### CBSE Class 10 Mathematics Basic Term 2 Sample Paper

**Class – X Exam 2021-22**

**Mathematics Basic (241)**

**Time Allowed: 120 minutes (****Maximum Marks: 40)**

**General Instructions:**

- The question paper consists of 14 questions divided into 3 sections A, B,
- All questions are
- Section A comprises of 6 questions of 2 marks Internal choice has been provided in two questions.
- Section B comprises of 4 questions of 3 marks Internal choice has been provided in one question.
- Section C comprises of 4 questions of 4 marks An internal choice has been provided in one question. It contains two case study based questions. (01)

**Section A**

1. If 3/5, a, 4 are three consecutive terms of an A.P., then find the value of a.

2. A vertical pole is 100 metres high. Find the angle subtended by the pole at a point on the ground 100 3 meters from the base of the pole.

3. PQ is a tangent to a circle with centre O at point P. If TOPQ is an isosceles triangle, then find +OQP.

4. If the radius of the sphere is increased by 100%, then how much volume of the corresponding sphere is increased ?

5. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. What is the length of the wire?

6. If the mean of the observation x x,,, +++ 357 x x and x + 10 is 9, the find the mean of the last three observation

**OR**

Find the class-marks of the classes 10-25 and 35-66.

**Section B**

7. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

8. Water is being pumped out through a circular pipe whose internal diameter is 8 cm. If the rate of flow of water is 80 cm/s, then how many litres of water is being pumped out through this pipe in one hour?

9. Compute the mode for the following frequency distribution:

Size of items (in cm) | 0-4 | 4-8 | 8-12 | 12-16 | 16-20 | 20-24 | 24-28 |

Frequency | 5 | 7 | 9 | 17 | 12 | 10 | 6 |

10. The mean of the following frequency distribution is 18. The frequency *f *in the class interval 19-21 is missing. Determine *f *.

Class interval | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |

Frequency | 3 | 6 | 9 | 13 | f |
5 | 4 |

**OR**

Compute the mode for the following frequency distribution:

Size of items (in cm) | 0- 4 | 4- 8 | 8- 12 | 12-16 | 16-20 | 20-24 | 24-28 |

Frequency | 5 | 7 | 9 | 17 | 12 | 10 | 6 |

11. If *S _{n} *denotes the sum of first

*n*terms of an AP, prove that,

*S*

_{30}= 3^

*S*

_{20}−

*S*

_{10}h

12. Draw two tangents to a circle of radius 4 cm, which are inclined to each other at an angle of 60c.

**OR**

Draw two concentric circle of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle.

13. Model Rocketry : A model rocket is a small rocket designed to reach low altitudes and be recovered by a variety of means. Flying model rockets is a relatively safe and inexpensive way for person to learn the basics of forces and the response of a vehicle to external forces. Like an airplane, a model rocket is subjected to the forces of weight, thrust, and aerodynamics during its flight.

Shalvi is a member of first rocket club of India named STAR Club. She launches her latest rocket from a large field. At the moment its fuel is exhausted, the rocket has a velocity of 240 ft/sec and an altitude of 544 ft. After *t *sec, its height *h *(*t*) above the ground is given by the function *h *(*t*) =− 16*t*2 + 240*t *+ 544 .

- What is the maximum height attained by the rocket?
- How many seconds was the rocket airborne after its fuel was exhausted?

14. Well Embankment : Well embankment is a raised wall that is built around the These are often constructed using soils obtained from a digging well. It provide protection to person from felling into the well.

A well of diameter 6 m is dug 14 m deep 1/15 of the earth taken out is spread evenly all around the well to form

- Find the volume of the earth taken out.
- If the height of embankment is 2 m, what is the width of the embankment ?