Page 1
Page 1 of 10
Class: XII Session: 202021
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. PartA 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 casebased
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 SectionV. 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 oneone or not.
OR
1
Page 2
Page 1 of 10
Class: XII Session: 202021
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. PartA 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 casebased
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 SectionV. 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 oneone 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: 202021
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. PartA 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 casebased
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 SectionV. 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 oneone 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 (1721) and (2226). Each question carries 1 mark
17 An architect designs a building for a multinational 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: 202021
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. PartA 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 casebased
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 SectionV. 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 oneone 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 (1721) and (2226). Each question carries 1 mark
17 An architect designs a building for a multinational 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 multinational company is interested in maximizing the area
of the whole floor including the semicircular 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: 202021
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. PartA 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 casebased
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 SectionV. 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 oneone 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 (1721) and (2226). Each question carries 1 mark
17 An architect designs a building for a multinational 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 multinational company is interested in maximizing the area
of the whole floor including the semicircular 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
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