### 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. (03)

**Section A**

1. Find the sum of first 8 multiples of 3.

2. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground where it makes an angle 30c. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree from where it is broken.

3. Two tangents making an angle of 60c between them are drawn to a circle of radius root 3 cm, then find the length of each tangent.

4. The curved surface area of a cylinder is 264 m^{2} and its volume is 924 m^{3}. Find the ratio of its height to its diameter.

5. A cylinder, a cone and a hemisphere have same base and same Find the ratio of their volumes.

6. The following data gives the distribution of total household expenditure of manual workers in a city.

Expenditure (in Rs) |
Frequency |

1000-1500 | 24 |

1500-2000 | 40 |

2000-2500 | 33 |

2500-3000 | 28 |

3000-3500 | 30 |

3500-4000 | 22 |

4000-4500 | 16 |

4500-5000 | 07 |

Then, find the average expenditure which is done by the maximum number of manual workers.

**OR**

The median and mode respectively of a frequency distribution are 26 and 29, find its mean.

**Section B**

** 7. **If tangents *PA *and *PB *drawn from an external point *P *to a circle with centre *O *are inclined to each other at an angle of 80c, then find +*POA*.

8. From a solid cylinder whose height is 15 cm and the diameter is 16 cm, a conical cavity of the same height and same diameter is hollowed out, Find the total surface area of remaining (Given your answer in terms of π).

9. Following frequency distribution shows the expenditure on milk of 30 households in a locality :

Daily expenditure on milk (Rs.) | 0-30 | 30-60 | 60-90 | 90-120 | 120-150 |

Number of households | 5 | 6 | 9 | 6 | 4 |

Find the mode for the above data.

10. Find the median of the following data :

Height (in cm) | Less than 120 | Less than 140 | Less than 160 | Less than 180 | Less than 200 |

No. of students | 12 | 26 | 34 | 40 | 50 |

**OR**

The sum of deviations of a set of values *x*_{1}, *x*_{2}, *x*_{3}, …………, x_{n} , measured from 50 is – 10 and the sum of deviations of the values from 46 is 70. Find the value of *n *and the mean.

**Section C**

** 1. **The first term of an AP is 3, the last term is 83 and the sum of all its terms is Find the number of terms and the common difference of the AP.

12. Draw a circle of radius 4 Draw two tangents to the circle inclined at an angle of 60c to each other.

**OR**

Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60c to each other.

13. Height of a Projectile : A projectile is thrown upward with an initial velocity of 176 ft/sec. After *t *sec, its height *h *(*t*) above the ground is given by the function *h *(*t*) =− 16*t*2 + 176*t.*

- What is the projectile’s height above the ground after 2
- How many seconds after it is thrown will the projectile strike the ground?

14. Raju is a design engineer at a large pharmacy He has to decide the shape of medicine and for this he has to chose between tablet or captab.

a. Tablet : This is circular tablet.

b. Captab : This is long tablet having semicircular at both The volume of medicine is 924 mm2 .

(i) If Raju decide to make tablet of diameter 14 mm, what is the thickness of tablet ?

(ii) If Raju decide to make captab of dimension 7 by 5 mm, what is the thickness of captab?