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CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
CBSE Board 
Class XII Mathematics 
Board Paper 2017 Solution 
All India   
      
SECTION – A 
1. ? A(adjA) | A|I 
? ? ?
? ? ?
8 0 1 0
| A|I 8 8I
0 8 0 1
det(A) | A| 8
 
 
 
2.   ? Since f(x) is continuous at x 3. 
?
?
?
?
?
??
??
??
?
? ? ? ?
??
?
??
??
?
? ? ? ? ? ?
? ? ?
??
x3
2
x3
x3
x3
x3
lim f(x) f(3)
(x 3) 36
lim k
x3
(x 3 6)(x 3 6)
lim k
x3
(x 9)(x 3)
lim k
x3
lim (x 9) k ( x 3, x 3 0)
3 9 k
k 12
 
  
3.  
?
?
22
sin x cos x
dx
sinxcosx
 
?
?
?
?
?
?
??
?
??
??
? ? ? ? ?
22
22
sin x cos x
dx
sin xcosx
(cos x sin x)
2 dx
2sin xcosx
cos2x
2 dx
sin2x
2cos2x
dx
sin2x
f '(x)
log|sin2x| C .......( dx log f(x) c)
f(x)
 
 
 
Page 2


  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
CBSE Board 
Class XII Mathematics 
Board Paper 2017 Solution 
All India   
      
SECTION – A 
1. ? A(adjA) | A|I 
? ? ?
? ? ?
8 0 1 0
| A|I 8 8I
0 8 0 1
det(A) | A| 8
 
 
 
2.   ? Since f(x) is continuous at x 3. 
?
?
?
?
?
??
??
??
?
? ? ? ?
??
?
??
??
?
? ? ? ? ? ?
? ? ?
??
x3
2
x3
x3
x3
x3
lim f(x) f(3)
(x 3) 36
lim k
x3
(x 3 6)(x 3 6)
lim k
x3
(x 9)(x 3)
lim k
x3
lim (x 9) k ( x 3, x 3 0)
3 9 k
k 12
 
  
3.  
?
?
22
sin x cos x
dx
sinxcosx
 
?
?
?
?
?
?
??
?
??
??
? ? ? ? ?
22
22
sin x cos x
dx
sin xcosx
(cos x sin x)
2 dx
2sin xcosx
cos2x
2 dx
sin2x
2cos2x
dx
sin2x
f '(x)
log|sin2x| C .......( dx log f(x) c)
f(x)
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
4.  
Since the ratio of the coefficients are the same
 
 
?
??
?
? ? ?
? ? ?
?
? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
1
1
2
2 1 2
that is, 
5 2.5 5
2 10 2
5 25 5
222
555
the planes are parallel.
2x y +2z = 5
Comparing with ax + by + cz + d = 0,
a = 2, b = -1, c = 2, d = -5
Consider, 5x 2.5y 5z 20
5
5x y 5z 20
2
10x 5y 10z 40
2x y 2z 8
Comparing with ax + by + cz + d = 0
? ? ? ? ?
?
?
? ? ?
? ? ?
?
??
?
?
?
2
12
2 2 2
,
a = 2, b = -1, c = 2, d = -8
Let, d be the distance between the given planes.
d = Length of the perpendicular from 2x y +2z = 5 to 2x y 2z 8,
|d d |
d=
2 ( 1) 2
5 ( 8)
d=
4 1 4
3
d=
9
3
d=
3
d = 1
Distance between the given planes is 1 unit.
 
 
 
 
 
 
 
 
 
 
Page 3


  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
CBSE Board 
Class XII Mathematics 
Board Paper 2017 Solution 
All India   
      
SECTION – A 
1. ? A(adjA) | A|I 
? ? ?
? ? ?
8 0 1 0
| A|I 8 8I
0 8 0 1
det(A) | A| 8
 
 
 
2.   ? Since f(x) is continuous at x 3. 
?
?
?
?
?
??
??
??
?
? ? ? ?
??
?
??
??
?
? ? ? ? ? ?
? ? ?
??
x3
2
x3
x3
x3
x3
lim f(x) f(3)
(x 3) 36
lim k
x3
(x 3 6)(x 3 6)
lim k
x3
(x 9)(x 3)
lim k
x3
lim (x 9) k ( x 3, x 3 0)
3 9 k
k 12
 
  
3.  
?
?
22
sin x cos x
dx
sinxcosx
 
?
?
?
?
?
?
??
?
??
??
? ? ? ? ?
22
22
sin x cos x
dx
sin xcosx
(cos x sin x)
2 dx
2sin xcosx
cos2x
2 dx
sin2x
2cos2x
dx
sin2x
f '(x)
log|sin2x| C .......( dx log f(x) c)
f(x)
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
4.  
Since the ratio of the coefficients are the same
 
 
?
??
?
? ? ?
? ? ?
?
? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
1
1
2
2 1 2
that is, 
5 2.5 5
2 10 2
5 25 5
222
555
the planes are parallel.
2x y +2z = 5
Comparing with ax + by + cz + d = 0,
a = 2, b = -1, c = 2, d = -5
Consider, 5x 2.5y 5z 20
5
5x y 5z 20
2
10x 5y 10z 40
2x y 2z 8
Comparing with ax + by + cz + d = 0
? ? ? ? ?
?
?
? ? ?
? ? ?
?
??
?
?
?
2
12
2 2 2
,
a = 2, b = -1, c = 2, d = -8
Let, d be the distance between the given planes.
d = Length of the perpendicular from 2x y +2z = 5 to 2x y 2z 8,
|d d |
d=
2 ( 1) 2
5 ( 8)
d=
4 1 4
3
d=
9
3
d=
3
d = 1
Distance between the given planes is 1 unit.
 
 
 
 
 
 
 
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
 
SECTION – B 
5. ? Since A is skew symmetric matrix. 
??
? ? ?
? ? ?
? ? ?
? ? ? ? ?
??
??
T
T
T3
T
T
Therefore,A A
AA
A ( 1) A
AA
A A ......(Since A A )
2 A 0
A0
 
 
 
6. Since a polynomial function is continuous and differentiable everywhere, 
? ? ? ?
? ? ? ?
??
? ? ? ? ? ? ? ? ?
? ? ?
? ? ?
?
3
3
therefore, f(x) is continuous on [ 3,0] and differentiable on ( 3,0).
Also, f( 3) 3 3 3 3 3 3 3 0
and f(0) 0 3 0 0
f( 3) f(0)
Thus, all the three conditions of Rolle's theorem are satisfied.
So, there exists a c ?
??
? ? ?
?
? ? ?
? ? ?
? ? ?
??
? ? ?
??
? ? ?
3
2
2
2
2
2
( 3,0) such that f '(c)= 0.
We have,
f(x) x 3x
f '(x) 3x 3
So, f '(x) 0
3x 3 0
3(x 1) 0
(x 1) 0
x1
x1
Clearly, only x = 1 lies in the interval ( 3,0).
Thus, c = 1 ( 3,0).
 
 
 
 
 
 
Page 4


  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
CBSE Board 
Class XII Mathematics 
Board Paper 2017 Solution 
All India   
      
SECTION – A 
1. ? A(adjA) | A|I 
? ? ?
? ? ?
8 0 1 0
| A|I 8 8I
0 8 0 1
det(A) | A| 8
 
 
 
2.   ? Since f(x) is continuous at x 3. 
?
?
?
?
?
??
??
??
?
? ? ? ?
??
?
??
??
?
? ? ? ? ? ?
? ? ?
??
x3
2
x3
x3
x3
x3
lim f(x) f(3)
(x 3) 36
lim k
x3
(x 3 6)(x 3 6)
lim k
x3
(x 9)(x 3)
lim k
x3
lim (x 9) k ( x 3, x 3 0)
3 9 k
k 12
 
  
3.  
?
?
22
sin x cos x
dx
sinxcosx
 
?
?
?
?
?
?
??
?
??
??
? ? ? ? ?
22
22
sin x cos x
dx
sin xcosx
(cos x sin x)
2 dx
2sin xcosx
cos2x
2 dx
sin2x
2cos2x
dx
sin2x
f '(x)
log|sin2x| C .......( dx log f(x) c)
f(x)
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
4.  
Since the ratio of the coefficients are the same
 
 
?
??
?
? ? ?
? ? ?
?
? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
1
1
2
2 1 2
that is, 
5 2.5 5
2 10 2
5 25 5
222
555
the planes are parallel.
2x y +2z = 5
Comparing with ax + by + cz + d = 0,
a = 2, b = -1, c = 2, d = -5
Consider, 5x 2.5y 5z 20
5
5x y 5z 20
2
10x 5y 10z 40
2x y 2z 8
Comparing with ax + by + cz + d = 0
? ? ? ? ?
?
?
? ? ?
? ? ?
?
??
?
?
?
2
12
2 2 2
,
a = 2, b = -1, c = 2, d = -8
Let, d be the distance between the given planes.
d = Length of the perpendicular from 2x y +2z = 5 to 2x y 2z 8,
|d d |
d=
2 ( 1) 2
5 ( 8)
d=
4 1 4
3
d=
9
3
d=
3
d = 1
Distance between the given planes is 1 unit.
 
 
 
 
 
 
 
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
 
SECTION – B 
5. ? Since A is skew symmetric matrix. 
??
? ? ?
? ? ?
? ? ?
? ? ? ? ?
??
??
T
T
T3
T
T
Therefore,A A
AA
A ( 1) A
AA
A A ......(Since A A )
2 A 0
A0
 
 
 
6. Since a polynomial function is continuous and differentiable everywhere, 
? ? ? ?
? ? ? ?
??
? ? ? ? ? ? ? ? ?
? ? ?
? ? ?
?
3
3
therefore, f(x) is continuous on [ 3,0] and differentiable on ( 3,0).
Also, f( 3) 3 3 3 3 3 3 3 0
and f(0) 0 3 0 0
f( 3) f(0)
Thus, all the three conditions of Rolle's theorem are satisfied.
So, there exists a c ?
??
? ? ?
?
? ? ?
? ? ?
? ? ?
??
? ? ?
??
? ? ?
3
2
2
2
2
2
( 3,0) such that f '(c)= 0.
We have,
f(x) x 3x
f '(x) 3x 3
So, f '(x) 0
3x 3 0
3(x 1) 0
(x 1) 0
x1
x1
Clearly, only x = 1 lies in the interval ( 3,0).
Thus, c = 1 ( 3,0).
 
 
 
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
 
7. Let x be the length of an edge of the cube, V be the volume and S be the surface area 
at any time t. 
 
?
??
?
??
??
??
??
??
??
??
??
??
??
? ? ?
??
??
32
3
3
2
2
2
2
2
x 10
Then,V x and S 6x .
It is given that,
dV
9 cm / sec
dt
d
(x ) 9 
dt
dx
3x 9 
dt
dx 3
 
dt
x
Now, S = 6x
dS dx
12x
dt dt
dS 3
12x
dt
x
dS 36
dt x
dS 36
3.6 cm / sec
dt 10
 
 
 
8. We have,  
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ? ?
? ? ? ? ?
?
32
2
2
2
2
f(x) x 3x 6x 100
f '(x) 3x 6x 6
f '(x) 3(x 2x 2)
f '(x) 3(x 2x 1 1)
f '(x) 3 [(x 1) 1) 0 for all real numbers
So, f(x) is increasing for all x R
 
 
 
 
 
 
 
 
 
Page 5


  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
CBSE Board 
Class XII Mathematics 
Board Paper 2017 Solution 
All India   
      
SECTION – A 
1. ? A(adjA) | A|I 
? ? ?
? ? ?
8 0 1 0
| A|I 8 8I
0 8 0 1
det(A) | A| 8
 
 
 
2.   ? Since f(x) is continuous at x 3. 
?
?
?
?
?
??
??
??
?
? ? ? ?
??
?
??
??
?
? ? ? ? ? ?
? ? ?
??
x3
2
x3
x3
x3
x3
lim f(x) f(3)
(x 3) 36
lim k
x3
(x 3 6)(x 3 6)
lim k
x3
(x 9)(x 3)
lim k
x3
lim (x 9) k ( x 3, x 3 0)
3 9 k
k 12
 
  
3.  
?
?
22
sin x cos x
dx
sinxcosx
 
?
?
?
?
?
?
??
?
??
??
? ? ? ? ?
22
22
sin x cos x
dx
sin xcosx
(cos x sin x)
2 dx
2sin xcosx
cos2x
2 dx
sin2x
2cos2x
dx
sin2x
f '(x)
log|sin2x| C .......( dx log f(x) c)
f(x)
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
4.  
Since the ratio of the coefficients are the same
 
 
?
??
?
? ? ?
? ? ?
?
? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
1
1
2
2 1 2
that is, 
5 2.5 5
2 10 2
5 25 5
222
555
the planes are parallel.
2x y +2z = 5
Comparing with ax + by + cz + d = 0,
a = 2, b = -1, c = 2, d = -5
Consider, 5x 2.5y 5z 20
5
5x y 5z 20
2
10x 5y 10z 40
2x y 2z 8
Comparing with ax + by + cz + d = 0
? ? ? ? ?
?
?
? ? ?
? ? ?
?
??
?
?
?
2
12
2 2 2
,
a = 2, b = -1, c = 2, d = -8
Let, d be the distance between the given planes.
d = Length of the perpendicular from 2x y +2z = 5 to 2x y 2z 8,
|d d |
d=
2 ( 1) 2
5 ( 8)
d=
4 1 4
3
d=
9
3
d=
3
d = 1
Distance between the given planes is 1 unit.
 
 
 
 
 
 
 
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
 
SECTION – B 
5. ? Since A is skew symmetric matrix. 
??
? ? ?
? ? ?
? ? ?
? ? ? ? ?
??
??
T
T
T3
T
T
Therefore,A A
AA
A ( 1) A
AA
A A ......(Since A A )
2 A 0
A0
 
 
 
6. Since a polynomial function is continuous and differentiable everywhere, 
? ? ? ?
? ? ? ?
??
? ? ? ? ? ? ? ? ?
? ? ?
? ? ?
?
3
3
therefore, f(x) is continuous on [ 3,0] and differentiable on ( 3,0).
Also, f( 3) 3 3 3 3 3 3 3 0
and f(0) 0 3 0 0
f( 3) f(0)
Thus, all the three conditions of Rolle's theorem are satisfied.
So, there exists a c ?
??
? ? ?
?
? ? ?
? ? ?
? ? ?
??
? ? ?
??
? ? ?
3
2
2
2
2
2
( 3,0) such that f '(c)= 0.
We have,
f(x) x 3x
f '(x) 3x 3
So, f '(x) 0
3x 3 0
3(x 1) 0
(x 1) 0
x1
x1
Clearly, only x = 1 lies in the interval ( 3,0).
Thus, c = 1 ( 3,0).
 
 
 
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
 
7. Let x be the length of an edge of the cube, V be the volume and S be the surface area 
at any time t. 
 
?
??
?
??
??
??
??
??
??
??
??
??
??
? ? ?
??
??
32
3
3
2
2
2
2
2
x 10
Then,V x and S 6x .
It is given that,
dV
9 cm / sec
dt
d
(x ) 9 
dt
dx
3x 9 
dt
dx 3
 
dt
x
Now, S = 6x
dS dx
12x
dt dt
dS 3
12x
dt
x
dS 36
dt x
dS 36
3.6 cm / sec
dt 10
 
 
 
8. We have,  
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ? ?
? ? ? ? ?
?
32
2
2
2
2
f(x) x 3x 6x 100
f '(x) 3x 6x 6
f '(x) 3(x 2x 2)
f '(x) 3(x 2x 1 1)
f '(x) 3 [(x 1) 1) 0 for all real numbers
So, f(x) is increasing for all x R
 
 
 
 
 
 
 
 
 
  
 
CBSE XII | Mathematics 
Board Paper 2017 – All India Set 1 Solution 
 
  
9. ? ? ? ? Given that line joining the point s P 2,2,1 and Q 5,1, 1 then ? 
       
Equation of the line is,
x 2 y 2 z 1
5 2 1 2 2 1
x 2 y 2 z 1
3 1 3
x2
3
x coordinate is 4.
42
3
2
3
Hence, z coordinate is,
z1
3
z 1 2
33
z 1 2
z1
Coordinate of z is 1.
? ? ?
? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
??
?
? ? ?
?
?
? ? ?
??
?
?
??
?
?
?
?
? ? ?
??
?
 
 
 
10. It is given that 
? ? ? ?
?
? ? ?
3 1 3 1
P(A) and P(B)
6 2 6 2
and P(A B)= P(Numbers that are even as well as red)
= P(Number appearing is 2)
1
=
6
Clearly, P(A B) P(A) P(B)
Hence, A and B are not independent events.
 
 
 
 
 
 
 
 
 
 
 
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FAQs on CBSE Past Year Paper Session (2017) Solutions, Math Class 12 - Mathematics (Maths) Class 12 - JEE

1. What are the CBSE past year paper sessions?
Ans. CBSE past year paper sessions refer to the practice sessions where students solve the previous year's question papers of the Central Board of Secondary Education (CBSE) exams. These sessions help students familiarize themselves with the exam pattern, marking scheme, and types of questions asked in the CBSE exams.
2. Why is it important to solve CBSE past year papers?
Ans. Solving CBSE past year papers is important as it helps students understand the exam pattern, identify important topics, and improve their time management skills. It also gives them an idea about the level of difficulty of the questions asked in the CBSE exams and helps in self-assessment and exam preparation.
3. What are the benefits of using CBSE past year paper solutions?
Ans. Using CBSE past year paper solutions helps students in understanding the step-by-step solutions to the questions asked in the previous year's exams. It provides them with a clear understanding of the concepts and techniques required to solve the questions correctly. Additionally, it helps students in identifying common mistakes and misconceptions and improves their problem-solving skills.
4. How can CBSE past year paper sessions help in scoring better marks?
Ans. CBSE past year paper sessions can help students in scoring better marks by providing them with an insight into the exam pattern, important topics, and marking scheme. By solving these papers, students can practice and improve their understanding of concepts, time management skills, and accuracy. They can also learn from their mistakes and rectify them before the actual exam, thereby enhancing their overall performance.
5. Where can I find CBSE past year paper solutions for Math Class 12?
Ans. CBSE past year paper solutions for Math Class 12 can be found on various educational websites, online study platforms, or through specialized books. These solutions are often available in the form of PDFs or online videos, providing step-by-step explanations for each question. Students can also approach their teachers or coaching institutes for guidance in accessing these solutions.
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