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: 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.
In an A.P, the sum of first n terms is \(\left(\frac{3 n^{2}}{2}+\frac{5 n}{2}\right)\). Find the 30th term and the nth term.
What is the sum of five positive integers in AP divisible by 6?
Question 2.
Solve for x if x = \(\frac{1}{3-\frac{1}{3-\frac{1}{3-x}}}\)
Question 3.
In the given figure, if ∠ATO = 30°. Find ∠AOT and ∠AOB.
Question 4.
How many spherical bullets can be made out of a solid cube of lead whose edge measures 66 cm, each bullet being 6 cm in diameter?
Question 5.
Find the median of the following observation:
Question 6.
Factorise: 3a2x2 + 8abx + 4b2 = 0.
OR
In a cricket match, Harbhajan took three wickets less than twice the number of wickets taken by Zahid. The product of the number of wickets taken by these two is 20. Represent the above situation in the form of quadratic equation.
Section – B (3 Marks Each)
Question 7.
Find the missing frequencies in the following observation table:
If median is 34.75 and sum of frequency is 75.
Answer:
Question 8.
Draw a line segment of length 12 cm and divide it into the ratio 6 : 7.
Question 9.
Calculate the mode of the following data:
Question 10.
A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 60° with the ground. The distance between the feet of the tree to the point where the top touches the ground is 16 m. Find the height of the tree.
OR
As observed from the top of lighthouse, 150 m high above sea level, the angle of depression of a ship sailing directly towards it, changes from 45° to 60°. Determine the distance travelled by the ship during the period of observations.
Section – C (4 Marks Each)
Question 11.
A circus tent is cylindrical up to a height of 12 m and conical above it. If the diameter of the base is 119 m and the slant height of the conical part is 77 m, find the total canvas used in making the tent.
Question 12.
If MA and MB are two tangents drawn from a exterior point M to a circle with centre O touching it at A and B, prove that MO is perpendicular bisector of AB.
OR
If two tangents inclined at an angle of 60° are drawn to a circle of radius 6 cm, then find the length of each tangent. Also find ∠AOB.
Case Study-1
Question 13.
Authority wants to construct a slide in a city park for children. The slide was to be constructed for children below the age of 12 years. Authority prefers the top of the slide at a height of 4 m above the ground and inclined at an angle of 30° to the ground.
Based on the following figure related to the slide answer the questions:
(i) Find the distance of AB. [2]
(ii) In the given figure, if AB + BC = 25 m and AC = 5 m, then find the value of BC. [2]
Case Study-2
Question 14.
Raj and Ajay are very dose friends. Both the families dedde to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km.
(i) What will be the distance covered by Ajay’s car in two hours ? Also, if the distance covered by Ajay in 2 hours is 90 km then find the speed of Raj’s car. [2]
(ii) If the product of speed of Raj’s and Ajay’s car is 84 km/hr, then find the both car’s speed. [2]