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

**Class â€“ 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. (05)

**Section A**

1. What is the sum of five positive integer divisible by 6.

**OR**

In an Arithmetic Progression, if *d *=âˆ’ 4, *n *= 7 , *a*_{n} = 4, then find *a *.

2. The top of two poles of height 20 m and 14 m are connected by a If the wire makes an angle of 30c with the horizontal, then find the length of the wire.

3. ABC is right triangle, right-angled at B , with BC = 6 cm and AB = 8 cm. A circle with centre O and radius r cm has been inscribed in âˆ† ABC as shown in the figure. Find the value of r.

4. Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes?

5. A solid metallic cone of radius 2 cm and height 8 cm is melted into a sphere. Find the radius of sphere.

6. Find the mean of first 10 composite numbers.

**OR**

If the difference of mode and median of a data is 24, then what is the difference of median and mean?

**Section B**

7. Prove that the rectangle circumscribing a circle is a square.

8. From a solid right circular cylinder of height 14 cm and base radius 6 cm, a right circular cone of same height and same base removed. Find the volume of the remaining solid.

9. The following frequency distribution shows the number of runs scored by some batsman of India in one-day cricket matches :

Run scored | 2000-4000 | 4000-6000 | 6000-8000 | 8000-10000 | 10000-12000 |

Number of batsmen | 9 | 8 | 10 | 2 | 1 |

Find the mode for the above data.

10. A group of students conducted a survey of their locality to collect the data regarding number of plants and recorded it in the following table :

Number of plants | 0-3 | 3-6 | 6-9 | 9-12 | 12-15 |

Number of houses | 2 | 4 | 5 | 1 | 2 |

Find the mode for the above data.

**OR**

Find the mode of the following frequency distribution:

Class-Interval | f |

25-35 | 7 |

35-45 | 31 |

45-55 | 33 |

55-65 | 17 |

65-75 | 11 |

75-85 | 1 |

**Section C**

11. The sum of first 20 terms of an AP is 400 and sum of first 40 terms is 1600. Find the sum of its first 10 terms.

12. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm, and taking B as centre draw another circle of radius 3 cm. Construct tangents to each circle of radius centre of the other circle.

**OR**

Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as center, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.

13. Building Sheep Pens : Darsh and Darpan are fencing off a large rectangular area to build some temporary holding pens. To prep the males, females, and kids, they are separated into three smaller and equal-size pens partitioned within the large rectangle.

(i) If 384 ft of fencing is available and the maximum area is desired, what will be the dimensions of the larger, outer rectangle?

(ii) What will be the dimensions of the smaller holding pens?

14. Rainfall is one of the most commonly shared experiences on Earth. Rainfall is also necessary, since it provides water to plants and ultimately fills rivers. Because rainfall is both a needed resources and a threat, it is important to better understand this natural phenomenon. The most common rainfall measurement is the total rainfall depth during a given period, expressed in millimeters (mm). For instance, we might want to know how many millimeters of rain fell over the course of 1 h, 1 day, 1 month, or 1 year.

The rain water from 22m #20m roof drains into cylindrical vessel of diameter 2 m and height 3.5 m.

(i) If the rain water collected from the roof fills 4th/5 of cylindrical vessel then find the rainfall in cm.

(ii) If rainfall is the 1.5 cm find the hight of water collected in cylindrical vessel.