Students can access the CBSE Sample Papers for Class 10 Maths with Solutions and marking scheme Term 2 Set 6 will help students in understanding the difficulty level of the exam.

## CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 6 for Practice

Time Allowed: 2 Hours

Maximum Marks: 40

General Instructions:

- The question paper consists of 14 questions divided into 3 sections A, B, C.
- All questions are compulsory.
- Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
- Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question.
- Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions

SECTION

(12 Marks)

Question 1.

If a, 7, b, 23 are in A.P., then find the values of a and b.

OR

Check whether -151 is a term of the A.P. 11, 8, 5, 2….. **(2)**

Question 2.

The mean of the following frequency distribution is 18. Find the frequency of class 19-21. **(2)**

Class Interval | Frequency |

11 – 13 | 3 |

13 – 15 | 6 |

15 – 17 | 9 |

17 – 19 | 13 |

19 – 21 | f |

21 – 23 | 5 |

23 – 25 | 4 |

Question 3.

In the given figure, if the radii of two concentric circles are 3 cm and 5 cm, find the length of PB. **(2)**

Question 4.

Find the value(s) of fa if the equation x^{2} – bx + 1 = 0 has no real roots. **(2)**

Question 5.

Which term of the A.P. 17, 16\(\frac{1}{5}\), 15\(\frac{2}{5}\), 14\(\frac{3}{5}\),….. is the first negative term? **(2)**

Question 6.

Ritu has a solid toy which is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then what is the ratio of height and radius of the conical part?

OR

A hollows cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm each. If it is assumed that \(\frac{1}{8}\)th of the space of cube remains unfilled with the marbles, then find the number of marbles fitted in the cube. **(2)**

SECTION – B

(12 Marks)

Question 7.

A life insurance agent found the following data for distribution of ages of 100 policy holders.

Age (in years) | Number of policy holders |

Below 20 | 2 |

Below 25 | 6 |

Below 30 | 24 |

Below 35 | 45 |

Below 40 | 78 |

Below 45 | 89 |

Below 50 | 92 |

Below 55 | 98 |

Below 60 | 100 |

Calculate the modal age, if policies are given to persons having age 15 years onwards but less than 60 years. **(3)**

Question 8.

Draw a circle of radius 3 cm. Take two points P and Q on one of its diameter extended on both sides, each at a distance of 4 cm on opposite sides of its centre. Construct tangents to the circle from the points P and Q. **(3)**

Question 9.

Find the median of the following data: **(3)**

Class Interval | Frequency |

0-10 | 2 |

10-20 | 2 |

20-30 | 4 |

30-40 | 6 |

40-50 | 6 |

50-60 | 5 |

60-70 | 2 |

70-80 | 4 |

80-90 | 4 |

Question 10.

From the top of a 60 m high building, the angles of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. Find the height of the tower. [Use \(\sqrt{3}\) = 1.732]

OR

The angle of elevation of the top of a tower from a point on the ground is 30°. On moving a distance 20 m towards the foot of the tower, the angle of elevation increases to 60°. Find the height of the tower. **(3)**

SECTION – C

(16 Marks)

Question 11.

The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14 cm long, is 88 cm^{2}. If the volume of metal used in making the cylinder is 176 cm^{3}, find the outer and inner radii of the cylinder. **(4)**

Question 12.

In the given figure, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30°.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. **(4)**

Question 13.

Case Study-1

Makar Sankranti is a festival which mark the end of winters and the beginning of spring in India. This festival is known for eating sesame sweets and flying kites. As this festival mark the beginning of spring, so flying kites gives us a healthy exposure in the sun, which is a rich source of vitamin D.

A boy standing on a horizontal plane finds a kite flying at a distance of 150 m from him at an elevation of 30°. A girl standing on the roof of a 30 m high building, find the elevation of the kite to be 60°. If the boy and girl are on opposite sides of the kite, then answer the following questions.

(A) Draw a labelled figure on the basis of given information and find the vertical height of the kite from the ground. **(2)**

(B) What is the horizontal distance between the boy and the girl? **(2)**

Question 14.

Case Study-2

A passenger while boarding a plane slipped from the stairs and got hurt. The pilot took the passenger to the emergency clinic at the airport for treatment. Due to this, plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/h than the usual speed.

If x represents the usual speed of the plane, then answer the following questions:

(A) Let x represent the ten’s digit. Then find the quadratic equation in x. **(2)**

(B) What is the original two-digit number? **(2)**