### 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. (10)

**SECTION A**

1. For what value(s) of *a *quadratic equation 30*ax*^{2} − 6*x *+ 1 = 0 has no real roots?

2. How many multiples of 4 lie between 11 and 266?

3. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact?

4. Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a solid Find the radius of the resulting sphere.

5. Change the following distribution to ‘more than type’ of distribution :

Daily income (in Rs.) | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |

Number of students | 12 | 14 | 8 | 6 | 10 |

6. Given below is a frequency distribution table showing daily income of 100 workers of a factory :

Daily income of workers (in Rs.) | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 |

Number of workers | 12 | 18 | 35 | 20 | 15 |

Convert this table to a cumulative frequency distribution table of ‘more than type’.

**OR**

Find the mean the following distribution :

Class | 3-5 | 5-7 | 7-9 | 9-11 | 11-13 |

Frequency | 5 | 10 | 10 | 7 | 8 |

**Section B**

7. If the ratio of the 11* ^{th}* term of an AP to its 18

*term is 2 : 3, find the ratio of the sum of the first five term of the sum of its first 10 terms.*

^{th}8. A 7 m long flagstaff is fixed on the top of a tower standing on the horizontal plane. From point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60º and 45º respectively. Find the height of the tower correct to one place of decimal.

9. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm.

10. A well of diameter 4 m dug 21 m The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.

**OR**

A solid sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged into water, by how much will the level of water rise in the cylindrical vessel ?

**OR**

Find the mode of the following frequency distribution:

Class Interval | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 |

Frequency | 25 | 34 | 50 | 42 | 38 | 14 |

**Section C**

11. In the given figure, *PA *and *PB *are tangents to the circle from an external point *P *. *CD *is another tangent touching the circle at *Q *. If *PA *= 12 cm, *QC *= *QD *= 3 cm, then find *PC *+ *PD*.

12. If the mean of the following frequency distribution is 91, and sum of frequency is 150, find the missing frequency *x *and *y:*

Class | 0- 30 | 30- 60 | 60- 90 | 90-120 | 120-150 | 150-180 |

Frequency | 12 | 21 | x |
52 | y |
11 |

13. Raju and his classmates planned a picnic in zoo. The total budget for picnic was Rs 2000 but 5 students failed to attend the picnic and thus the contribution for each student was increased by Rs 20.

The expanse of different item was as follows.

S. No. | Article | Cost per student |

1 | Entry ticket | Rs 5 |

2 | Coffee | Rs 10 |

3 | Food | Rs 25 |

4 | Travelling cost | Rs 50 |

5 | Ice-cream | Rs 15 |

- If
*x*is the number of students planned for picnic, which is the correct quadratic equation that describe the situation. - What is the number of students planned for picnic ?

14. CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, The tower includes a rotating restaurant high above the ground.

From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c .

- How tall is the CN Tower?
- How far below the pinnacle of the tower is the restaurant located?