Students can access the CBSE Sample Papers for Class 10 Maths with Solutions and marking scheme Term 2 Set 10 will help students in understanding the difficulty level of the exam.
CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 10 for Practice
Time: 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 – A [2 Marks Each]
Question 1.
If x = \(\frac{2}{3}\) and x = – 3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Question 2.
Find the common difference and next term of the A.P. \(\frac{1}{p}, \frac{1-p}{p}, \frac{1-2 p}{p}, \ldots \ldots \ldots \ldots . .\)
OR
Find the value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an A.P.
Question 3.
If two tangents inclined at 60° are drawn to a circle of radius 3 cm, then find length of each tangent.
Question 4.
Isha is 10 years old girl. On the result day, Isha and her father Suresh were very happy as she got first position in the class. While coming back to their home, Isha asked for a treat from her father as a reward for her success. They went to a juice shop and asked for two glasses of juice.
Aisha, a juice seller, was serving juice to her customers in two type of glasses. Both the glasses had inner radius 3 cm. The height of both the glasses was 10 cm.
First type: A Glass with hemispherical raised bottom.
Second type: A glass with conical raised bottom of height 1.5 cm.
Isha insisted to have the juice in first type of glass and her father decided to have the juice in second type of glass. Out of the two, Isha or her father Suresh, who got more quantity of juice to drink and by how much ?
Question 5.
The mean of the following distribution is 18. Find the frequency f of the class 19-21.
Question 6.
How many terms of the A.P – 6, \(\frac{-11}{2}\), – 5, \(\frac{9}{2}\)………… are needed to give their sum zero.
OR
In an A.P. of 50 terms, the sum of the first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.
Section – B [3 Marks Each]
Question 7.
Find the mode of the following data:
Answer:
Question 8.
Draw a circle of radius 1-5 cm. Take a point P outside it. Without using the centre draw two tangents to the circle from the point P.
Question 9.
Find the mean of the following distribution :
Question 10.
The angles of depression of the top and bottom of a building 50 meters high as observed from the top of a tower are 30° and 60° respectively. Find the height of the tower and also the horizontal distance between the building and the tower.
OR
A vertical tower stands on horizontal plane and is surmounted by a vertical flag-staff of height 6 m. The angles of elevations at a point on the bottom and top of the flag-staff with the ground are 30° and 45° respectively. Find the height of the tower. (Take √3 = 1.73)
Section – C [4 Marks Each]
Question 11.
A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3 : 4.
Question 12.
In the adjoining figure, if ∆ABC is circumscribing a circle, then find the length of BC. ISO
OR
In the given figure, O is the centre of the circle. Determine ∠APC, if DA and DC are tangents and ∠ADC = 50°.
Case Study-1
Question 13.
An electrician has to repaired an electric fault on the pole of height 5 m. He needs to reach a point 1.3 m below the top of the pole to undertake the repair work (see figure)
(i) What should be the length of Ladder, when inclined at an angle of 60° to the horizontal ? (2)
(ii) How for from the foot of pole should he place the foot of the ladder ? (2)
Case Study-2
Question 14.
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.
Based on the above information, answer the following questions:
(i) Find the production during first year. (2)
(ii) In which year, the production was ₹ 29,200 ? (2)