Students can access the CBSE Sample Papers for Class 10 Maths with Solutions and marking scheme Term 2 Set 7 will help students in understanding the difficulty level of the exam.

## CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 2 Set 7 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.
- 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 questions.
- Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 marks)

Question 1.

What is the value ofx, in terms, of a, b, c. (2)

\(\frac{a}{x-a}+\frac{b}{x-b}=\frac{2 c}{x-c}\) ≠ a, b, c

Question 2.

Circumference of the edge of a hemispherical bowl is 132 cm. What is the capacity of the bowl? [Use π = \(\frac{22}{7}\)]

OR

A grain storage is in the shape of a cuboid of size 8mx6mx3m. If a bag of grain occupies a space of 0.65 m3. How many bags can be stored in that granary ? (2)

Question 3.

Amira scored 36 marks in English, 44 marks in Hindi, 75 marks in Mathematics and x marks in Science. If she had scored an average of 50 marks, then find the value of x. (2)

Question 4.

Is it true to say that – 1, \(\frac{-3}{2},-2, \frac{-5}{2}\) Form an A.P.

OR

Which term of the A.P. 3,14, 25, 36, …….. is 99 more than its 25th term? (2)

Question 5.

What is the median of the following data?

Marks obtained | No. of Students |

20 | 3 |

29 | 4 |

28 | 5 |

42 | 7 |

19 | 9 |

35 | 2 |

51 | 3 |

Question 6.

If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm. Then, what is the length of the tangent. (2)

Section – B (12 marks)

Question 7.

A sum of ₹ 1,000 is invested at 8% simple interest p.a. Calculate the interest at the end of 1, 2, 3… years. Is the sequence of interests, forms an A.P.? Find the interest at the end of 30 years. (3)

Question 8.

In the quadratic px<sup>2</sup> + qx + q = 0, if ratio of the roots is a : b, prove that:

\(\sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}+\sqrt{\frac{q}{r}}\) = 0

OR

What are the roots of quadratic equation 5x<sup>2</sup> – 6x – 2 = 0, by completing the square method? (3)

Question 9.

In the given figure, if TP and TQ are two tangents to a circle with circle O, such that ∠POQ = 110°. Then, what is the measure of ∠PTQ? (3)

Question 10.

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s attitude is 30°, then when it is 60°, what is the height of the tower? (3)

Section – C (16 marks)

Question 11.

A 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 in water, by how much will the level of water rise in the cylindrical vessel

OR

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour ? (4)

Question 12.

A student begin to note the number of cars passing through a point on a road for 100 periods each of 3 min and summarized it in the table given below:

Numbers of cars | Frequency |

0-10 | 7 |

10-20 | 14 |

20-30 | 13 |

30-40 | 12 |

40-50 | 20 |

50-60 | 11 |

60-70 | 15 |

70-80 | 8 |

Find mode of the data and also it mean value. (4)

Question 13.

Case Study—1

Board Exams Term-ll is- shortly going to approach. The exams are going to be subjective; so a detailed understanding of all the chapters are needed for getting the good marks.

So, Mrs. sharma planned a surprise test for the students to check their knowledge of tangents and circle. She made a simple test and few questions of these test are given below:

Try to solve the following questions, to test your knowledge:

(A) If PA and PB are two tangents drawn to a circle with centre O from P such that ∠PBA = 50°, then what is the m ∠OAB? (2)

(B) In the figure below, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 70°, then what is the measure of ∠BAT? (2)

Question 14.

Case Study—2

Sholu faces lots of trouble in picking the things, placed high up on the almirahs, wardrobes, etc. So she went to market, to find a solution for it. She saw a wooden stool, and found its length appropriate for her usage.

She bought that wooden bar stooL, so she could collect the things placed high.

The wooden stool has a square top of side 2 m and have a height of 6m above the ground. Also, each leg is inclined at a angle of 60° to the ground as shown in the figure.

(A) What is the length of each leg considering both are equal? (2)

(B) What is the length of side PQ as shown in the 2-D diagram of the stool? (2)