### 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. (07)

**SECTION A**

1. If α and β are the roots of *ax*^{2} − *bx *+ *c *= 0 (*a *C 0), then calculate α + β.

2. Find the AP whose third term is 5 and seventh term is 9.

3. In Figure, common tangents *AB *and *CD *to the two circle with centres *O*_{1} and *O*_{2} intersect at *E*. Prove that *AB *= *CD*.

4. A cone of height 24 cm and radius of base 6 cm is made up of If we reshape it into a sphere, find the radius of sphere.

5. Find the mean of the following frequency distribution:

Class | 0-6 | 6-12 | 12-18 | 18-24 | 24-30 |

Frequency | 7 | 5 | 10 | 12 | 6 |

6. The mean of the following frequency distribution is Find the value of *p*.

Class interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency | 4 | 6 | 10 | 6 | p |

**OR**

The mode of the following frequency distribution is 36. Find the missing frequency *f *.

Class | 0- 10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

Frequency | 8 | 10 | f |
16 | 12 | 6 | 7 |

**Section B**

7. The sum of first 7 terms of an AP is 63 and sum of its next 7 terms is Find 28* ^{th}* term of AP.

8. A man on the top of a vertical tower observes a car moving at a uniform speed towards If it takes 12 min. for the angle of depression to change from 30c to 45c, how soon after this, the car will reach the tower ?

9. Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.

10. The rain water from 22m #20 m roof drains into cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills 4th/5 of cylindrical vessel then find the rainfall in cm.

**OR**

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. Use π = 22/7.

**Section C**

** 11. **In given figure, *PA *and *PB *are tangents from a point *P *to the circle with centre *O *. At the point *M *, other tangent to the circle is drawn cutting *PA *and *PB *at *K *and *N *. Prove that the perimeter of T*PNK *= 2*PB *.

12. Monthly expenditures on milk in 100 families of a housing society are given in the following frequency distribution:

Monthly expenditure (in Rs.) | 0- 175 | 175-350 | 350-525 | 525-700 | 700-875 | 875-1050 | 1050-1125 |

Number of families | 10 | 14 | 15 | 21 | 28 | 7 | 5 |

Find the mode and median for the distribution.

**OR**

The mode of the following data is 67. Find the missing frequency *x *.

Class | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |

Frequency | 5 | x |
15 | 12 | 7 |

13. Braking Distance : The distance that a car travels between the time the driver makes the decision to hit the brakes and the time the car actually stops is called the braking distance. For a certain car traveling *v *, the braking distance *d *is given by *d *= *v + 1/2c V2*

- Find the braking distance when
*v*is 50 km/h. - If a driver decides to brake 120 metre from a stop sign, how fast can the car be going and still stop by the time it reaches the sign?

14. Eiffel Tower: The Eiffel Tower is a landmark and an early example of wrought-iron construction on a gigantic The lower section consists of four immense arched legs set on masonry piers. The legs curve inward until they unite in a single tapered tower. Platforms, each with an observation deck, are at three levels; on the first is also a restaurant.

The tower, constructed of about 7000 tons of iron, has stairs and elevators. A meteorological station, a radio communications station, and a television transmission antenna, as well as a suite of rooms that were used by Eiffel are located near the top of the tower.

- For a person standing 324 m from the center of the base of the Eiffel Tower, the angle of elevation to the top of the tower is 45c . How tall is the Eiffel Tower?
- A car is moving at uniform speed towards the Eiffel It takes 15 minutes for the angle of depression from the top of tower to the car to change from 30c to 60c . After how much time after this, the car will reach the base of the tower?