Class 12 Mathematics (Maths) Previous Year Paper - 2

 Page 1


65/1/1 JJJJ Page 1 P .T .O.
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code on 
the title page of the answer-book. 
Series 
E F 1 G H / 1 
 S E T ~ 1
     
   
 
Q.P. Code  
Roll No. 
 
 
 
J{UV 
MATHEMATICS 
* 
: 3 : 80
Time allowed : 3 hours Maximum Marks : 80
 
NOTE :
(i)
- 23
 Please check that this question paper contains 23 printed pages. 
(ii)
- - -
-
 Q.P. Code given on the right hand side of the question paper should be written on the title 
page of the answer-book by the candidate. 
(iii)
- 38 
 Please check that this question paper contains 38 questions.  
(iv)
-
 Please write down the serial number of the question in the answer-book before 
attempting it. 
(v)
- 15 -
10.15 10.15 10.30 -
-
 15 minute time has been allotted to read this question paper. The question paper will be 
 distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the 
question paper only and will not write any answer on the answer-book during this period. 
65/1/1
Page 2


65/1/1 JJJJ Page 1 P .T .O.
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code on 
the title page of the answer-book. 
Series 
E F 1 G H / 1 
 S E T ~ 1
     
   
 
Q.P. Code  
Roll No. 
 
 
 
J{UV 
MATHEMATICS 
* 
: 3 : 80
Time allowed : 3 hours Maximum Marks : 80
 
NOTE :
(i)
- 23
 Please check that this question paper contains 23 printed pages. 
(ii)
- - -
-
 Q.P. Code given on the right hand side of the question paper should be written on the title 
page of the answer-book by the candidate. 
(iii)
- 38 
 Please check that this question paper contains 38 questions.  
(iv)
-
 Please write down the serial number of the question in the answer-book before 
attempting it. 
(v)
- 15 -
10.15 10.15 10.30 -
-
 15 minute time has been allotted to read this question paper. The question paper will be 
 distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the 
question paper only and will not write any answer on the answer-book during this period. 
65/1/1
65/1/1 JJJJ Page 3 P .T .O.
General Instructions : 
Read the following instructions very carefully and strictly follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.  
(ii) This question paper is divided into five Sections  A, B, C, D and E. 
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and 
questions number 19 and 20 are Assertion-Reason based questions of 1 mark 
each.  
(iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type 
questions, carrying 2 marks each.  
(v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions, 
carrying 3 marks each. 
(vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions 
carrying 5 marks each.  
(vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 
4 marks each.   
(viii) There is no overall choice. However, an internal choice has been provided in 
2 questions in Section B, 3 questions in Section C, 2 questions in Section D and 
2 questions in Section E.  
(ix) Use of calculators is not allowed. 
SECTION A 
This section comprises multiple choice questions (MCQs) of 1 mark each. 
 
1. If for a square matrix A, A
2
  3A + I = O and A
1
 = xA + yI, then the 
value of x + y is : 
(a)  2  (b) 2 
(c) 3  (d)  3
2. If |A| = 2, where A is a 2  2 matrix, then |4A
1
| equals : 
(a) 4  (b) 2 
(c) 8  (d) 
32
1
3. Let A be a 3  3 matrix such that |adj A| = 64. Then |A| is equal to : 
(a) 8 only (b)  8 only 
(c) 64  (d) 8 or  8 
Page 3


65/1/1 JJJJ Page 1 P .T .O.
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code on 
the title page of the answer-book. 
Series 
E F 1 G H / 1 
 S E T ~ 1
     
   
 
Q.P. Code  
Roll No. 
 
 
 
J{UV 
MATHEMATICS 
* 
: 3 : 80
Time allowed : 3 hours Maximum Marks : 80
 
NOTE :
(i)
- 23
 Please check that this question paper contains 23 printed pages. 
(ii)
- - -
-
 Q.P. Code given on the right hand side of the question paper should be written on the title 
page of the answer-book by the candidate. 
(iii)
- 38 
 Please check that this question paper contains 38 questions.  
(iv)
-
 Please write down the serial number of the question in the answer-book before 
attempting it. 
(v)
- 15 -
10.15 10.15 10.30 -
-
 15 minute time has been allotted to read this question paper. The question paper will be 
 distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the 
question paper only and will not write any answer on the answer-book during this period. 
65/1/1
65/1/1 JJJJ Page 3 P .T .O.
General Instructions : 
Read the following instructions very carefully and strictly follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.  
(ii) This question paper is divided into five Sections  A, B, C, D and E. 
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and 
questions number 19 and 20 are Assertion-Reason based questions of 1 mark 
each.  
(iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type 
questions, carrying 2 marks each.  
(v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions, 
carrying 3 marks each. 
(vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions 
carrying 5 marks each.  
(vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 
4 marks each.   
(viii) There is no overall choice. However, an internal choice has been provided in 
2 questions in Section B, 3 questions in Section C, 2 questions in Section D and 
2 questions in Section E.  
(ix) Use of calculators is not allowed. 
SECTION A 
This section comprises multiple choice questions (MCQs) of 1 mark each. 
 
1. If for a square matrix A, A
2
  3A + I = O and A
1
 = xA + yI, then the 
value of x + y is : 
(a)  2  (b) 2 
(c) 3  (d)  3
2. If |A| = 2, where A is a 2  2 matrix, then |4A
1
| equals : 
(a) 4  (b) 2 
(c) 8  (d) 
32
1
3. Let A be a 3  3 matrix such that |adj A| = 64. Then |A| is equal to : 
(a) 8 only (b)  8 only 
(c) 64  (d) 8 or  8 
65/1/1 JJJJ Page 5 P .T .O.
4. If A = 
2 5
4 3
and 2A + B is a null matrix, then B is equal to :
(a) 
4 10
8 6
 (b) 
4 10
8 6
 
(c) 
3 10
8 5
 (d) 
3 10
8 5
 
5. If 
dx
d
(f(x)) = log x, then f(x) equals : 
(a)  C
x
1
 (b) x(log x  1) + C 
(c) x(log x + x) + C (d) C
x
1
6. dx )
6
x ( sec
2
6
0
 is equal to : 
(a) 
3
1
  (b)  
3
1
 
(c) 3  (d)  3 
7. The sum of the order and the degree of the differential equation 
y sin
dx
dy
dx
y d
3
2
2
  is : 
(a) 5  (b) 2 
(c) 3  (d) 4
8. The value of p for which the vectors 2
^
i + p
^
j + 
^
k and  4
^
i  6
^
j + 26
^
k 
are perpendicular to each other, is :  
(a) 3  (b)  3 
(c)  
3
17
 (d) 
3
17
 
Page 4


65/1/1 JJJJ Page 1 P .T .O.
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code on 
the title page of the answer-book. 
Series 
E F 1 G H / 1 
 S E T ~ 1
     
   
 
Q.P. Code  
Roll No. 
 
 
 
J{UV 
MATHEMATICS 
* 
: 3 : 80
Time allowed : 3 hours Maximum Marks : 80
 
NOTE :
(i)
- 23
 Please check that this question paper contains 23 printed pages. 
(ii)
- - -
-
 Q.P. Code given on the right hand side of the question paper should be written on the title 
page of the answer-book by the candidate. 
(iii)
- 38 
 Please check that this question paper contains 38 questions.  
(iv)
-
 Please write down the serial number of the question in the answer-book before 
attempting it. 
(v)
- 15 -
10.15 10.15 10.30 -
-
 15 minute time has been allotted to read this question paper. The question paper will be 
 distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the 
question paper only and will not write any answer on the answer-book during this period. 
65/1/1
65/1/1 JJJJ Page 3 P .T .O.
General Instructions : 
Read the following instructions very carefully and strictly follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.  
(ii) This question paper is divided into five Sections  A, B, C, D and E. 
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and 
questions number 19 and 20 are Assertion-Reason based questions of 1 mark 
each.  
(iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type 
questions, carrying 2 marks each.  
(v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions, 
carrying 3 marks each. 
(vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions 
carrying 5 marks each.  
(vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 
4 marks each.   
(viii) There is no overall choice. However, an internal choice has been provided in 
2 questions in Section B, 3 questions in Section C, 2 questions in Section D and 
2 questions in Section E.  
(ix) Use of calculators is not allowed. 
SECTION A 
This section comprises multiple choice questions (MCQs) of 1 mark each. 
 
1. If for a square matrix A, A
2
  3A + I = O and A
1
 = xA + yI, then the 
value of x + y is : 
(a)  2  (b) 2 
(c) 3  (d)  3
2. If |A| = 2, where A is a 2  2 matrix, then |4A
1
| equals : 
(a) 4  (b) 2 
(c) 8  (d) 
32
1
3. Let A be a 3  3 matrix such that |adj A| = 64. Then |A| is equal to : 
(a) 8 only (b)  8 only 
(c) 64  (d) 8 or  8 
65/1/1 JJJJ Page 5 P .T .O.
4. If A = 
2 5
4 3
and 2A + B is a null matrix, then B is equal to :
(a) 
4 10
8 6
 (b) 
4 10
8 6
 
(c) 
3 10
8 5
 (d) 
3 10
8 5
 
5. If 
dx
d
(f(x)) = log x, then f(x) equals : 
(a)  C
x
1
 (b) x(log x  1) + C 
(c) x(log x + x) + C (d) C
x
1
6. dx )
6
x ( sec
2
6
0
 is equal to : 
(a) 
3
1
  (b)  
3
1
 
(c) 3  (d)  3 
7. The sum of the order and the degree of the differential equation 
y sin
dx
dy
dx
y d
3
2
2
  is : 
(a) 5  (b) 2 
(c) 3  (d) 4
8. The value of p for which the vectors 2
^
i + p
^
j + 
^
k and  4
^
i  6
^
j + 26
^
k 
are perpendicular to each other, is :  
(a) 3  (b)  3 
(c)  
3
17
 (d) 
3
17
 
65/1/1 JJJJ Page 7 P .T .O.
9. The value of (
^
i
^
j ) .
^
j + (
^
j
^
i ) .
^
k is :
(a) 2  (b) 0 
(c) 1  (d)  1
10. If a + b = 
^
i and a = 2
^
i  2
^
j + 2
^
k , then | b | equals : 
(a) 14  (b) 3 
(c) 12  (d) 17 
11. Direction cosines of the line  
2
1 x
 = 
3
y 1
 = 
12
1 z 2
 are : 
(a) 
7
2
, 
7
3
, 
7
6
 (b) 
157
2
,  
157
3
, 
157
12
 
(c) 
7
2
,  
7
3
,  
7
6
 (d) 
7
2
,  
7
3
, 
7
6
12. If P
B
A
 = 0·3, P(A) = 0·4 and P(B) = 0·8, then P
A
B
 is equal to : 
(a) 0·6  (b) 0·3 
(c) 0·06  (d) 0·4 
13. The value of k for which  
2 x , kx
2 x , 5 x 3
) x ( f
2
  is a continuous function, is : 
(a)  
4
11
 (b) 
11
4
 
(c) 11  (d) 
4
11
14. If 
0 1
1 0
A and (3 I + 4 A) (3 I  4 A) = x
2
I, then the value(s) x is/are : 
(a)  7 (b) 0 
(c)  5  (d) 25 
Page 5


65/1/1 JJJJ Page 1 P .T .O.
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code on 
the title page of the answer-book. 
Series 
E F 1 G H / 1 
 S E T ~ 1
     
   
 
Q.P. Code  
Roll No. 
 
 
 
J{UV 
MATHEMATICS 
* 
: 3 : 80
Time allowed : 3 hours Maximum Marks : 80
 
NOTE :
(i)
- 23
 Please check that this question paper contains 23 printed pages. 
(ii)
- - -
-
 Q.P. Code given on the right hand side of the question paper should be written on the title 
page of the answer-book by the candidate. 
(iii)
- 38 
 Please check that this question paper contains 38 questions.  
(iv)
-
 Please write down the serial number of the question in the answer-book before 
attempting it. 
(v)
- 15 -
10.15 10.15 10.30 -
-
 15 minute time has been allotted to read this question paper. The question paper will be 
 distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the 
question paper only and will not write any answer on the answer-book during this period. 
65/1/1
65/1/1 JJJJ Page 3 P .T .O.
General Instructions : 
Read the following instructions very carefully and strictly follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.  
(ii) This question paper is divided into five Sections  A, B, C, D and E. 
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and 
questions number 19 and 20 are Assertion-Reason based questions of 1 mark 
each.  
(iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type 
questions, carrying 2 marks each.  
(v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions, 
carrying 3 marks each. 
(vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions 
carrying 5 marks each.  
(vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 
4 marks each.   
(viii) There is no overall choice. However, an internal choice has been provided in 
2 questions in Section B, 3 questions in Section C, 2 questions in Section D and 
2 questions in Section E.  
(ix) Use of calculators is not allowed. 
SECTION A 
This section comprises multiple choice questions (MCQs) of 1 mark each. 
 
1. If for a square matrix A, A
2
  3A + I = O and A
1
 = xA + yI, then the 
value of x + y is : 
(a)  2  (b) 2 
(c) 3  (d)  3
2. If |A| = 2, where A is a 2  2 matrix, then |4A
1
| equals : 
(a) 4  (b) 2 
(c) 8  (d) 
32
1
3. Let A be a 3  3 matrix such that |adj A| = 64. Then |A| is equal to : 
(a) 8 only (b)  8 only 
(c) 64  (d) 8 or  8 
65/1/1 JJJJ Page 5 P .T .O.
4. If A = 
2 5
4 3
and 2A + B is a null matrix, then B is equal to :
(a) 
4 10
8 6
 (b) 
4 10
8 6
 
(c) 
3 10
8 5
 (d) 
3 10
8 5
 
5. If 
dx
d
(f(x)) = log x, then f(x) equals : 
(a)  C
x
1
 (b) x(log x  1) + C 
(c) x(log x + x) + C (d) C
x
1
6. dx )
6
x ( sec
2
6
0
 is equal to : 
(a) 
3
1
  (b)  
3
1
 
(c) 3  (d)  3 
7. The sum of the order and the degree of the differential equation 
y sin
dx
dy
dx
y d
3
2
2
  is : 
(a) 5  (b) 2 
(c) 3  (d) 4
8. The value of p for which the vectors 2
^
i + p
^
j + 
^
k and  4
^
i  6
^
j + 26
^
k 
are perpendicular to each other, is :  
(a) 3  (b)  3 
(c)  
3
17
 (d) 
3
17
 
65/1/1 JJJJ Page 7 P .T .O.
9. The value of (
^
i
^
j ) .
^
j + (
^
j
^
i ) .
^
k is :
(a) 2  (b) 0 
(c) 1  (d)  1
10. If a + b = 
^
i and a = 2
^
i  2
^
j + 2
^
k , then | b | equals : 
(a) 14  (b) 3 
(c) 12  (d) 17 
11. Direction cosines of the line  
2
1 x
 = 
3
y 1
 = 
12
1 z 2
 are : 
(a) 
7
2
, 
7
3
, 
7
6
 (b) 
157
2
,  
157
3
, 
157
12
 
(c) 
7
2
,  
7
3
,  
7
6
 (d) 
7
2
,  
7
3
, 
7
6
12. If P
B
A
 = 0·3, P(A) = 0·4 and P(B) = 0·8, then P
A
B
 is equal to : 
(a) 0·6  (b) 0·3 
(c) 0·06  (d) 0·4 
13. The value of k for which  
2 x , kx
2 x , 5 x 3
) x ( f
2
  is a continuous function, is : 
(a)  
4
11
 (b) 
11
4
 
(c) 11  (d) 
4
11
14. If 
0 1
1 0
A and (3 I + 4 A) (3 I  4 A) = x
2
I, then the value(s) x is/are : 
(a)  7 (b) 0 
(c)  5  (d) 25 
65/1/1 JJJJ Page 9 P .T .O.
15. The general solution of the differential equation x dy  (1 + x
2
) dx = dx 
is : 
(a) y = 2x + 
3
x
3
 + C (b) y = 2 log x + 
3
x
3
 + C 
(c) y = 
2
x
2
 + C (d) y = 2 log x + 
2
x
2
 + C
16. If f(x) = a(x  cos x) is strictly decreasing in  
(a) {0}  (b) (0, ) 
(c) ( , 0) (d) ( , ) 
17. The corner points of the feasible region in the graphical representation 
of a linear programming problem are (2, 72), (15, 20) and (40, 15). If  
z = 18x + 9y be the objective function, then : 
(a) z is maximum at (2, 72), minimum at (15, 20) 
(b) z is maximum at (15, 20), minimum at (40, 15) 
(c) z is maximum at (40, 15), minimum at (15, 20) 
(d) z is maximum at (40, 15), minimum at (2, 72) 
18. The number of corner points of the feasible region determined by the 
constraints x  y  0,  2y  x + 2,  x  0,  y  0 is : 
(a) 2  (b) 3 
(c) 4  (d) 5 
Questions number 19 and 20 are Assertion and Reason based questions carrying 
1 mark each. Two statements are given, one labelled Assertion (A) and the other 
labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d)
as given below.  
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the 
correct explanation of the Assertion (A). 
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not 
the correct explanation of the Assertion (A). 
(c) Assertion (A) is true and Reason (R) is false.  
(d) Assertion (A) is false and Reason (R) is true.