Class 12 Mathematics (Maths) Official Sample Question Paper (2020-21) | Mathematics (Maths) Class 12 - JEE PDF Download

 Page 1


Page 1 of 10 
 
Class: XII Session: 2020-21 
Subject: Mathematics  
Sample Question Paper (Theory) 
 
  Time Allowed: 3 Hours                                                                        Maximum Marks: 80 
 
  General Instructions: 
 
1. This question paper contains two parts A and B. Each part is compulsory. Part A 
     carries 24 marks and Part B carries 56 marks 
2. Part-A has Objective Type Questions and Part -B has Descriptive Type 
Questions  
3. Both Part A and Part B have choices. 
 
Part – A: 
 
1. It consists of two sections- I and II.  
2. Section I comprises of 16 very short answer type questions.  
3. Section II contains 2 case studies. Each case study comprises of 5 case-based 
MCQs. An examinee is to attempt any 4 out of 5 MCQs. 
 
Part – B: 
 
1. It consists of three sections- III, IV and V. 
2. Section III comprises of 10 questions of 2 marks each. 
3. Section IV comprises of 7 questions of 3 marks each. 
4. Section V comprises of 3 questions of 5 marks each. 
5. Internal choice is provided in 3 questions of Section –III, 2 questions of Section-
IV and 3 questions of Section-V. You have to attempt only one of the alternatives 
in all such questions. 
Sr. 
No. 
Part – A  Mark
s 
 Section I 
 
All questions are compulsory.  In case of internal choices attempt any 
one.   
 
 
1 Check whether the function ?? : ?? ? ?? defined as ?? (?? ) = ?? 3
 is one-one or not.  
 
OR 
 
1 
 
 
 
Page 2


Page 1 of 10 
 
Class: XII Session: 2020-21 
Subject: Mathematics  
Sample Question Paper (Theory) 
 
  Time Allowed: 3 Hours                                                                        Maximum Marks: 80 
 
  General Instructions: 
 
1. This question paper contains two parts A and B. Each part is compulsory. Part A 
     carries 24 marks and Part B carries 56 marks 
2. Part-A has Objective Type Questions and Part -B has Descriptive Type 
Questions  
3. Both Part A and Part B have choices. 
 
Part – A: 
 
1. It consists of two sections- I and II.  
2. Section I comprises of 16 very short answer type questions.  
3. Section II contains 2 case studies. Each case study comprises of 5 case-based 
MCQs. An examinee is to attempt any 4 out of 5 MCQs. 
 
Part – B: 
 
1. It consists of three sections- III, IV and V. 
2. Section III comprises of 10 questions of 2 marks each. 
3. Section IV comprises of 7 questions of 3 marks each. 
4. Section V comprises of 3 questions of 5 marks each. 
5. Internal choice is provided in 3 questions of Section –III, 2 questions of Section-
IV and 3 questions of Section-V. You have to attempt only one of the alternatives 
in all such questions. 
Sr. 
No. 
Part – A  Mark
s 
 Section I 
 
All questions are compulsory.  In case of internal choices attempt any 
one.   
 
 
1 Check whether the function ?? : ?? ? ?? defined as ?? (?? ) = ?? 3
 is one-one or not.  
 
OR 
 
1 
 
 
 
Page 2 of 10 
 
How many reflexive relations are possible in a set A whose ?? (?? ) = 3. 
 
1 
2 A relation R in ?? = { 1,2,3} is defined as ?? = { (1, 1), (1, 2), (2, 2), (3, 3)}. Which 
element(s) of relation R be removed to make R an equivalence relation? 
 
1 
3 
A relation R in the set of real numbers R defined as ?? = { (?? , ?? ): v?? = ?? } is a 
function or not. Justify 
 
OR 
 
An equivalence relation R in A divides it into equivalence classes ?? 1
, ?? 2
, ?? 3
. 
What is the value of ?? 1
 ? ?? 2
 ? ?? 3
 and ?? 1
 n ?? 2
 n ?? 3
 
 
1 
 
 
 
 
1 
4 If A and B are matrices of order 3 × ?? and ?? × 5 respectively, then find the 
order of matrix 5A – 3B, given that it is defined. 
 
1 
5 Find the value of ?? 2
, where A is a 2×2 matrix whose elements are given by  
?? ????
= {
1
0
 
????
????
  
?? ? ?? ?? = ?? 
 
OR 
 
Given that A is a square matrix of order 3×3 and |A| = - 4. Find |adj A| 
 
1 
 
 
 
 
 
1 
6 
Let A = [?? ????
] be a square matrix of order 3×3 and |A|= -7. Find the value of  
?? 11
 ?? 21
+ ?? 12
?? 22
+ ?? 13
 ?? 23
 
where ?? ????
 is the cofactor of element ?? ????
 
 
1 
7     Find ? ?? ?? (1 - cot?? + ?????????? 2
?? ) ????  
 
    OR 
    Evaluate ? ?? 2
sin?? ????
?? 2
-
?? 2
 
 
1 
 
 
1 
8 Find the area bounded by ?? = ?? 2
, ?? h?? ?? - axis and the lines                          
?? = -1  and ?? = 1. 
 
1 
9 How many arbitrary constants are there in the particular solution of the 
differential equation 
????
????
= -4????
2
 ; y (0) = 1 
 
 
 
OR 
 
For what value of n is the following a homogeneous differential equation: 
????
????
= 
?? 3
- ?? ?? ?? 2
?? + ????
2
 
 
1 
 
 
 
 
 
 
1 
 10      
Find a unit vector in the direction opposite to -
3
4
 ?? ^ 
 
1 
11 Find the area of the triangle whose two sides are represented by the vectors 
2?? ^ ?????? - 3?? . ^ 
1 
Page 3


Page 1 of 10 
 
Class: XII Session: 2020-21 
Subject: Mathematics  
Sample Question Paper (Theory) 
 
  Time Allowed: 3 Hours                                                                        Maximum Marks: 80 
 
  General Instructions: 
 
1. This question paper contains two parts A and B. Each part is compulsory. Part A 
     carries 24 marks and Part B carries 56 marks 
2. Part-A has Objective Type Questions and Part -B has Descriptive Type 
Questions  
3. Both Part A and Part B have choices. 
 
Part – A: 
 
1. It consists of two sections- I and II.  
2. Section I comprises of 16 very short answer type questions.  
3. Section II contains 2 case studies. Each case study comprises of 5 case-based 
MCQs. An examinee is to attempt any 4 out of 5 MCQs. 
 
Part – B: 
 
1. It consists of three sections- III, IV and V. 
2. Section III comprises of 10 questions of 2 marks each. 
3. Section IV comprises of 7 questions of 3 marks each. 
4. Section V comprises of 3 questions of 5 marks each. 
5. Internal choice is provided in 3 questions of Section –III, 2 questions of Section-
IV and 3 questions of Section-V. You have to attempt only one of the alternatives 
in all such questions. 
Sr. 
No. 
Part – A  Mark
s 
 Section I 
 
All questions are compulsory.  In case of internal choices attempt any 
one.   
 
 
1 Check whether the function ?? : ?? ? ?? defined as ?? (?? ) = ?? 3
 is one-one or not.  
 
OR 
 
1 
 
 
 
Page 2 of 10 
 
How many reflexive relations are possible in a set A whose ?? (?? ) = 3. 
 
1 
2 A relation R in ?? = { 1,2,3} is defined as ?? = { (1, 1), (1, 2), (2, 2), (3, 3)}. Which 
element(s) of relation R be removed to make R an equivalence relation? 
 
1 
3 
A relation R in the set of real numbers R defined as ?? = { (?? , ?? ): v?? = ?? } is a 
function or not. Justify 
 
OR 
 
An equivalence relation R in A divides it into equivalence classes ?? 1
, ?? 2
, ?? 3
. 
What is the value of ?? 1
 ? ?? 2
 ? ?? 3
 and ?? 1
 n ?? 2
 n ?? 3
 
 
1 
 
 
 
 
1 
4 If A and B are matrices of order 3 × ?? and ?? × 5 respectively, then find the 
order of matrix 5A – 3B, given that it is defined. 
 
1 
5 Find the value of ?? 2
, where A is a 2×2 matrix whose elements are given by  
?? ????
= {
1
0
 
????
????
  
?? ? ?? ?? = ?? 
 
OR 
 
Given that A is a square matrix of order 3×3 and |A| = - 4. Find |adj A| 
 
1 
 
 
 
 
 
1 
6 
Let A = [?? ????
] be a square matrix of order 3×3 and |A|= -7. Find the value of  
?? 11
 ?? 21
+ ?? 12
?? 22
+ ?? 13
 ?? 23
 
where ?? ????
 is the cofactor of element ?? ????
 
 
1 
7     Find ? ?? ?? (1 - cot?? + ?????????? 2
?? ) ????  
 
    OR 
    Evaluate ? ?? 2
sin?? ????
?? 2
-
?? 2
 
 
1 
 
 
1 
8 Find the area bounded by ?? = ?? 2
, ?? h?? ?? - axis and the lines                          
?? = -1  and ?? = 1. 
 
1 
9 How many arbitrary constants are there in the particular solution of the 
differential equation 
????
????
= -4????
2
 ; y (0) = 1 
 
 
 
OR 
 
For what value of n is the following a homogeneous differential equation: 
????
????
= 
?? 3
- ?? ?? ?? 2
?? + ????
2
 
 
1 
 
 
 
 
 
 
1 
 10      
Find a unit vector in the direction opposite to -
3
4
 ?? ^ 
 
1 
11 Find the area of the triangle whose two sides are represented by the vectors 
2?? ^ ?????? - 3?? . ^ 
1 
Page 3 of 10 
 
12 
Find the angle between the unit vectors ?? ^ ?????? ?? ^
, given that | ?? ^ + ?? ^
| = 1 
 
1 
13 Find the direction cosines of the normal to YZ plane? 
 
1 
14 
Find the coordinates of the point where the line 
?? +3
3
=
?? -1
-1
=
?? -5
-5
 cuts the XY 
plane. 
 
1 
15 
The probabilities of A and B solving a problem independently are 
1
3
 ?????? 
1
4
 
respectively. If both of them try to solve the problem independently, what is the 
probability that the problem is solved? 
 
1 
16 The probability that it will rain on any particular day is 50%. Find the probability 
that it rains only on first 4 days of the week.  
 
1 
 Section II 
Both the Case study based questions are compulsory. Attempt any 4 sub 
parts from each question (17-21) and (22-26). Each question carries 1 mark   
 
 
17 An architect designs a building for a multi-national company. The floor consists 
of a rectangular region with semicircular ends having a perimeter of 200m as 
shown below: 
 
               Design of Floor 
 
 
 
 
 
 
                                                 Building 
 
 
 
                                                       
 
Based on the above information answer the following: 
 
 
 
  
(i) If x and y represents the length and breadth of the rectangular region, then 
the relation between the variables is 
 
a) x + p y = 100 
b) 2x + p y = 200 
c) p x + y = 50 
d) x + y = 100 
 
 
Page 4


Page 1 of 10 
 
Class: XII Session: 2020-21 
Subject: Mathematics  
Sample Question Paper (Theory) 
 
  Time Allowed: 3 Hours                                                                        Maximum Marks: 80 
 
  General Instructions: 
 
1. This question paper contains two parts A and B. Each part is compulsory. Part A 
     carries 24 marks and Part B carries 56 marks 
2. Part-A has Objective Type Questions and Part -B has Descriptive Type 
Questions  
3. Both Part A and Part B have choices. 
 
Part – A: 
 
1. It consists of two sections- I and II.  
2. Section I comprises of 16 very short answer type questions.  
3. Section II contains 2 case studies. Each case study comprises of 5 case-based 
MCQs. An examinee is to attempt any 4 out of 5 MCQs. 
 
Part – B: 
 
1. It consists of three sections- III, IV and V. 
2. Section III comprises of 10 questions of 2 marks each. 
3. Section IV comprises of 7 questions of 3 marks each. 
4. Section V comprises of 3 questions of 5 marks each. 
5. Internal choice is provided in 3 questions of Section –III, 2 questions of Section-
IV and 3 questions of Section-V. You have to attempt only one of the alternatives 
in all such questions. 
Sr. 
No. 
Part – A  Mark
s 
 Section I 
 
All questions are compulsory.  In case of internal choices attempt any 
one.   
 
 
1 Check whether the function ?? : ?? ? ?? defined as ?? (?? ) = ?? 3
 is one-one or not.  
 
OR 
 
1 
 
 
 
Page 2 of 10 
 
How many reflexive relations are possible in a set A whose ?? (?? ) = 3. 
 
1 
2 A relation R in ?? = { 1,2,3} is defined as ?? = { (1, 1), (1, 2), (2, 2), (3, 3)}. Which 
element(s) of relation R be removed to make R an equivalence relation? 
 
1 
3 
A relation R in the set of real numbers R defined as ?? = { (?? , ?? ): v?? = ?? } is a 
function or not. Justify 
 
OR 
 
An equivalence relation R in A divides it into equivalence classes ?? 1
, ?? 2
, ?? 3
. 
What is the value of ?? 1
 ? ?? 2
 ? ?? 3
 and ?? 1
 n ?? 2
 n ?? 3
 
 
1 
 
 
 
 
1 
4 If A and B are matrices of order 3 × ?? and ?? × 5 respectively, then find the 
order of matrix 5A – 3B, given that it is defined. 
 
1 
5 Find the value of ?? 2
, where A is a 2×2 matrix whose elements are given by  
?? ????
= {
1
0
 
????
????
  
?? ? ?? ?? = ?? 
 
OR 
 
Given that A is a square matrix of order 3×3 and |A| = - 4. Find |adj A| 
 
1 
 
 
 
 
 
1 
6 
Let A = [?? ????
] be a square matrix of order 3×3 and |A|= -7. Find the value of  
?? 11
 ?? 21
+ ?? 12
?? 22
+ ?? 13
 ?? 23
 
where ?? ????
 is the cofactor of element ?? ????
 
 
1 
7     Find ? ?? ?? (1 - cot?? + ?????????? 2
?? ) ????  
 
    OR 
    Evaluate ? ?? 2
sin?? ????
?? 2
-
?? 2
 
 
1 
 
 
1 
8 Find the area bounded by ?? = ?? 2
, ?? h?? ?? - axis and the lines                          
?? = -1  and ?? = 1. 
 
1 
9 How many arbitrary constants are there in the particular solution of the 
differential equation 
????
????
= -4????
2
 ; y (0) = 1 
 
 
 
OR 
 
For what value of n is the following a homogeneous differential equation: 
????
????
= 
?? 3
- ?? ?? ?? 2
?? + ????
2
 
 
1 
 
 
 
 
 
 
1 
 10      
Find a unit vector in the direction opposite to -
3
4
 ?? ^ 
 
1 
11 Find the area of the triangle whose two sides are represented by the vectors 
2?? ^ ?????? - 3?? . ^ 
1 
Page 3 of 10 
 
12 
Find the angle between the unit vectors ?? ^ ?????? ?? ^
, given that | ?? ^ + ?? ^
| = 1 
 
1 
13 Find the direction cosines of the normal to YZ plane? 
 
1 
14 
Find the coordinates of the point where the line 
?? +3
3
=
?? -1
-1
=
?? -5
-5
 cuts the XY 
plane. 
 
1 
15 
The probabilities of A and B solving a problem independently are 
1
3
 ?????? 
1
4
 
respectively. If both of them try to solve the problem independently, what is the 
probability that the problem is solved? 
 
1 
16 The probability that it will rain on any particular day is 50%. Find the probability 
that it rains only on first 4 days of the week.  
 
1 
 Section II 
Both the Case study based questions are compulsory. Attempt any 4 sub 
parts from each question (17-21) and (22-26). Each question carries 1 mark   
 
 
17 An architect designs a building for a multi-national company. The floor consists 
of a rectangular region with semicircular ends having a perimeter of 200m as 
shown below: 
 
               Design of Floor 
 
 
 
 
 
 
                                                 Building 
 
 
 
                                                       
 
Based on the above information answer the following: 
 
 
 
  
(i) If x and y represents the length and breadth of the rectangular region, then 
the relation between the variables is 
 
a) x + p y = 100 
b) 2x + p y = 200 
c) p x + y = 50 
d) x + y = 100 
 
 
Page 4 of 10 
 
 (ii)The area of the rectangular region A expressed as a function of x is 
 
 
a) 
2
?? ( 100 ?? - ?? 2
) 
b) 
1
?? ( 100 ?? - ?? 2
) 
c) 
?? ?? ( 100 - ?? ) 
d) ?? ?? 2
+ 
2
?? ( 100 ?? - ?? 2
) 
 
1 
 (iii) The maximum value of area A is 
 
 
a) 
?? 3200
?? 2
 
b) 
3200
?? ?? 2
 
c) 
5000
?? ?? 2
 
d) 
1000
?? ?? 2
 
 
1 
 (iv) The CEO of the multi-national company is interested in maximizing the area 
of the whole floor including the semi-circular ends. For this to happen the valve 
of x should be 
 
 
a) 0 m 
b) 30 m 
c) 50 m 
d) 80 m 
 
1 
 (v) The extra area generated if the area of the whole floor is  maximized is : 
  
a) 
3000
?? ?? 2
 
b) 
5000
?? ?? 2
 
c) 
7000
?? ?? 2
 
d) No change Both areas are equal 
 
1 
Page 5


Page 1 of 10 
 
Class: XII Session: 2020-21 
Subject: Mathematics  
Sample Question Paper (Theory) 
 
  Time Allowed: 3 Hours                                                                        Maximum Marks: 80 
 
  General Instructions: 
 
1. This question paper contains two parts A and B. Each part is compulsory. Part A 
     carries 24 marks and Part B carries 56 marks 
2. Part-A has Objective Type Questions and Part -B has Descriptive Type 
Questions  
3. Both Part A and Part B have choices. 
 
Part – A: 
 
1. It consists of two sections- I and II.  
2. Section I comprises of 16 very short answer type questions.  
3. Section II contains 2 case studies. Each case study comprises of 5 case-based 
MCQs. An examinee is to attempt any 4 out of 5 MCQs. 
 
Part – B: 
 
1. It consists of three sections- III, IV and V. 
2. Section III comprises of 10 questions of 2 marks each. 
3. Section IV comprises of 7 questions of 3 marks each. 
4. Section V comprises of 3 questions of 5 marks each. 
5. Internal choice is provided in 3 questions of Section –III, 2 questions of Section-
IV and 3 questions of Section-V. You have to attempt only one of the alternatives 
in all such questions. 
Sr. 
No. 
Part – A  Mark
s 
 Section I 
 
All questions are compulsory.  In case of internal choices attempt any 
one.   
 
 
1 Check whether the function ?? : ?? ? ?? defined as ?? (?? ) = ?? 3
 is one-one or not.  
 
OR 
 
1 
 
 
 
Page 2 of 10 
 
How many reflexive relations are possible in a set A whose ?? (?? ) = 3. 
 
1 
2 A relation R in ?? = { 1,2,3} is defined as ?? = { (1, 1), (1, 2), (2, 2), (3, 3)}. Which 
element(s) of relation R be removed to make R an equivalence relation? 
 
1 
3 
A relation R in the set of real numbers R defined as ?? = { (?? , ?? ): v?? = ?? } is a 
function or not. Justify 
 
OR 
 
An equivalence relation R in A divides it into equivalence classes ?? 1
, ?? 2
, ?? 3
. 
What is the value of ?? 1
 ? ?? 2
 ? ?? 3
 and ?? 1
 n ?? 2
 n ?? 3
 
 
1 
 
 
 
 
1 
4 If A and B are matrices of order 3 × ?? and ?? × 5 respectively, then find the 
order of matrix 5A – 3B, given that it is defined. 
 
1 
5 Find the value of ?? 2
, where A is a 2×2 matrix whose elements are given by  
?? ????
= {
1
0
 
????
????
  
?? ? ?? ?? = ?? 
 
OR 
 
Given that A is a square matrix of order 3×3 and |A| = - 4. Find |adj A| 
 
1 
 
 
 
 
 
1 
6 
Let A = [?? ????
] be a square matrix of order 3×3 and |A|= -7. Find the value of  
?? 11
 ?? 21
+ ?? 12
?? 22
+ ?? 13
 ?? 23
 
where ?? ????
 is the cofactor of element ?? ????
 
 
1 
7     Find ? ?? ?? (1 - cot?? + ?????????? 2
?? ) ????  
 
    OR 
    Evaluate ? ?? 2
sin?? ????
?? 2
-
?? 2
 
 
1 
 
 
1 
8 Find the area bounded by ?? = ?? 2
, ?? h?? ?? - axis and the lines                          
?? = -1  and ?? = 1. 
 
1 
9 How many arbitrary constants are there in the particular solution of the 
differential equation 
????
????
= -4????
2
 ; y (0) = 1 
 
 
 
OR 
 
For what value of n is the following a homogeneous differential equation: 
????
????
= 
?? 3
- ?? ?? ?? 2
?? + ????
2
 
 
1 
 
 
 
 
 
 
1 
 10      
Find a unit vector in the direction opposite to -
3
4
 ?? ^ 
 
1 
11 Find the area of the triangle whose two sides are represented by the vectors 
2?? ^ ?????? - 3?? . ^ 
1 
Page 3 of 10 
 
12 
Find the angle between the unit vectors ?? ^ ?????? ?? ^
, given that | ?? ^ + ?? ^
| = 1 
 
1 
13 Find the direction cosines of the normal to YZ plane? 
 
1 
14 
Find the coordinates of the point where the line 
?? +3
3
=
?? -1
-1
=
?? -5
-5
 cuts the XY 
plane. 
 
1 
15 
The probabilities of A and B solving a problem independently are 
1
3
 ?????? 
1
4
 
respectively. If both of them try to solve the problem independently, what is the 
probability that the problem is solved? 
 
1 
16 The probability that it will rain on any particular day is 50%. Find the probability 
that it rains only on first 4 days of the week.  
 
1 
 Section II 
Both the Case study based questions are compulsory. Attempt any 4 sub 
parts from each question (17-21) and (22-26). Each question carries 1 mark   
 
 
17 An architect designs a building for a multi-national company. The floor consists 
of a rectangular region with semicircular ends having a perimeter of 200m as 
shown below: 
 
               Design of Floor 
 
 
 
 
 
 
                                                 Building 
 
 
 
                                                       
 
Based on the above information answer the following: 
 
 
 
  
(i) If x and y represents the length and breadth of the rectangular region, then 
the relation between the variables is 
 
a) x + p y = 100 
b) 2x + p y = 200 
c) p x + y = 50 
d) x + y = 100 
 
 
Page 4 of 10 
 
 (ii)The area of the rectangular region A expressed as a function of x is 
 
 
a) 
2
?? ( 100 ?? - ?? 2
) 
b) 
1
?? ( 100 ?? - ?? 2
) 
c) 
?? ?? ( 100 - ?? ) 
d) ?? ?? 2
+ 
2
?? ( 100 ?? - ?? 2
) 
 
1 
 (iii) The maximum value of area A is 
 
 
a) 
?? 3200
?? 2
 
b) 
3200
?? ?? 2
 
c) 
5000
?? ?? 2
 
d) 
1000
?? ?? 2
 
 
1 
 (iv) The CEO of the multi-national company is interested in maximizing the area 
of the whole floor including the semi-circular ends. For this to happen the valve 
of x should be 
 
 
a) 0 m 
b) 30 m 
c) 50 m 
d) 80 m 
 
1 
 (v) The extra area generated if the area of the whole floor is  maximized is : 
  
a) 
3000
?? ?? 2
 
b) 
5000
?? ?? 2
 
c) 
7000
?? ?? 2
 
d) No change Both areas are equal 
 
1 
Page 5 of 10 
 
 
 
18 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
In an office three employees Vinay, Sonia and Iqbal process incoming copies of 
a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal 
the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an 
error rate of 0.04 and Iqbal has an error rate of 0.03 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Based on the above information answer the following: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (i) The conditional probability that an error is committed in processing given that 
Sonia processed the form is : 
 
a) 0.0210 
b) 0.04 
c) 0.47 
d) 0.06 
 
 
 
 
 
 
 
1 
 (ii)The probability that Sonia processed the form and committed an error is : 
 
a) 0.005 
b) 0.006 
c) 0.008 
d) 0.68 
 
1 
 (iii)The total probability of committing an error in processing the form is 
 
a) 0 
b) 0.047 
c) 0.234 
1