Class 11 Mathematics (Maths) Previous Year Paper - 2 | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


XI B Page 1 of 3 
 
 
 
Date:                               Class: XI 
Mathematics (Set - B) 
Time: 3 hours                                              M. M: 100  
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises of 6 
questions of 1 mark each. Section B comprises of 13 questions of 4 marks each and Section C comprises of 7 
questions of 6 marks each. 
3. Use of calculators is not permitted. 
 
Section A 
 
1 
Describe the set 
1	,


,


,


…….  in set builder form. 1 
 
2 In a circle of diameter 40 cm, the length of a chord is 20cm.Find the length of minor arc of the chord. 1 
 
3 
If  

!


!


!
			 Find x . 1 
 
4 
Express the function   f : A?R, f(x) = x² - 1, where A = { -4, 0, 1, 4} as a set of ordered pairs. 1 
5 Let   L , M , N be the feet of the perpendiculars drawn from a point P(3,4,5) on the  x , y and z- axes 
respectively. Find the coordinates of L and M. 
1 
 
6 Find the  H.C.F of 		3!,4!,5!		 
1 
 Section B 
 
7 Let A and B be two sets , if  n  n  Ø   and  ?  ?   for some set ,	  prove that  
   A = B. 
OR 
Let A and B  be two sets .Prove that :  
(A-B)?    if and only if B  is subset of A. 
 
4 
8 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of 
these  
(i) Cards of the same colour. 
(ii)  Four cards belong to four different suits. 
(iii) Two are red card and two are black.   
 
4 
9 Redefine the function :  f(x) = |1||6|  .  Write its domain also. 
 
4 
10 Prove the following by the principle of mathematical induction: 
      
( )( )
1 1 1 1
1.3 3.5 5.7 2 1 2 1 2 1
n
n n n
+ + + + =
- + +
K
 
  
4 
Page 2


XI B Page 1 of 3 
 
 
 
Date:                               Class: XI 
Mathematics (Set - B) 
Time: 3 hours                                              M. M: 100  
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises of 6 
questions of 1 mark each. Section B comprises of 13 questions of 4 marks each and Section C comprises of 7 
questions of 6 marks each. 
3. Use of calculators is not permitted. 
 
Section A 
 
1 
Describe the set 
1	,


,


,


…….  in set builder form. 1 
 
2 In a circle of diameter 40 cm, the length of a chord is 20cm.Find the length of minor arc of the chord. 1 
 
3 
If  

!


!


!
			 Find x . 1 
 
4 
Express the function   f : A?R, f(x) = x² - 1, where A = { -4, 0, 1, 4} as a set of ordered pairs. 1 
5 Let   L , M , N be the feet of the perpendiculars drawn from a point P(3,4,5) on the  x , y and z- axes 
respectively. Find the coordinates of L and M. 
1 
 
6 Find the  H.C.F of 		3!,4!,5!		 
1 
 Section B 
 
7 Let A and B be two sets , if  n  n  Ø   and  ?  ?   for some set ,	  prove that  
   A = B. 
OR 
Let A and B  be two sets .Prove that :  
(A-B)?    if and only if B  is subset of A. 
 
4 
8 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of 
these  
(i) Cards of the same colour. 
(ii)  Four cards belong to four different suits. 
(iii) Two are red card and two are black.   
 
4 
9 Redefine the function :  f(x) = |1||6|  .  Write its domain also. 
 
4 
10 Prove the following by the principle of mathematical induction: 
      
( )( )
1 1 1 1
1.3 3.5 5.7 2 1 2 1 2 1
n
n n n
+ + + + =
- + +
K
 
  
4 
XI B Page 2 of 3 
 
 
11 
 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - .  
4 
 
12 
 
If !"# 	


  ,$%!& 	
'(

  where x and y in the second quadrant, find the value of   sin	&.
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
(./0(12
(./0 (1'
 
 
4 
 
13 
Find the domain and range of the real function 3 

2
4
 
OR 
Find the domain and range of the  real function 3 	

'
4

 
4 
 
14 Solve for x:       
('

5
'(
6

('

  ,				 ? 8   and represent the solution on number line. 4 
15 A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting 
mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, 
how many litres of the 2% solution will have to be added?  
 
4 
 
16 If in a ?ABC	,		
=>? 	@
=>?A

=>? @'B
=>? B'A
	.	Prove	that	K
(
,L
(
	
,$
(
		are	in	A.P.	 4 
17 A relation R is defined from a set A={2,3,4,7} to a set B={ 3,6,9,10}  as follows  
    8  
,& ?8 :		is relatively prime to &;	 ? ,& ?  
Express R as a set of ordered pairs and determine the domain and range. 
 
4 
18 How many words can be formed from all the letters of the word ALLAHABAD? How many of these 
words will not contain L together. 
OR 
The letters of the word ‘RANDOM’ are written in all possible orders and these words are written out 
as in dictionary. Find the rank of the word ‘RANDOM’.  
 
4 
19 There are 200 individuals with a skin disorder. 120 had been exposed to chemical C1, 50 to chemical 
C2 and 30 to both C1 and C2. Find the number of individuals exposed to  
(i) Chemical C1 but not Chemical C2 
(ii) Chemical C2 but not Chemical C1 
(iii) Chemical C1 or Chemical C2. 
 
4 
 
Section C  
20 
 Using principle of mathematical induction prove that  
2 2
5 24 25
n
n
+
- - is divisible by 576 for all       
n N ? . 
OR 
Using principle of mathematical induction prove that  
  	!"#O !"#2O!"#3O?sin#O 	
0RST
UVW	
4
X1Y>?
UZ
4
Y>?
Z
4
  for all  # ?[.	 
6 
 
21 (i) Find the general solution of the following equation: 
\K#
(
O1v3\K#Ov3 0 
(ii) Find the value of   cos570°!"#510°sin330°cos390° 
4+2 
Page 3


XI B Page 1 of 3 
 
 
 
Date:                               Class: XI 
Mathematics (Set - B) 
Time: 3 hours                                              M. M: 100  
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises of 6 
questions of 1 mark each. Section B comprises of 13 questions of 4 marks each and Section C comprises of 7 
questions of 6 marks each. 
3. Use of calculators is not permitted. 
 
Section A 
 
1 
Describe the set 
1	,


,


,


…….  in set builder form. 1 
 
2 In a circle of diameter 40 cm, the length of a chord is 20cm.Find the length of minor arc of the chord. 1 
 
3 
If  

!


!


!
			 Find x . 1 
 
4 
Express the function   f : A?R, f(x) = x² - 1, where A = { -4, 0, 1, 4} as a set of ordered pairs. 1 
5 Let   L , M , N be the feet of the perpendiculars drawn from a point P(3,4,5) on the  x , y and z- axes 
respectively. Find the coordinates of L and M. 
1 
 
6 Find the  H.C.F of 		3!,4!,5!		 
1 
 Section B 
 
7 Let A and B be two sets , if  n  n  Ø   and  ?  ?   for some set ,	  prove that  
   A = B. 
OR 
Let A and B  be two sets .Prove that :  
(A-B)?    if and only if B  is subset of A. 
 
4 
8 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of 
these  
(i) Cards of the same colour. 
(ii)  Four cards belong to four different suits. 
(iii) Two are red card and two are black.   
 
4 
9 Redefine the function :  f(x) = |1||6|  .  Write its domain also. 
 
4 
10 Prove the following by the principle of mathematical induction: 
      
( )( )
1 1 1 1
1.3 3.5 5.7 2 1 2 1 2 1
n
n n n
+ + + + =
- + +
K
 
  
4 
XI B Page 2 of 3 
 
 
11 
 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - .  
4 
 
12 
 
If !"# 	


  ,$%!& 	
'(

  where x and y in the second quadrant, find the value of   sin	&.
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
(./0(12
(./0 (1'
 
 
4 
 
13 
Find the domain and range of the real function 3 

2
4
 
OR 
Find the domain and range of the  real function 3 	

'
4

 
4 
 
14 Solve for x:       
('

5
'(
6

('

  ,				 ? 8   and represent the solution on number line. 4 
15 A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting 
mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, 
how many litres of the 2% solution will have to be added?  
 
4 
 
16 If in a ?ABC	,		
=>? 	@
=>?A

=>? @'B
=>? B'A
	.	Prove	that	K
(
,L
(
	
,$
(
		are	in	A.P.	 4 
17 A relation R is defined from a set A={2,3,4,7} to a set B={ 3,6,9,10}  as follows  
    8  
,& ?8 :		is relatively prime to &;	 ? ,& ?  
Express R as a set of ordered pairs and determine the domain and range. 
 
4 
18 How many words can be formed from all the letters of the word ALLAHABAD? How many of these 
words will not contain L together. 
OR 
The letters of the word ‘RANDOM’ are written in all possible orders and these words are written out 
as in dictionary. Find the rank of the word ‘RANDOM’.  
 
4 
19 There are 200 individuals with a skin disorder. 120 had been exposed to chemical C1, 50 to chemical 
C2 and 30 to both C1 and C2. Find the number of individuals exposed to  
(i) Chemical C1 but not Chemical C2 
(ii) Chemical C2 but not Chemical C1 
(iii) Chemical C1 or Chemical C2. 
 
4 
 
Section C  
20 
 Using principle of mathematical induction prove that  
2 2
5 24 25
n
n
+
- - is divisible by 576 for all       
n N ? . 
OR 
Using principle of mathematical induction prove that  
  	!"#O !"#2O!"#3O?sin#O 	
0RST
UVW	
4
X1Y>?
UZ
4
Y>?
Z
4
  for all  # ?[.	 
6 
 
21 (i) Find the general solution of the following equation: 
\K#
(
O1v3\K#Ov3 0 
(ii) Find the value of   cos570°!"#510°sin330°cos390° 
4+2 
XI B Page 3 of 3 
 
 
 
 
 
22 
 
 
In any  ?b  
Show that  :     !"#
(
@
(
!"#
(
B
(
!"#
(
A
(
 12!"#
@
(
!"#
B
(
!"#
A
(
       
 
 
6 
 
23 
  
There are 10 points in a plane, no three of which are in the same straight line, excepting 4 points, 
which are collinear.  
Find : (i) the number of straight  lines obtained from the pair of these points. 
          (ii) the number of triangles that can be formed with the vertices as these points. 
 
6 
24  In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% families buy 
newspaper B and 10% families buy newspaper C. 5% families buy A and B, 3% buy B and C and 4% 
buy A and C. If 2% families buy all the three newspapers, find the number of families which buy: 
 (i) C only  (ii) A but not B.  (iii) none of A, B and C.   
Write certain values which inculcate if a child read newspapers daily. 
 
6 
25 (i) A point R with x – coordinate 4 lies on the line segment joining the points  P (2, -3, 4) and  
Q (8, 0, 10). Find the coordinates of the point R. 
(ii) The mid points of the sides of the triangle are (5,7,11),(0,8,5) and  (2,3,-1).Find its vertices and 
the coordinates of centroid.      
 
2+4 
26 Solve the following system of inequalities graphically:             
  4x + 3y < 60,  y> 2x,  x > 3,  x > 0 , y > 0 
OR 
Solve the following system of inequalities graphically    2& 5 4, & d 3	,				23& e 6 
6 
 
 
Page 4


XI B Page 1 of 3 
 
 
 
Date:                               Class: XI 
Mathematics (Set - B) 
Time: 3 hours                                              M. M: 100  
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises of 6 
questions of 1 mark each. Section B comprises of 13 questions of 4 marks each and Section C comprises of 7 
questions of 6 marks each. 
3. Use of calculators is not permitted. 
 
Section A 
 
1 
Describe the set 
1	,


,


,


…….  in set builder form. 1 
 
2 In a circle of diameter 40 cm, the length of a chord is 20cm.Find the length of minor arc of the chord. 1 
 
3 
If  

!


!


!
			 Find x . 1 
 
4 
Express the function   f : A?R, f(x) = x² - 1, where A = { -4, 0, 1, 4} as a set of ordered pairs. 1 
5 Let   L , M , N be the feet of the perpendiculars drawn from a point P(3,4,5) on the  x , y and z- axes 
respectively. Find the coordinates of L and M. 
1 
 
6 Find the  H.C.F of 		3!,4!,5!		 
1 
 Section B 
 
7 Let A and B be two sets , if  n  n  Ø   and  ?  ?   for some set ,	  prove that  
   A = B. 
OR 
Let A and B  be two sets .Prove that :  
(A-B)?    if and only if B  is subset of A. 
 
4 
8 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of 
these  
(i) Cards of the same colour. 
(ii)  Four cards belong to four different suits. 
(iii) Two are red card and two are black.   
 
4 
9 Redefine the function :  f(x) = |1||6|  .  Write its domain also. 
 
4 
10 Prove the following by the principle of mathematical induction: 
      
( )( )
1 1 1 1
1.3 3.5 5.7 2 1 2 1 2 1
n
n n n
+ + + + =
- + +
K
 
  
4 
XI B Page 2 of 3 
 
 
11 
 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - .  
4 
 
12 
 
If !"# 	


  ,$%!& 	
'(

  where x and y in the second quadrant, find the value of   sin	&.
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
(./0(12
(./0 (1'
 
 
4 
 
13 
Find the domain and range of the real function 3 

2
4
 
OR 
Find the domain and range of the  real function 3 	

'
4

 
4 
 
14 Solve for x:       
('

5
'(
6

('

  ,				 ? 8   and represent the solution on number line. 4 
15 A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting 
mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, 
how many litres of the 2% solution will have to be added?  
 
4 
 
16 If in a ?ABC	,		
=>? 	@
=>?A

=>? @'B
=>? B'A
	.	Prove	that	K
(
,L
(
	
,$
(
		are	in	A.P.	 4 
17 A relation R is defined from a set A={2,3,4,7} to a set B={ 3,6,9,10}  as follows  
    8  
,& ?8 :		is relatively prime to &;	 ? ,& ?  
Express R as a set of ordered pairs and determine the domain and range. 
 
4 
18 How many words can be formed from all the letters of the word ALLAHABAD? How many of these 
words will not contain L together. 
OR 
The letters of the word ‘RANDOM’ are written in all possible orders and these words are written out 
as in dictionary. Find the rank of the word ‘RANDOM’.  
 
4 
19 There are 200 individuals with a skin disorder. 120 had been exposed to chemical C1, 50 to chemical 
C2 and 30 to both C1 and C2. Find the number of individuals exposed to  
(i) Chemical C1 but not Chemical C2 
(ii) Chemical C2 but not Chemical C1 
(iii) Chemical C1 or Chemical C2. 
 
4 
 
Section C  
20 
 Using principle of mathematical induction prove that  
2 2
5 24 25
n
n
+
- - is divisible by 576 for all       
n N ? . 
OR 
Using principle of mathematical induction prove that  
  	!"#O !"#2O!"#3O?sin#O 	
0RST
UVW	
4
X1Y>?
UZ
4
Y>?
Z
4
  for all  # ?[.	 
6 
 
21 (i) Find the general solution of the following equation: 
\K#
(
O1v3\K#Ov3 0 
(ii) Find the value of   cos570°!"#510°sin330°cos390° 
4+2 
XI B Page 3 of 3 
 
 
 
 
 
22 
 
 
In any  ?b  
Show that  :     !"#
(
@
(
!"#
(
B
(
!"#
(
A
(
 12!"#
@
(
!"#
B
(
!"#
A
(
       
 
 
6 
 
23 
  
There are 10 points in a plane, no three of which are in the same straight line, excepting 4 points, 
which are collinear.  
Find : (i) the number of straight  lines obtained from the pair of these points. 
          (ii) the number of triangles that can be formed with the vertices as these points. 
 
6 
24  In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% families buy 
newspaper B and 10% families buy newspaper C. 5% families buy A and B, 3% buy B and C and 4% 
buy A and C. If 2% families buy all the three newspapers, find the number of families which buy: 
 (i) C only  (ii) A but not B.  (iii) none of A, B and C.   
Write certain values which inculcate if a child read newspapers daily. 
 
6 
25 (i) A point R with x – coordinate 4 lies on the line segment joining the points  P (2, -3, 4) and  
Q (8, 0, 10). Find the coordinates of the point R. 
(ii) The mid points of the sides of the triangle are (5,7,11),(0,8,5) and  (2,3,-1).Find its vertices and 
the coordinates of centroid.      
 
2+4 
26 Solve the following system of inequalities graphically:             
  4x + 3y < 60,  y> 2x,  x > 3,  x > 0 , y > 0 
OR 
Solve the following system of inequalities graphically    2& 5 4, & d 3	,				23& e 6 
6 
 
 
 
Mathematics (Set B) (ANSWER KEY)  
Date:                                                  Class: XI 
Time: 3 hrs                                                                      M. M: 100  
 
 
Section A 
1 
Describe the set 
1,


,


,


…….
  in set builder form. 
Ans. 
	 : 


	, ? 
 
1 
2 
In a circle of diameter 40 cm ,the length of a chord is 20cm .Find the length of minor 
arc of the chord. 
Ans.


	 
1 
3 
If  

!


!


!
			 Find x . 
Ans. 64 
1 
4 
Express the function   f : A?R, f(x) = x² - 1, where A = { -4, 0, 1, 4} as a set of ordered 
pairs. 
Ans. { (-4,15),(0,-1),(1,0),(4,15)} 
1 
5 
Let   L , M , N be the feet of the perpendiculars drawn from a point P(3,4,5) on the  x , 
y and z- axes respectively. Find the coordinates of L and M .  
Ans. (3,0,0)  (0,4,0) 
1 
 
6 
Find the  H.C.F of 		3!		4!		5!		" 
Ans 6 
1 
 Section B 
 
 
7 
Let A and B be two sets , if  #n% &n% Ø   and  #?% &?%   for some 
set %,	  prove that  A = B  
OR 
Let A and B  be two sets .Prove that :  
(A-B)?& #  if and only if B  is subset of A. 
Ans. First  take An on both side of #?% &?% we get  
A = AnB……..(2) 
Similarly by taking Bn on both side of #?%  &?% we get  
B = AnB 
Hence A = B ….(2) 
OR 
Consider (A-B)?& # 
Apply formula of A-B and distributive property we get A?B =A 
 So  B  is subset of A…….(2) 
Conversely by taking L.H.S (A-B)?& and using  B  is subset of A we get  R.H.S…..(2) 
 
4 
8 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In 4 
Page 5


XI B Page 1 of 3 
 
 
 
Date:                               Class: XI 
Mathematics (Set - B) 
Time: 3 hours                                              M. M: 100  
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises of 6 
questions of 1 mark each. Section B comprises of 13 questions of 4 marks each and Section C comprises of 7 
questions of 6 marks each. 
3. Use of calculators is not permitted. 
 
Section A 
 
1 
Describe the set 
1	,


,


,


…….  in set builder form. 1 
 
2 In a circle of diameter 40 cm, the length of a chord is 20cm.Find the length of minor arc of the chord. 1 
 
3 
If  

!


!


!
			 Find x . 1 
 
4 
Express the function   f : A?R, f(x) = x² - 1, where A = { -4, 0, 1, 4} as a set of ordered pairs. 1 
5 Let   L , M , N be the feet of the perpendiculars drawn from a point P(3,4,5) on the  x , y and z- axes 
respectively. Find the coordinates of L and M. 
1 
 
6 Find the  H.C.F of 		3!,4!,5!		 
1 
 Section B 
 
7 Let A and B be two sets , if  n  n  Ø   and  ?  ?   for some set ,	  prove that  
   A = B. 
OR 
Let A and B  be two sets .Prove that :  
(A-B)?    if and only if B  is subset of A. 
 
4 
8 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of 
these  
(i) Cards of the same colour. 
(ii)  Four cards belong to four different suits. 
(iii) Two are red card and two are black.   
 
4 
9 Redefine the function :  f(x) = |1||6|  .  Write its domain also. 
 
4 
10 Prove the following by the principle of mathematical induction: 
      
( )( )
1 1 1 1
1.3 3.5 5.7 2 1 2 1 2 1
n
n n n
+ + + + =
- + +
K
 
  
4 
XI B Page 2 of 3 
 
 
11 
 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - .  
4 
 
12 
 
If !"# 	


  ,$%!& 	
'(

  where x and y in the second quadrant, find the value of   sin	&.
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
(./0(12
(./0 (1'
 
 
4 
 
13 
Find the domain and range of the real function 3 

2
4
 
OR 
Find the domain and range of the  real function 3 	

'
4

 
4 
 
14 Solve for x:       
('

5
'(
6

('

  ,				 ? 8   and represent the solution on number line. 4 
15 A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting 
mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, 
how many litres of the 2% solution will have to be added?  
 
4 
 
16 If in a ?ABC	,		
=>? 	@
=>?A

=>? @'B
=>? B'A
	.	Prove	that	K
(
,L
(
	
,$
(
		are	in	A.P.	 4 
17 A relation R is defined from a set A={2,3,4,7} to a set B={ 3,6,9,10}  as follows  
    8  
,& ?8 :		is relatively prime to &;	 ? ,& ?  
Express R as a set of ordered pairs and determine the domain and range. 
 
4 
18 How many words can be formed from all the letters of the word ALLAHABAD? How many of these 
words will not contain L together. 
OR 
The letters of the word ‘RANDOM’ are written in all possible orders and these words are written out 
as in dictionary. Find the rank of the word ‘RANDOM’.  
 
4 
19 There are 200 individuals with a skin disorder. 120 had been exposed to chemical C1, 50 to chemical 
C2 and 30 to both C1 and C2. Find the number of individuals exposed to  
(i) Chemical C1 but not Chemical C2 
(ii) Chemical C2 but not Chemical C1 
(iii) Chemical C1 or Chemical C2. 
 
4 
 
Section C  
20 
 Using principle of mathematical induction prove that  
2 2
5 24 25
n
n
+
- - is divisible by 576 for all       
n N ? . 
OR 
Using principle of mathematical induction prove that  
  	!"#O !"#2O!"#3O?sin#O 	
0RST
UVW	
4
X1Y>?
UZ
4
Y>?
Z
4
  for all  # ?[.	 
6 
 
21 (i) Find the general solution of the following equation: 
\K#
(
O1v3\K#Ov3 0 
(ii) Find the value of   cos570°!"#510°sin330°cos390° 
4+2 
XI B Page 3 of 3 
 
 
 
 
 
22 
 
 
In any  ?b  
Show that  :     !"#
(
@
(
!"#
(
B
(
!"#
(
A
(
 12!"#
@
(
!"#
B
(
!"#
A
(
       
 
 
6 
 
23 
  
There are 10 points in a plane, no three of which are in the same straight line, excepting 4 points, 
which are collinear.  
Find : (i) the number of straight  lines obtained from the pair of these points. 
          (ii) the number of triangles that can be formed with the vertices as these points. 
 
6 
24  In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% families buy 
newspaper B and 10% families buy newspaper C. 5% families buy A and B, 3% buy B and C and 4% 
buy A and C. If 2% families buy all the three newspapers, find the number of families which buy: 
 (i) C only  (ii) A but not B.  (iii) none of A, B and C.   
Write certain values which inculcate if a child read newspapers daily. 
 
6 
25 (i) A point R with x – coordinate 4 lies on the line segment joining the points  P (2, -3, 4) and  
Q (8, 0, 10). Find the coordinates of the point R. 
(ii) The mid points of the sides of the triangle are (5,7,11),(0,8,5) and  (2,3,-1).Find its vertices and 
the coordinates of centroid.      
 
2+4 
26 Solve the following system of inequalities graphically:             
  4x + 3y < 60,  y> 2x,  x > 3,  x > 0 , y > 0 
OR 
Solve the following system of inequalities graphically    2& 5 4, & d 3	,				23& e 6 
6 
 
 
 
Mathematics (Set B) (ANSWER KEY)  
Date:                                                  Class: XI 
Time: 3 hrs                                                                      M. M: 100  
 
 
Section A 
1 
Describe the set 
1,


,


,


…….
  in set builder form. 
Ans. 
	 : 


	, ? 
 
1 
2 
In a circle of diameter 40 cm ,the length of a chord is 20cm .Find the length of minor 
arc of the chord. 
Ans.


	 
1 
3 
If  

!


!


!
			 Find x . 
Ans. 64 
1 
4 
Express the function   f : A?R, f(x) = x² - 1, where A = { -4, 0, 1, 4} as a set of ordered 
pairs. 
Ans. { (-4,15),(0,-1),(1,0),(4,15)} 
1 
5 
Let   L , M , N be the feet of the perpendiculars drawn from a point P(3,4,5) on the  x , 
y and z- axes respectively. Find the coordinates of L and M .  
Ans. (3,0,0)  (0,4,0) 
1 
 
6 
Find the  H.C.F of 		3!		4!		5!		" 
Ans 6 
1 
 Section B 
 
 
7 
Let A and B be two sets , if  #n% &n% Ø   and  #?% &?%   for some 
set %,	  prove that  A = B  
OR 
Let A and B  be two sets .Prove that :  
(A-B)?& #  if and only if B  is subset of A. 
Ans. First  take An on both side of #?% &?% we get  
A = AnB……..(2) 
Similarly by taking Bn on both side of #?%  &?% we get  
B = AnB 
Hence A = B ….(2) 
OR 
Consider (A-B)?& # 
Apply formula of A-B and distributive property we get A?B =A 
 So  B  is subset of A…….(2) 
Conversely by taking L.H.S (A-B)?& and using  B  is subset of A we get  R.H.S…..(2) 
 
4 
8 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In 4 
many of these  
(i)     Cards of the same colour. 
(ii)     Four cards belong to four different suits. 
(iii) Two are red card and two are black.   
Ans.    270725 
           (i) 29900 
             (ii)  13×13×13×1328561	
            (iii)325×325		105625 
9 
Redefine the function :  f(x) = |/1|/|6|  .  Write its domain also. 
Ans.  f(x) = |/1|/|6|   
 Redefine  f(x) =  7    x=-6 
                         -2x-5   -6= x <1 
                        -7    x= 1                  Domain of this function is R .  (3+1) 
4 
 
10 
Prove the following by the principle of mathematical induction: 
      
( )( )
1 1 1 1
1.3 3.5 5.7 2 1 2 1 2 1
n
n n n
+ + + + =
- + +
K
 
 Ans. statement is true for n =1,   ………   (1mark) 
suppose for  n = k then prove for n = k+1 .  ………    (1marks) 
Hence by PMI  it is true for n = k+1  (2mark) 
 Using PMI, hence proved. 
 
4 
11 
 
Find the coordinates of the points which trisect the line segment joining the points 
( ) 4,2, 6 P - and ( ) 10, 16,6 Q - .  
Ans. Using section formula  
A = (6,-4,-2)  and B = (8,-10,2) 
4 
12 
 
If 34	


  ,536	


  where x and y in the second quadrant , find the value of   
sin	6".
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
<=>?@
<=>?
 
Ans. Cosx /
B

  ….(1.5) 
 siny 


  …..(1.5) 
sin (x+y) = -56/65   ….(1)  
OR 
Ans write tan in terms of sin and cos   
Then multiply and divide by 2  
Apply trigonometric formulas we get …………..(2) 
DEF?DEF°
DEF?@DEF
	
<=> ?@
<=> ?
……………….(2) 
4 
13 
Find the domain and range of the real function G"

@
H
 
OR 
Find the domain and range of the  real function G"	


H
"
 
Ans. Domain  = R     
Range = [-1/2,1/2]      ……(1+3) 
4