Class 11 Mathematics (Maths) Previous Year Paper - 5 | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


XI A Page 1 of 3 
 
 
 
Date:                              Class: XI 
Mathematics (Set - A) 
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 
Write the set 	1	,


,


,


……. in the set builder form. 1 
 
2 If 
1 1
,
9! 10! 11!
x
+ = find x . 1 
3 Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes 
an arc of length 21 cm. 
1 
 
4 Find the  L.C.M. of 		6!	,8!	,7!	 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 N. 
1 
 
6 Express the function   f : A?R, f(x) = x² - 1, where A = { -2, 0, 3, 4} as a set of ordered pairs. 
1 
 Section B 
 
7 
Prove the following by the principle of mathematical induction: 
      
( ) ( )( )
1
1.3 2.4 3.5 . 2 1 2 7
6
n n n n n + + + + = + + K 
4 
 
8 If in a ?ABC	,		
	




	.	Prove	that	&
'
,(
'
	
,)
'
		are	in	A.P.	
 
4 
9 How many words can be formed using 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 
10 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 
Page 2


XI A Page 1 of 3 
 
 
 
Date:                              Class: XI 
Mathematics (Set - A) 
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 
Write the set 	1	,


,


,


……. in the set builder form. 1 
 
2 If 
1 1
,
9! 10! 11!
x
+ = find x . 1 
3 Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes 
an arc of length 21 cm. 
1 
 
4 Find the  L.C.M. of 		6!	,8!	,7!	 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 N. 
1 
 
6 Express the function   f : A?R, f(x) = x² - 1, where A = { -2, 0, 3, 4} as a set of ordered pairs. 
1 
 Section B 
 
7 
Prove the following by the principle of mathematical induction: 
      
( ) ( )( )
1
1.3 2.4 3.5 . 2 1 2 7
6
n n n n n + + + + = + + K 
4 
 
8 If in a ?ABC	,		
	




	.	Prove	that	&
'
,(
'
	
,)
'
		are	in	A.P.	
 
4 
9 How many words can be formed using 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 
10 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 
XI A Page 2 of 3 
 
 
11 
 
Redefine the function :  f(x) = |34 1|5 |35 5| . Write its domain also. 4 
 
12 
 
Solve for x  :    235 1	8 34
9

  8 2	,				3 ? ; . Represent the solution on number line.                 4 
 
13 If 
3
cos
5
x = - and x lies in the III rd quadrant, find the values of cos ,sin ,sin 2
2 2
x x
x
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
'>?@'AB
'>?@'A
  
4 
 
14 
Find the domain and range of the real function C3 
9
B9
D
 
OR 
Find the domain and range of the  real function C3 	

9
D

  
 
4 
15 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 
16 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In  how many of 
these  
(i)     Four cards of four different suits. 
(ii)     Four cards of the same suit. 
(iii)    Are face cards. 
 
4 
 
17 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - . 
 
4 
18 A relation R is defined from a set A ={2,3,4,5} to a set B  ={ 3,6,7,10}  as follows :  
;  3,E ? ; : 3		is relatively prime to E;		3 ? , ,E ? /. Express R as a set of ordered pairs and 
determine the domain and range. 
 
4 
19 A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must 
be added to it so that the acid content in the resulting mixture will be more than 15% but less than 
18%? 
4 
 
Section C  
20  Solve the following system of inequalities graphically:             
  4x + 3y < 60,  y > 2x,  x 8 3 
OR 
Solve the following system of inequalities graphically:         
    234 E H 2, 35 E I 1	,			34 2E J 8 
6 
Page 3


XI A Page 1 of 3 
 
 
 
Date:                              Class: XI 
Mathematics (Set - A) 
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 
Write the set 	1	,


,


,


……. in the set builder form. 1 
 
2 If 
1 1
,
9! 10! 11!
x
+ = find x . 1 
3 Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes 
an arc of length 21 cm. 
1 
 
4 Find the  L.C.M. of 		6!	,8!	,7!	 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 N. 
1 
 
6 Express the function   f : A?R, f(x) = x² - 1, where A = { -2, 0, 3, 4} as a set of ordered pairs. 
1 
 Section B 
 
7 
Prove the following by the principle of mathematical induction: 
      
( ) ( )( )
1
1.3 2.4 3.5 . 2 1 2 7
6
n n n n n + + + + = + + K 
4 
 
8 If in a ?ABC	,		
	




	.	Prove	that	&
'
,(
'
	
,)
'
		are	in	A.P.	
 
4 
9 How many words can be formed using 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 
10 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 
XI A Page 2 of 3 
 
 
11 
 
Redefine the function :  f(x) = |34 1|5 |35 5| . Write its domain also. 4 
 
12 
 
Solve for x  :    235 1	8 34
9

  8 2	,				3 ? ; . Represent the solution on number line.                 4 
 
13 If 
3
cos
5
x = - and x lies in the III rd quadrant, find the values of cos ,sin ,sin 2
2 2
x x
x
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
'>?@'AB
'>?@'A
  
4 
 
14 
Find the domain and range of the real function C3 
9
B9
D
 
OR 
Find the domain and range of the  real function C3 	

9
D

  
 
4 
15 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 
16 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In  how many of 
these  
(i)     Four cards of four different suits. 
(ii)     Four cards of the same suit. 
(iii)    Are face cards. 
 
4 
 
17 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - . 
 
4 
18 A relation R is defined from a set A ={2,3,4,5} to a set B  ={ 3,6,7,10}  as follows :  
;  3,E ? ; : 3		is relatively prime to E;		3 ? , ,E ? /. Express R as a set of ordered pairs and 
determine the domain and range. 
 
4 
19 A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must 
be added to it so that the acid content in the resulting mixture will be more than 15% but less than 
18%? 
4 
 
Section C  
20  Solve the following system of inequalities graphically:             
  4x + 3y < 60,  y > 2x,  x 8 3 
OR 
Solve the following system of inequalities graphically:         
    234 E H 2, 35 E I 1	,			34 2E J 8 
6 
XI A Page 3 of 3 
 
 
21 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 
 
22 
 
In any  ?,/K  
Show that  :     LMN
'

'
4 LMN
'

'
4 LMN
'

'
 15 2LMN

'
LMN

'
LMN

'
   
6 
 
23 
(i)  Find the general solution of the following equation: 
 
0 3
sin
3
cot
2
= + +
?
? 
(ii) Find the value of   tan225°)OP405°4 P&N765°)OP675° 
4+2 
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) A only  (ii) B only   (iii) none of A, B and C.   
Write certain values which inculcate if a child read newspapers daily.  
6 
 
 
25 Using principle of mathematical induction prove that  
2 3 3 1
7 2 .3
n n n - - + is divisible by 25 for all N ? S.	 
OR 
Using principle of mathematical induction prove that  
  	LMNT4 LMN2T4 LMN3T4 ?4 sinNT 	
@XYZ
[\]	
D
^A	_
[`
D
_
`
D
  for all  N ? S.	 
6 
26 (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 
 
 
Page 4


XI A Page 1 of 3 
 
 
 
Date:                              Class: XI 
Mathematics (Set - A) 
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 
Write the set 	1	,


,


,


……. in the set builder form. 1 
 
2 If 
1 1
,
9! 10! 11!
x
+ = find x . 1 
3 Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes 
an arc of length 21 cm. 
1 
 
4 Find the  L.C.M. of 		6!	,8!	,7!	 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 N. 
1 
 
6 Express the function   f : A?R, f(x) = x² - 1, where A = { -2, 0, 3, 4} as a set of ordered pairs. 
1 
 Section B 
 
7 
Prove the following by the principle of mathematical induction: 
      
( ) ( )( )
1
1.3 2.4 3.5 . 2 1 2 7
6
n n n n n + + + + = + + K 
4 
 
8 If in a ?ABC	,		
	




	.	Prove	that	&
'
,(
'
	
,)
'
		are	in	A.P.	
 
4 
9 How many words can be formed using 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 
10 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 
XI A Page 2 of 3 
 
 
11 
 
Redefine the function :  f(x) = |34 1|5 |35 5| . Write its domain also. 4 
 
12 
 
Solve for x  :    235 1	8 34
9

  8 2	,				3 ? ; . Represent the solution on number line.                 4 
 
13 If 
3
cos
5
x = - and x lies in the III rd quadrant, find the values of cos ,sin ,sin 2
2 2
x x
x
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
'>?@'AB
'>?@'A
  
4 
 
14 
Find the domain and range of the real function C3 
9
B9
D
 
OR 
Find the domain and range of the  real function C3 	

9
D

  
 
4 
15 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 
16 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In  how many of 
these  
(i)     Four cards of four different suits. 
(ii)     Four cards of the same suit. 
(iii)    Are face cards. 
 
4 
 
17 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - . 
 
4 
18 A relation R is defined from a set A ={2,3,4,5} to a set B  ={ 3,6,7,10}  as follows :  
;  3,E ? ; : 3		is relatively prime to E;		3 ? , ,E ? /. Express R as a set of ordered pairs and 
determine the domain and range. 
 
4 
19 A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must 
be added to it so that the acid content in the resulting mixture will be more than 15% but less than 
18%? 
4 
 
Section C  
20  Solve the following system of inequalities graphically:             
  4x + 3y < 60,  y > 2x,  x 8 3 
OR 
Solve the following system of inequalities graphically:         
    234 E H 2, 35 E I 1	,			34 2E J 8 
6 
XI A Page 3 of 3 
 
 
21 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 
 
22 
 
In any  ?,/K  
Show that  :     LMN
'

'
4 LMN
'

'
4 LMN
'

'
 15 2LMN

'
LMN

'
LMN

'
   
6 
 
23 
(i)  Find the general solution of the following equation: 
 
0 3
sin
3
cot
2
= + +
?
? 
(ii) Find the value of   tan225°)OP405°4 P&N765°)OP675° 
4+2 
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) A only  (ii) B only   (iii) none of A, B and C.   
Write certain values which inculcate if a child read newspapers daily.  
6 
 
 
25 Using principle of mathematical induction prove that  
2 3 3 1
7 2 .3
n n n - - + is divisible by 25 for all N ? S.	 
OR 
Using principle of mathematical induction prove that  
  	LMNT4 LMN2T4 LMN3T4 ?4 sinNT 	
@XYZ
[\]	
D
^A	_
[`
D
_
`
D
  for all  N ? S.	 
6 
26 (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 
 
 
Mathematics (Set A) (ANSWER KEY)  
Date:                                          Class: XI 
Time: 3 hrs                                                                        M. M: 100  
 
 
Section A 
1 
Write the set 	1	,


,


,


……. in the set builder form. 
Ans.  {x: x = 




	,? 
1 
2 
If 
1 1
,
9! 10! 11!
x
+ = find x . 
Ans.  121 
1 
3 
Find the angle in radian through which a pendulum swings if its length is 75 cm and the 
tip describes an arc of length 21 cm. 
Ans. 7/25 
1 
4 
Find the  L.C.M. of 		6!		8!		7!	 
Ans. 8!		 
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 N . 
Ans. (3,0,0)  (0,0,5) 
1 
 
6 
Express the function   f : A?R, f(x) = x² - 1, where A = { -2, 0, 3, 4} as a set of ordered 
pairs . 
Ans.{ (-2,3),(0,-1),(3,8),(4,15)} 
1 
 Section B 
 
 
7 
Prove the following by the principle of mathematical induction: 
      
( ) ( )( )
1
1.3 2.4 3.5 . 2 1 2 7
6
n 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 
8 
If in a ?ABC	,		
	
 
!
"
" 
	.	Prove	that	+

,,

	
,-

		are	in	A.P.	
Ans.	Use	sine	formula	and	substitute	the	value	of	A	and	C	in	L.H.S	
We	get	=>

?@=>

A! 	=>

B@=>

?	use	sine	formula	again		
We	get	the	result.2+2 
4 
9 
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 
4 
Page 5


XI A Page 1 of 3 
 
 
 
Date:                              Class: XI 
Mathematics (Set - A) 
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 
Write the set 	1	,


,


,


……. in the set builder form. 1 
 
2 If 
1 1
,
9! 10! 11!
x
+ = find x . 1 
3 Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes 
an arc of length 21 cm. 
1 
 
4 Find the  L.C.M. of 		6!	,8!	,7!	 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 N. 
1 
 
6 Express the function   f : A?R, f(x) = x² - 1, where A = { -2, 0, 3, 4} as a set of ordered pairs. 
1 
 Section B 
 
7 
Prove the following by the principle of mathematical induction: 
      
( ) ( )( )
1
1.3 2.4 3.5 . 2 1 2 7
6
n n n n n + + + + = + + K 
4 
 
8 If in a ?ABC	,		
	




	.	Prove	that	&
'
,(
'
	
,)
'
		are	in	A.P.	
 
4 
9 How many words can be formed using 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 
10 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 
XI A Page 2 of 3 
 
 
11 
 
Redefine the function :  f(x) = |34 1|5 |35 5| . Write its domain also. 4 
 
12 
 
Solve for x  :    235 1	8 34
9

  8 2	,				3 ? ; . Represent the solution on number line.                 4 
 
13 If 
3
cos
5
x = - and x lies in the III rd quadrant, find the values of cos ,sin ,sin 2
2 2
x x
x
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
'>?@'AB
'>?@'A
  
4 
 
14 
Find the domain and range of the real function C3 
9
B9
D
 
OR 
Find the domain and range of the  real function C3 	

9
D

  
 
4 
15 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 
16 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In  how many of 
these  
(i)     Four cards of four different suits. 
(ii)     Four cards of the same suit. 
(iii)    Are face cards. 
 
4 
 
17 
Find the coordinates of the points which trisect the line segment joining the points ( ) 4,2, 6 P - and 
( ) 10, 16,6 Q - . 
 
4 
18 A relation R is defined from a set A ={2,3,4,5} to a set B  ={ 3,6,7,10}  as follows :  
;  3,E ? ; : 3		is relatively prime to E;		3 ? , ,E ? /. Express R as a set of ordered pairs and 
determine the domain and range. 
 
4 
19 A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must 
be added to it so that the acid content in the resulting mixture will be more than 15% but less than 
18%? 
4 
 
Section C  
20  Solve the following system of inequalities graphically:             
  4x + 3y < 60,  y > 2x,  x 8 3 
OR 
Solve the following system of inequalities graphically:         
    234 E H 2, 35 E I 1	,			34 2E J 8 
6 
XI A Page 3 of 3 
 
 
21 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 
 
22 
 
In any  ?,/K  
Show that  :     LMN
'

'
4 LMN
'

'
4 LMN
'

'
 15 2LMN

'
LMN

'
LMN

'
   
6 
 
23 
(i)  Find the general solution of the following equation: 
 
0 3
sin
3
cot
2
= + +
?
? 
(ii) Find the value of   tan225°)OP405°4 P&N765°)OP675° 
4+2 
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) A only  (ii) B only   (iii) none of A, B and C.   
Write certain values which inculcate if a child read newspapers daily.  
6 
 
 
25 Using principle of mathematical induction prove that  
2 3 3 1
7 2 .3
n n n - - + is divisible by 25 for all N ? S.	 
OR 
Using principle of mathematical induction prove that  
  	LMNT4 LMN2T4 LMN3T4 ?4 sinNT 	
@XYZ
[\]	
D
^A	_
[`
D
_
`
D
  for all  N ? S.	 
6 
26 (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 
 
 
Mathematics (Set A) (ANSWER KEY)  
Date:                                          Class: XI 
Time: 3 hrs                                                                        M. M: 100  
 
 
Section A 
1 
Write the set 	1	,


,


,


……. in the set builder form. 
Ans.  {x: x = 




	,? 
1 
2 
If 
1 1
,
9! 10! 11!
x
+ = find x . 
Ans.  121 
1 
3 
Find the angle in radian through which a pendulum swings if its length is 75 cm and the 
tip describes an arc of length 21 cm. 
Ans. 7/25 
1 
4 
Find the  L.C.M. of 		6!		8!		7!	 
Ans. 8!		 
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 N . 
Ans. (3,0,0)  (0,0,5) 
1 
 
6 
Express the function   f : A?R, f(x) = x² - 1, where A = { -2, 0, 3, 4} as a set of ordered 
pairs . 
Ans.{ (-2,3),(0,-1),(3,8),(4,15)} 
1 
 Section B 
 
 
7 
Prove the following by the principle of mathematical induction: 
      
( ) ( )( )
1
1.3 2.4 3.5 . 2 1 2 7
6
n 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 
8 
If in a ?ABC	,		
	
 
!
"
" 
	.	Prove	that	+

,,

	
,-

		are	in	A.P.	
Ans.	Use	sine	formula	and	substitute	the	value	of	A	and	C	in	L.H.S	
We	get	=>

?@=>

A! 	=>

B@=>

?	use	sine	formula	again		
We	get	the	result.2+2 
4 
9 
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 
4 
are written out as in dictionary. Find the rank of the word ‘RANDOM’. 
Ans.				EFG	HIJ	K>G=H	L+GH 			B=.7560...(1.5) 
EFG	HIJ	=J-FO	L+GH										
P!
Q!!
@
R!
Q!
!5880   ….(2.5) 
OR 
Rank of the word RANDOM = 5×120+2×6+2 =614     (1+1+1+1) 
 
10 
Let A and B be two sets , if  BnU! ?nU! Ø   and  B?U! ??U   for some 
set U,	  prove that  A = B .  
OR 
Let A and B  be two sets .Prove that :  
(A-B)??!B  if and only if B  is subset of A. 
 
Ans.  First  take An on both side of B?U !??U we get  
A = AnB……..(2) 
Similarly by taking Bn on both side of B?U!??U we get  
B = AnB 
Hence A = B ….(2) 
OR 
Consider (A-B)?? !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 
11 
 
Redefine the function :  f(x) = |Y+1|@|Y@5|  .  Write its domain also. 
Ans.   f(x) = |Y+1|@|Y@5|   
 Redefine  f(x) =   -6    x=-1 
                         2x-4   -1 = x <5 
                         6           x= 5                  Domain of this function is R .  (3+1) 
4 
12 
 
Solve for x  :    2Y@1	]Y+
^

  ]2	,				Y?_. Represent the solution on number 
line.                 
 Ans.Solve the inequality  we get   -1/2 < x < 5/2    
Represent the solution on number line. (2.5 +1.5) 
 
4 
13 
If 
3
cos
5
x = - and x lies in the III rd quadrant, find the values of cos ,sin ,sin 2
2 2
x x
x
 
OR 
Show that  : tan(60°+?)tan(60°-?) = 
bcdef
bcde
 
Ans.   Cos
^

!@

v
  ….(1.5) 
 sin
^

!

v
  …..(1.5) 
sin 2x = -24/25   ….(1)  
OR 
4