Class 10 Mathematics (Standard) Term II: CBSE (Official) Sample Question Paper (2021-22) | Mathematics (Maths) Class 10 PDF Download

 Page 1


 
Sample Question Paper 
Mathematics- Standard (041) 
Class- X, Session: 2021-22 
TERM II 
 
 
Time Allowed: 2 hours                                            Maximum Marks: 40 
General Instructions: 
1. The question paper consists of 14 questions divided into 3 sections A, B, C.  
2. All questions are compulsory. 
3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in 
two questions. 
4. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in 
one question. 
5. 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  
 
 
Q No  Marks 
1 Find the value of a25 - a15 for the AP: 6, 9, 12, 15, ……….. 
                                               OR 
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then 
find the value of its 12
th 
 term. 
2 
2 Find the value of ?? so that the quadratic equation ???? (5?? - 6) = 0 has two 
equal roots. 
2 
3 From a point P, two tangents PA and PB are drawn to a circle C(0, r).  
If OP = 2r, then find ??????? . What type of triangle is APB? 
 
2 
4 The curved surface area of a right circular cone is 12320 cm². If the radius of its 
base is 56cm, then find its height. 
2 
5 Mrs. Garg recorded the marks obtained by her students in the following table. 
She calculated the modal marks of the students of the class as 45. While 
printing the data, a blank was left. Find the missing frequency in the table given 
below 
. 
Marks 
Obtained 
0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 
2 
 
O 
A 
B 
P 
r 
2r 
Page 2


 
Sample Question Paper 
Mathematics- Standard (041) 
Class- X, Session: 2021-22 
TERM II 
 
 
Time Allowed: 2 hours                                            Maximum Marks: 40 
General Instructions: 
1. The question paper consists of 14 questions divided into 3 sections A, B, C.  
2. All questions are compulsory. 
3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in 
two questions. 
4. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in 
one question. 
5. 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  
 
 
Q No  Marks 
1 Find the value of a25 - a15 for the AP: 6, 9, 12, 15, ……….. 
                                               OR 
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then 
find the value of its 12
th 
 term. 
2 
2 Find the value of ?? so that the quadratic equation ???? (5?? - 6) = 0 has two 
equal roots. 
2 
3 From a point P, two tangents PA and PB are drawn to a circle C(0, r).  
If OP = 2r, then find ??????? . What type of triangle is APB? 
 
2 
4 The curved surface area of a right circular cone is 12320 cm². If the radius of its 
base is 56cm, then find its height. 
2 
5 Mrs. Garg recorded the marks obtained by her students in the following table. 
She calculated the modal marks of the students of the class as 45. While 
printing the data, a blank was left. Find the missing frequency in the table given 
below 
. 
Marks 
Obtained 
0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 
2 
 
O 
A 
B 
P 
r 
2r 
Number of 
Students 
5 10 --- 6 3 
 
6 If Ritu were younger by 5 years than what she really is, then the square of her 
age would have been 11 more than five times her present age. What is her 
present age? 
OR 
Solve for x: 9x² - 6px  + (p² - q²) = 0 
2 
 Section-B 
 
 
7 Following is the distribution of the long jump competition in which 250 students 
participated. Find the median distance jumped by the students. Interpret the 
median 
 
Distance 
 (in m) 
0 - 1 1 - 2 2 - 3 3 - 4 4 - 5 
Number of 
Students 
40 80 62 38 30 
 
 
3 
8 Construct a pair of tangents to a circle of radius 4cm, which are inclined to 
each other at an angle of 60°. 
 
3 
9 The distribution given below shows the runs scored by batsmen in one-day 
cricket matches. Find the mean number of runs. 
 
Runs 
scored 
0 - 40 40 - 80 80 - 120 120 - 160 160 - 200 
Number of 
batsmen 
12 20 35 30 23 
 
 
3 
10 Two vertical poles of different heights are standing 20m away from each other 
on the level ground. The angle of elevation of the top of the first pole from the 
foot of the second pole is 60° and angle of elevation of the top of the second 
pole from the foot of the first pole is 30°. Find the difference between the heights 
of two poles. (Take v3 = 1.73) 
OR 
A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. 
The angle of elevation of the top of the building from his eye is 60°. Calculate 
the height of the building. (Take v3 = 1.73) 
3 
 Section-C 
 
 
11 The internal and external radii of a spherical shell are 3cm and 5cm 
respectively. It is melted and recast into a solid cylinder of diameter 14cm, find 
the height of the cylinder. Also find the total surface area of the cylinder. 
 (Take ?? = 
22
7
) 
 
4 
Page 3


 
Sample Question Paper 
Mathematics- Standard (041) 
Class- X, Session: 2021-22 
TERM II 
 
 
Time Allowed: 2 hours                                            Maximum Marks: 40 
General Instructions: 
1. The question paper consists of 14 questions divided into 3 sections A, B, C.  
2. All questions are compulsory. 
3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in 
two questions. 
4. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in 
one question. 
5. 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  
 
 
Q No  Marks 
1 Find the value of a25 - a15 for the AP: 6, 9, 12, 15, ……….. 
                                               OR 
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then 
find the value of its 12
th 
 term. 
2 
2 Find the value of ?? so that the quadratic equation ???? (5?? - 6) = 0 has two 
equal roots. 
2 
3 From a point P, two tangents PA and PB are drawn to a circle C(0, r).  
If OP = 2r, then find ??????? . What type of triangle is APB? 
 
2 
4 The curved surface area of a right circular cone is 12320 cm². If the radius of its 
base is 56cm, then find its height. 
2 
5 Mrs. Garg recorded the marks obtained by her students in the following table. 
She calculated the modal marks of the students of the class as 45. While 
printing the data, a blank was left. Find the missing frequency in the table given 
below 
. 
Marks 
Obtained 
0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 
2 
 
O 
A 
B 
P 
r 
2r 
Number of 
Students 
5 10 --- 6 3 
 
6 If Ritu were younger by 5 years than what she really is, then the square of her 
age would have been 11 more than five times her present age. What is her 
present age? 
OR 
Solve for x: 9x² - 6px  + (p² - q²) = 0 
2 
 Section-B 
 
 
7 Following is the distribution of the long jump competition in which 250 students 
participated. Find the median distance jumped by the students. Interpret the 
median 
 
Distance 
 (in m) 
0 - 1 1 - 2 2 - 3 3 - 4 4 - 5 
Number of 
Students 
40 80 62 38 30 
 
 
3 
8 Construct a pair of tangents to a circle of radius 4cm, which are inclined to 
each other at an angle of 60°. 
 
3 
9 The distribution given below shows the runs scored by batsmen in one-day 
cricket matches. Find the mean number of runs. 
 
Runs 
scored 
0 - 40 40 - 80 80 - 120 120 - 160 160 - 200 
Number of 
batsmen 
12 20 35 30 23 
 
 
3 
10 Two vertical poles of different heights are standing 20m away from each other 
on the level ground. The angle of elevation of the top of the first pole from the 
foot of the second pole is 60° and angle of elevation of the top of the second 
pole from the foot of the first pole is 30°. Find the difference between the heights 
of two poles. (Take v3 = 1.73) 
OR 
A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. 
The angle of elevation of the top of the building from his eye is 60°. Calculate 
the height of the building. (Take v3 = 1.73) 
3 
 Section-C 
 
 
11 The internal and external radii of a spherical shell are 3cm and 5cm 
respectively. It is melted and recast into a solid cylinder of diameter 14cm, find 
the height of the cylinder. Also find the total surface area of the cylinder. 
 (Take ?? = 
22
7
) 
 
4 
12 Prove that the angle between the two tangents drawn from an external point to 
a circle is supplementary to the angle subtended by the line segment joining the 
points of contact to the centre. 
OR 
Two tangents TP and TQ are drawn to a circle with centre O from an external 
point T. Prove that ??????? = 2???????  
 
 
4 
13 Case Study-1 
 
Trigonometry in the form of triangulation forms the basis of navigation, whether 
it is by land, sea or air. GPS a radio navigation system helps to locate our 
position on earth with the help of satellites. 
 A guard, stationed at the top of a 240m tower, observed an unidentified boat 
coming towards it. A clinometer or inclinometer is an instrument used for 
measuring angles or slopes(tilt). The guard used the clinometer to measure the 
angle of depression of the boat coming towards the lighthouse and found it to 
be 30°. 
 
 
 
(Lighthouse of Mumbai Harbour. Picture credits - Times of India Travel) 
 
i) Make a labelled figure on the basis of the given information and calculate 
the distance of the boat from the foot of the observation tower.                                               
ii) After 10 minutes, the guard observed that the boat was approaching the 
tower and its distance from tower is reduced by 240(v3 - 1) m. He 
immediately raised the alarm. What was the new angle of depression of 
the boat from the top of the observation tower?                                
  
                       
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
2 
 
 
     2    
14 Case Study-2 
 
Push-ups are a fast and effective exercise for building strength. These are 
helpful in almost all sports including athletics. While the push-up primarily 
targets the muscles of the chest, arms, and shoulders, support required from 
other muscles helps in toning up the whole body.  
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 4


 
Sample Question Paper 
Mathematics- Standard (041) 
Class- X, Session: 2021-22 
TERM II 
 
 
Time Allowed: 2 hours                                            Maximum Marks: 40 
General Instructions: 
1. The question paper consists of 14 questions divided into 3 sections A, B, C.  
2. All questions are compulsory. 
3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in 
two questions. 
4. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in 
one question. 
5. 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  
 
 
Q No  Marks 
1 Find the value of a25 - a15 for the AP: 6, 9, 12, 15, ……….. 
                                               OR 
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then 
find the value of its 12
th 
 term. 
2 
2 Find the value of ?? so that the quadratic equation ???? (5?? - 6) = 0 has two 
equal roots. 
2 
3 From a point P, two tangents PA and PB are drawn to a circle C(0, r).  
If OP = 2r, then find ??????? . What type of triangle is APB? 
 
2 
4 The curved surface area of a right circular cone is 12320 cm². If the radius of its 
base is 56cm, then find its height. 
2 
5 Mrs. Garg recorded the marks obtained by her students in the following table. 
She calculated the modal marks of the students of the class as 45. While 
printing the data, a blank was left. Find the missing frequency in the table given 
below 
. 
Marks 
Obtained 
0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 
2 
 
O 
A 
B 
P 
r 
2r 
Number of 
Students 
5 10 --- 6 3 
 
6 If Ritu were younger by 5 years than what she really is, then the square of her 
age would have been 11 more than five times her present age. What is her 
present age? 
OR 
Solve for x: 9x² - 6px  + (p² - q²) = 0 
2 
 Section-B 
 
 
7 Following is the distribution of the long jump competition in which 250 students 
participated. Find the median distance jumped by the students. Interpret the 
median 
 
Distance 
 (in m) 
0 - 1 1 - 2 2 - 3 3 - 4 4 - 5 
Number of 
Students 
40 80 62 38 30 
 
 
3 
8 Construct a pair of tangents to a circle of radius 4cm, which are inclined to 
each other at an angle of 60°. 
 
3 
9 The distribution given below shows the runs scored by batsmen in one-day 
cricket matches. Find the mean number of runs. 
 
Runs 
scored 
0 - 40 40 - 80 80 - 120 120 - 160 160 - 200 
Number of 
batsmen 
12 20 35 30 23 
 
 
3 
10 Two vertical poles of different heights are standing 20m away from each other 
on the level ground. The angle of elevation of the top of the first pole from the 
foot of the second pole is 60° and angle of elevation of the top of the second 
pole from the foot of the first pole is 30°. Find the difference between the heights 
of two poles. (Take v3 = 1.73) 
OR 
A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. 
The angle of elevation of the top of the building from his eye is 60°. Calculate 
the height of the building. (Take v3 = 1.73) 
3 
 Section-C 
 
 
11 The internal and external radii of a spherical shell are 3cm and 5cm 
respectively. It is melted and recast into a solid cylinder of diameter 14cm, find 
the height of the cylinder. Also find the total surface area of the cylinder. 
 (Take ?? = 
22
7
) 
 
4 
12 Prove that the angle between the two tangents drawn from an external point to 
a circle is supplementary to the angle subtended by the line segment joining the 
points of contact to the centre. 
OR 
Two tangents TP and TQ are drawn to a circle with centre O from an external 
point T. Prove that ??????? = 2???????  
 
 
4 
13 Case Study-1 
 
Trigonometry in the form of triangulation forms the basis of navigation, whether 
it is by land, sea or air. GPS a radio navigation system helps to locate our 
position on earth with the help of satellites. 
 A guard, stationed at the top of a 240m tower, observed an unidentified boat 
coming towards it. A clinometer or inclinometer is an instrument used for 
measuring angles or slopes(tilt). The guard used the clinometer to measure the 
angle of depression of the boat coming towards the lighthouse and found it to 
be 30°. 
 
 
 
(Lighthouse of Mumbai Harbour. Picture credits - Times of India Travel) 
 
i) Make a labelled figure on the basis of the given information and calculate 
the distance of the boat from the foot of the observation tower.                                               
ii) After 10 minutes, the guard observed that the boat was approaching the 
tower and its distance from tower is reduced by 240(v3 - 1) m. He 
immediately raised the alarm. What was the new angle of depression of 
the boat from the top of the observation tower?                                
  
                       
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
2 
 
 
     2    
14 Case Study-2 
 
Push-ups are a fast and effective exercise for building strength. These are 
helpful in almost all sports including athletics. While the push-up primarily 
targets the muscles of the chest, arms, and shoulders, support required from 
other muscles helps in toning up the whole body.  
 
 
 
 
 
 
 
 
 
 
 
 
 
Nitesh wants to participate in the push-up challenge. He can currently make 
3000 push-ups in one hour. But he wants to achieve a target of 3900 push-ups 
in 1 hour for which he practices regularly. With each day of practice, he is able 
to make 5 more push-ups in one hour as compared to the previous day. If on 
first day of practice he makes 3000 push-ups and continues to practice regularly 
till his target is achieved. Keeping the above situation in mind answer the 
following questions: 
 
i) Form an A.P representing the number of push-ups per day and hence 
find the minimum number of days he needs to practice before the day 
his goal is accomplished?                                                          
ii) Find the total number of push-ups performed by Nitesh up to the day his 
goal is achieved. 
                                                                                                             
 
 
 
 
 
 
     
 
  2 
 
 
   2