle =3a/5

Radius of the circle = a

Circumference of the circle =2πa=132

⟹a=132/2π=21

Now, area of the rectangle = length × breadth

=(3/5)×21×8=100.8 cm2

**Q3. The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is second largest angle of the triangle?**

(a) 80°

(b) 60°

(c) 120°

(d) Cannot be determined

3. Ans.(b)

Sol.

(2x+4x+7x+5x)=18x=360°

⟹ x=20°

∴ Smallest angle of the quadrilateral =2x=2×20=40°

So the smallest angle of the triangle =40°

Remaining two angles of the triangle are

40×2=80° and 180-(80+40)

=180-120=60°

**Q4. Cuboidal water tank contains 216 liters of water. Its depth is 1/3 of its length and breadth is 1/2 of 1/3 of the difference between the length and the depth. The length of the tank is:**

(a) 72 dm

(b) 18 dm

(c) 6 dm

(d) 2 dm

**Q5. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27th of the volume of the given cone, at what height above the base is the section made?**

(a) 19 cm

(b) 20 cm

(c) 12 cm

(d) 15 cm

5. Ans.(b)

Let, H and R be the height and radius of bigger cone and h and r

be the height and radius of smaller cone.

be the height and radius of smaller cone.

**Q6. A field is in the form a rectangle of length 18 m and width 15 m. A pit, 7.5 m long, 6 m board and 0.8 m deep, is dug in a corner of the field and the earth taken out is evenly spread over the remaining area of the filed. The level of the field raised is:**

(a) 12 cm

(b) 14 cm

(c) 16 cm

(d) 18 cm

**Q7. A man bought a motor-cycle for Rs. 32500. He sold it for Rs. 35000, the gain per cent is:**

**Q8. If on a marked price, the difference of selling prices with a discount of 30% and two successive discounts of 20% and 10% is Rs. 72, then the marked price (in rupees) is:**

(a) 3,600

(b) 3,000

(c) 2,500

(d) 2,400

**Q9. Rohit invested some amount at the rate of 6 per cent pa and at the end of 3 years he got**

**Rs. 8730 simple interest. How much compound interest he will get on same amount and same rate of interest after 2 years.**

(a) Rs. 5820

(b) Rs. 5949.60

(c) Rs. 5900

(d) Rs. 5994.60

**Q10. Raghu invested a certain sum in Scheme X for 4 years. Scheme X offers simple interest at 12 per cent pa for the first two years and compound interest (compounded annually) at 20 per cent pa for the next two years. The total interest earned by him after 4 years is Rs. 11016. What was the sum invested by Raghu in Scheme X?**

(a) Rs. 17400

(b) Rs. 18400

(c) Rs. 16200

(d) Rs. 11400