### CBSE Class 10 Mathematics Term 2 Sample Paper

**Class – X Exam 2021-22**

**Mathematics Standard (041)**

**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. (09)

**SECTION A**

1. What are the real roots of the equation *x*^{2/3} + *x*^{1/3} − 2 = 0?

2. In an AP of 50 terms, the sum of the first 10 terms is 210 and the sum of its last 15 terms is Find the AP.

3. In the given figure, if *AB *= *AC *, prove that *BE *= *CE*.

4. A metallic solid sphere of radius 2 cm is melted and recast into the shape of a solid cylinder of radius 6 cm. Find the height of the cylinder.

5. Convert the following cumulative distribution to a frequency distribution :

Height (in cm) | less than 140 | less than 145 | less than 150 | less than 155 | less than 160 | less than 165 |

Number of students | 4 | 11 | 29 | 40 | 46 | 51 |

6. Prepare a cumulative frequency distribution of ‘more than type’ for the following data :

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Number of students | 3 | 8 | 15 | 7 | 5 |

**OR**

Find the mean of the following data :

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |

Frequency | 20 | 35 | 52 | 44 | 38 | 31 |

**Section B**

7. If *m ^{th} *term of an AP is 1/n and

*n*term is 1/m find the sum of first

^{th}*mn*terms.

8. A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60c to 30c. Find the speed of the boat in metres per minute.

9. Draw a circle of radius 4 cm. Construct a pair of tangents of it, the angle between which is 60c. Also justify the Measure the distance between the centre of the circle and the point of intersection of tangents.

10. A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel.

**OR**

A metallic solid sphere of radius 10.5 cm melted and recasted into smaller solid cones each of radius 3.5 cm and height 3 cm. How may cones will be made ?

**Section C**

11. In the given figure, *AD *is a diameter of a circle with centre *O *and *AB *is a tangent at *A*. *C *is a point on the circle such that *DC *produced intersects the tangent at *B *and +*ABC *= 50c. Find +*AOC *.

12. Find the value of *x *and *y *, if the median for the following data is 31.

Classes | 0- 10 | 10- 20 | 20- 30 | 30- 40 | 40- 50 | 50- 60 | Total |

Frequency | 5 | x |
6 | y |
6 | 5 | 40 |

**OR**

The arithmetic mean of the following frequency distribution is 53. Find the value of *k*.

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |

Frequency | 12 | 15 | 32 | k |
13 |

13. Auditorium, the part of a public building where an audience sits, as distinct from the stage, the area on which the performance or other object of the audience’s attention is presented. In a large theatre an auditorium includes a number of floor levels frequently designed as stalls, private boxes, dress circle, balcony or upper circle, and A sloping floor allows the seats to be arranged to give a clear view of the stage. The walls and ceiling usually contain concealed light and sound equipment and air extracts or inlets and may be highly decorated.

In an auditorium, seats are arranged in rows and columns. The number of rows are equal to the number of seats in each row. When the number of rows are doubled and the number of seats in each row is reduced by 10, the total number of seats increases by 300.

- If
*x*is taken as number of row in original arrangement which of the following quadratic equation describes the situation ? - How many number of rows are there in the original arrangement?

14. On a warm and lazy Saturday, Rishi is watching a county maintenance crew mow the park across the street. He notices the mower takes 16 sec to pass through 60c of rotation from one end of the park to the other.

If the corner of the park is 40 meter directly across the street from his house.

- How wide is the park?
- How fast (in kmph) does the mower travel as it cuts the grass?