CBSE Class 10 Mathematics Term 2 Sample Paper
Class – X Exam 202122
Mathematics Standard (041)
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. (06)
SECTION A
1. If 2 is a root of the equation x^{2} + kx + 12 = 0 and the equation x^{2} + kx + q = 0 has equal roots, find the value of q .
2. The fifth term of an AP is 26 and its 10^{th} term is Find the AP.
3. In figure, O is the centre of a PT are tangents to the circle from an external point P . If +TPQ = 70c, find +TRQ .
4. Find the number of coins of 5 cm diameter and 0.2 cm thickness to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
5. Given below is a frequency distribution showing the marks by 50 students of a class :
Marks  Number of students 
Below 20  17 
Below 40  22 
Below 60  29 
Below 80  37 
Below 100  50 
Form the distribution table for the above data.
6. Find the mode of the following frequency distribution :
Classes  06  612  1218  1824  2430 
Frequency  7  5  10  12  6 
OR
If median is 137 and mean is 137.05, then what is the value of mode ?
Section B
7. The 13^{th} term of an AP is four times its 3^{rd} If the fifth term is 16, then find the sum of its first ten terms.
8. As observed from the top of a 100 m high light house from the sealevel, the angles of depression of two ships are 30c and 45c. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships.
9. Draw a circle with the help of a Take a point outside the circle. Construct the pair of tangents from this point to the circle.
10. A solid rightcircular cone of height 60 cm and radius 30 cm is dropped in a rightcircular cylinder full of water of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder in cubic metre.
OR
A glass is in the shape of a cylinder of radius 7 cm and height 10 cm. Find the volume of juice in litre required to fill 6 such glasses.
Section C
11. AB is a chord of circle with centre O . At B , a tangent PB is drawn such that its length is 24 The distance of P from the centre is 26 cm. If the chord AB is 16 cm, find its distance from the centre.
12. If the median of the following frequency distribution is 32.5. Find the values of f_{1} and f_{2.}
Class  0 10  1020  2030  3040  4050  5060  6070  Total 
Frequency  f_{1}  5  9  12  f_{2}  3  2  40 
OR
The median of the following data is 16. Find the missing frequencies a and b , if the total of the frequencies is 70.
Class  05  510  1015  1520  2025  2530  3035  3540 
Frequency  12  ‘a’  12  15  b  6  6  4 
13. Drama Ticket : Last year, 300 people attended the Ravindra Manch Drama Club’s winter The ticket price was Rs 70. The advisor estimates that 20 fewer people would attend for each Rs 10 increase in ticket price.

 What ticket price would give the most income for the Drama Club?
 If the Drama Club raised its tickets to this price, how much income should it expect to bring in?
14. Statue of Unity : It is a colossal statue of Indian statesman and independence activist Sardar Vallabh bhai Patel, who was the first Deputy Prime Minister and Home minister of independent Patel was highly respected for his leadership in uniting the 562 princely states of India to form the single Union of India. It is located in the state of Gujarat and it is the world’s tallest statue.
 For a person standing 240 m from the center of the base of the statue, the angle of elevation to the top of the statue is 45c . How tall is the statue?
 A cop in helicopter near the top of the statue, notices a car wreck some distance from the If the angle of depression from the cop’s eyes to the wreck is 60c , how far away is the accident from the centre of base of the statue?