### 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. (04)

**Section A**

1. What is the common difference of an AP in which *a*_{21} − *a*_{7} = 84?

**OR**

Which term of the AP 27, 24, 21,…..is zero?

2. A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60c. Find the height of the tower.

3. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

4. The circumference of the edge of a hemisphere bowl is 132 cm. When π is taken as 22/7 ind the capacity of the

bowl in cm^{3}.

5. A solid sphere of radius *r *melted and recast into the shape of a solid cone of height *r *. Find the radius of the base of a cone.

6. For the following distribution what is the modal class:

Marks | Number of students |

Below 10 | 3 |

Below 20 | 12 |

Below 30 | 27 |

Below 40 | 57 |

Below 50 | 75 |

Below 60 | 80 |

**OR**

In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. What is the lower limit of the class?

**Section B**

** 7. **An isosceles triangle *ABC *, with *AB *= *AC *, circumscribes a circle, touching *BC *at *P *, *AC *at *Q *and *AB *at *R *. Prove that the contact point *P *bisects *BC *.

8. The volume of a right circular cylinder with its height equal to the radius is 25,1/7 cm^{3}. Find the height of the cylinder.

9. Heights of students of class X are given in the following distribution :

Heights (in cm) | 150-155 | 155-160 | 160-165 | 165-170 | 170-175 |

Number of students | 15 | 8 | 20 | 12 | 5 |

Find the modal height.

10. A school conducted a test (of 100 marks) in English for students of Class X . The marks obtained by students are

shown in the following table :

Marks obtained | 0- 10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

Number of students | 1 | 2 | 4 | 15 | 15 | 25 | 15 | 10 | 2 | 1 |

Find the modal marks.

**OR**

The mode of a distribution is 55 and the modal class is 45-60 and the frequency preceding the modal class is 5 and the frequency after the modal class is 10. Find the frequency of the modal class.

**Section C**

11. How many terms of the Arithmetic Progression 45, 39, 33, … must be taken so that their sum is 180? Explain the double answer.

12. Draw a circle of radius 3 cm. From a point P, 7 cm away from centre draw two tangents to the circle. Measure the length of each tangent.

**OR**

Draw a circle of radius of 3 cm. Take two points P and Q one of its diameter extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points.

13. Fencing a Backyard : Tina and Shriya have just purchased a purebred German Shepherd, and need to fence in their backyard so the dog can run.

(i) What is the maximum rectangular area they can enclose with 200 ft of fencing, if they use fencing material along all four sides? What are the dimensions of the rectangle?

(ii) What is the maximum area if they use the house as one of the sides? What are the dimensions of this rectangle?

14. Silo : A silo is a structure for storing bulk materials. Silos are used in agriculture to store grain or fermented feed known as silage. Silos are commonly used for bulk storage of grain, coal, cement, carbon black, woodchips, food products and sawdust.

A silo is in the shape of cylinder surmounted by a conical top. The height and diameter of cylindrical part are 40 feet and 42 feet respectively and the slant height of conical part is 29 feet.

(i) How much metal sheet is required to make this silo ?

(ii) What is the storage capacity of silo ?