Class 11 Mathematics (Maths) Previous Year Paper - 4 | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


  
 
 
                  
                   - 
 
                                        Class: XI 
Mathematics(041) (Set –B) 
 
Time: 3 hrs                                                                        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 Three vertices of a parallelogram ABCD are
? ? 3, 1,2 A ? , 
? ? 1,2, 4 B ? and 
? ? 1,1,2 C ? . Find the 
coordinates of the fourth vertex. 
1 
  2 
Find the multiplicative inverse of the complex numberv     
1 
3 
Reduce the equation v          in normal form. 
1 
  4 Write the converse of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
  5 Find the component statements of the following and check whether they are true or not. 
“A rectangle is a quadrilateral or a 5 sided polygon’’ 1 
 
6 
 Evaluate : 
0
1 3 1 3
lim
x
xx
x
?
? ? ?
 1 
 Section B 
 
7 
 
 
Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 
8. 
4 
  8 Let A ={1,2,3,4,6}.Let R be a relation on A defined by      
? ? ? ?
, : , , is exactly divisible by a b a b A b a ? 
                (i) Write R in Roster form (ii) Find the domain of R 
(iii) Find the range of R . 
4 
  9 Find n ,if the ratio of  fifth term from the beginning to the fifth term from the end in the expansion of    
 v 
 
  
 
v 
 
 
 
  is v    
4 
 
10 Evaluate:    
? ? ? ?
0
sec sec
lim
y
x y x y x x
y
?
? ? ?
 
OR 
Evaluate:       
     
         
 
4 
11 
 
A survey shows that 63% of the American like cheese where 76% like apples. If x% of the Americans 
like both cheese and apples, find the value of x. 
OR 
In a survey of 600 students in a school, 150 students were found to be drinking Tea  and 225 drinking 
4 
Page 2


  
 
 
                  
                   - 
 
                                        Class: XI 
Mathematics(041) (Set –B) 
 
Time: 3 hrs                                                                        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 Three vertices of a parallelogram ABCD are
? ? 3, 1,2 A ? , 
? ? 1,2, 4 B ? and 
? ? 1,1,2 C ? . Find the 
coordinates of the fourth vertex. 
1 
  2 
Find the multiplicative inverse of the complex numberv     
1 
3 
Reduce the equation v          in normal form. 
1 
  4 Write the converse of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
  5 Find the component statements of the following and check whether they are true or not. 
“A rectangle is a quadrilateral or a 5 sided polygon’’ 1 
 
6 
 Evaluate : 
0
1 3 1 3
lim
x
xx
x
?
? ? ?
 1 
 Section B 
 
7 
 
 
Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 
8. 
4 
  8 Let A ={1,2,3,4,6}.Let R be a relation on A defined by      
? ? ? ?
, : , , is exactly divisible by a b a b A b a ? 
                (i) Write R in Roster form (ii) Find the domain of R 
(iii) Find the range of R . 
4 
  9 Find n ,if the ratio of  fifth term from the beginning to the fifth term from the end in the expansion of    
 v 
 
  
 
v 
 
 
 
  is v    
4 
 
10 Evaluate:    
? ? ? ?
0
sec sec
lim
y
x y x y x x
y
?
? ? ?
 
OR 
Evaluate:       
     
         
 
4 
11 
 
A survey shows that 63% of the American like cheese where 76% like apples. If x% of the Americans 
like both cheese and apples, find the value of x. 
OR 
In a survey of 600 students in a school, 150 students were found to be drinking Tea  and 225 drinking 
4 
XI B 2 of 3 
 
coffee,100 were drinking both Tea and coffee. Find how many students were drinking neither Tea nor 
Coffee. 
12 
 
Find the ratio in which the join of A (1,2,3) and B(-3,4,-5)  is divided by the     plane 
Also ,find the coordinates of the point of division. 
4 
 
 
13 
 Prove that  
tan tan
44
cosec 2
tan tan
44
AA
AA
??
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
. 
OR 
In any triangle ABC , If  a cos A = b cos B,  Show that the triangle is either isosceles or right angled. 
 
4 
14 
Find the equation of the circle which passes through the points (1,3) and (2,-1), and has its centre on 
the line 2x+ y -4 =0. 
OR 
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the 
eccentricity and the length of the latus rectum of the ellipse: 400 25 16
2 2
? ? y x . 
4 
 
15 Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0)   
to the line    
 
 
      
 
 
           is  
 
  
 
4 
 
16 Using the Principle of Mathematical Induction prove the following for all : N n ? 
   ? ?
2
2
1
1 2
1 ....
9
7
1
4
5
1
1
3
1 ? ? ?
?
?
?
?
? ?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? n
n
n
  
4 
 
17 How many four letter words can be formed using the letter of the word INEFFECTIVE. 4 
 
18 If       
 
       then show that    
 
 
 
 
 
    
 
  
 
   
4 
19 Find the equation of line passing through the point of intersection of two lines 
                and having y intercept equal to 4. 
4 
 
Section C  
 
20 Prove that :                                  
 
 
        
6 
 
21 
Find the sum of n term of the series:
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
            
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
6 
22 Find the mean deviation about median of the following data: 
Height 
(in cm) 
95-105 105-115 115-125 125-135 135-145 145-155 
Number of 
boys 
9 13 25 30 13 10 
OR 
Given below the diameters of the circles (in mm) drawn in a design . 
Diameter 33-36 37-40 41-44 45-48 49-52 
Number of 
circles 
15 17 21 22 25 
Calculate the mean diameter of the circles and variance. 
6 
Page 3


  
 
 
                  
                   - 
 
                                        Class: XI 
Mathematics(041) (Set –B) 
 
Time: 3 hrs                                                                        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 Three vertices of a parallelogram ABCD are
? ? 3, 1,2 A ? , 
? ? 1,2, 4 B ? and 
? ? 1,1,2 C ? . Find the 
coordinates of the fourth vertex. 
1 
  2 
Find the multiplicative inverse of the complex numberv     
1 
3 
Reduce the equation v          in normal form. 
1 
  4 Write the converse of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
  5 Find the component statements of the following and check whether they are true or not. 
“A rectangle is a quadrilateral or a 5 sided polygon’’ 1 
 
6 
 Evaluate : 
0
1 3 1 3
lim
x
xx
x
?
? ? ?
 1 
 Section B 
 
7 
 
 
Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 
8. 
4 
  8 Let A ={1,2,3,4,6}.Let R be a relation on A defined by      
? ? ? ?
, : , , is exactly divisible by a b a b A b a ? 
                (i) Write R in Roster form (ii) Find the domain of R 
(iii) Find the range of R . 
4 
  9 Find n ,if the ratio of  fifth term from the beginning to the fifth term from the end in the expansion of    
 v 
 
  
 
v 
 
 
 
  is v    
4 
 
10 Evaluate:    
? ? ? ?
0
sec sec
lim
y
x y x y x x
y
?
? ? ?
 
OR 
Evaluate:       
     
         
 
4 
11 
 
A survey shows that 63% of the American like cheese where 76% like apples. If x% of the Americans 
like both cheese and apples, find the value of x. 
OR 
In a survey of 600 students in a school, 150 students were found to be drinking Tea  and 225 drinking 
4 
XI B 2 of 3 
 
coffee,100 were drinking both Tea and coffee. Find how many students were drinking neither Tea nor 
Coffee. 
12 
 
Find the ratio in which the join of A (1,2,3) and B(-3,4,-5)  is divided by the     plane 
Also ,find the coordinates of the point of division. 
4 
 
 
13 
 Prove that  
tan tan
44
cosec 2
tan tan
44
AA
AA
??
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
. 
OR 
In any triangle ABC , If  a cos A = b cos B,  Show that the triangle is either isosceles or right angled. 
 
4 
14 
Find the equation of the circle which passes through the points (1,3) and (2,-1), and has its centre on 
the line 2x+ y -4 =0. 
OR 
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the 
eccentricity and the length of the latus rectum of the ellipse: 400 25 16
2 2
? ? y x . 
4 
 
15 Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0)   
to the line    
 
 
      
 
 
           is  
 
  
 
4 
 
16 Using the Principle of Mathematical Induction prove the following for all : N n ? 
   ? ?
2
2
1
1 2
1 ....
9
7
1
4
5
1
1
3
1 ? ? ?
?
?
?
?
? ?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? n
n
n
  
4 
 
17 How many four letter words can be formed using the letter of the word INEFFECTIVE. 4 
 
18 If       
 
       then show that    
 
 
 
 
 
    
 
  
 
   
4 
19 Find the equation of line passing through the point of intersection of two lines 
                and having y intercept equal to 4. 
4 
 
Section C  
 
20 Prove that :                                  
 
 
        
6 
 
21 
Find the sum of n term of the series:
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
            
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
6 
22 Find the mean deviation about median of the following data: 
Height 
(in cm) 
95-105 105-115 115-125 125-135 135-145 145-155 
Number of 
boys 
9 13 25 30 13 10 
OR 
Given below the diameters of the circles (in mm) drawn in a design . 
Diameter 33-36 37-40 41-44 45-48 49-52 
Number of 
circles 
15 17 21 22 25 
Calculate the mean diameter of the circles and variance. 
6 
XI B 3 of 3 
 
 
23 (i) Differentiate             using first principle. 
(ii)  For the function    given by       
 
       prove that 
 
 
      
 
     
 
    
4+2 
 
24 
a) If 4 digit  numbers greater than 5000 are randomly formed from the digits 0,1,3,5,and 7  what 
is the probability of forming a number divisible by 5 when  
(i) the digits are repeated? 
      (ii) the repetition of digits is not allowed? 
b) The probability that a person will get an electric contract is 
 
 
 and the probability that he will 
not get a plumbing contract is 
 
 
.  If the probability of getting atleast one contract is 
 
 
  what is 
the probability that he will get both? 
 
4+2 
25       Solve the following system of linear inequality graphically: 
x + 2y = 6  ,  2x + y = 6  ,  x = 1  ,  y = 1 
 
6 
 26       Differentiate the following w.r.t. x  
(i) 
         
         
 
(ii) v     
 
      ) 
(iii)
 
   
      
    
 
 
2+2+
2 
 
 
Page 4


  
 
 
                  
                   - 
 
                                        Class: XI 
Mathematics(041) (Set –B) 
 
Time: 3 hrs                                                                        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 Three vertices of a parallelogram ABCD are
? ? 3, 1,2 A ? , 
? ? 1,2, 4 B ? and 
? ? 1,1,2 C ? . Find the 
coordinates of the fourth vertex. 
1 
  2 
Find the multiplicative inverse of the complex numberv     
1 
3 
Reduce the equation v          in normal form. 
1 
  4 Write the converse of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
  5 Find the component statements of the following and check whether they are true or not. 
“A rectangle is a quadrilateral or a 5 sided polygon’’ 1 
 
6 
 Evaluate : 
0
1 3 1 3
lim
x
xx
x
?
? ? ?
 1 
 Section B 
 
7 
 
 
Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 
8. 
4 
  8 Let A ={1,2,3,4,6}.Let R be a relation on A defined by      
? ? ? ?
, : , , is exactly divisible by a b a b A b a ? 
                (i) Write R in Roster form (ii) Find the domain of R 
(iii) Find the range of R . 
4 
  9 Find n ,if the ratio of  fifth term from the beginning to the fifth term from the end in the expansion of    
 v 
 
  
 
v 
 
 
 
  is v    
4 
 
10 Evaluate:    
? ? ? ?
0
sec sec
lim
y
x y x y x x
y
?
? ? ?
 
OR 
Evaluate:       
     
         
 
4 
11 
 
A survey shows that 63% of the American like cheese where 76% like apples. If x% of the Americans 
like both cheese and apples, find the value of x. 
OR 
In a survey of 600 students in a school, 150 students were found to be drinking Tea  and 225 drinking 
4 
XI B 2 of 3 
 
coffee,100 were drinking both Tea and coffee. Find how many students were drinking neither Tea nor 
Coffee. 
12 
 
Find the ratio in which the join of A (1,2,3) and B(-3,4,-5)  is divided by the     plane 
Also ,find the coordinates of the point of division. 
4 
 
 
13 
 Prove that  
tan tan
44
cosec 2
tan tan
44
AA
AA
??
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
. 
OR 
In any triangle ABC , If  a cos A = b cos B,  Show that the triangle is either isosceles or right angled. 
 
4 
14 
Find the equation of the circle which passes through the points (1,3) and (2,-1), and has its centre on 
the line 2x+ y -4 =0. 
OR 
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the 
eccentricity and the length of the latus rectum of the ellipse: 400 25 16
2 2
? ? y x . 
4 
 
15 Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0)   
to the line    
 
 
      
 
 
           is  
 
  
 
4 
 
16 Using the Principle of Mathematical Induction prove the following for all : N n ? 
   ? ?
2
2
1
1 2
1 ....
9
7
1
4
5
1
1
3
1 ? ? ?
?
?
?
?
? ?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? n
n
n
  
4 
 
17 How many four letter words can be formed using the letter of the word INEFFECTIVE. 4 
 
18 If       
 
       then show that    
 
 
 
 
 
    
 
  
 
   
4 
19 Find the equation of line passing through the point of intersection of two lines 
                and having y intercept equal to 4. 
4 
 
Section C  
 
20 Prove that :                                  
 
 
        
6 
 
21 
Find the sum of n term of the series:
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
            
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
6 
22 Find the mean deviation about median of the following data: 
Height 
(in cm) 
95-105 105-115 115-125 125-135 135-145 145-155 
Number of 
boys 
9 13 25 30 13 10 
OR 
Given below the diameters of the circles (in mm) drawn in a design . 
Diameter 33-36 37-40 41-44 45-48 49-52 
Number of 
circles 
15 17 21 22 25 
Calculate the mean diameter of the circles and variance. 
6 
XI B 3 of 3 
 
 
23 (i) Differentiate             using first principle. 
(ii)  For the function    given by       
 
       prove that 
 
 
      
 
     
 
    
4+2 
 
24 
a) If 4 digit  numbers greater than 5000 are randomly formed from the digits 0,1,3,5,and 7  what 
is the probability of forming a number divisible by 5 when  
(i) the digits are repeated? 
      (ii) the repetition of digits is not allowed? 
b) The probability that a person will get an electric contract is 
 
 
 and the probability that he will 
not get a plumbing contract is 
 
 
.  If the probability of getting atleast one contract is 
 
 
  what is 
the probability that he will get both? 
 
4+2 
25       Solve the following system of linear inequality graphically: 
x + 2y = 6  ,  2x + y = 6  ,  x = 1  ,  y = 1 
 
6 
 26       Differentiate the following w.r.t. x  
(i) 
         
         
 
(ii) v     
 
      ) 
(iii)
 
   
      
    
 
 
2+2+
2 
 
 
Mathematics answer key(Set –B) 
Date:                                           Class: XI 
Time: 3 hours                                                              M. M: 100  
 
 
Section A 
1 
Three vertices of a parallelogram ABCD are
? ? 3, 1,2 A ? , 
? ? 1,2, 4 B ? and 
? ? 1,1,2 C ? . Find the 
coordinates of the fourth vertex. 
Ans. (1,-2,8) 
 
2 
Find the multiplicative inverse of the complex numberv     
Ans.
v    
 
 
 
3 
Reduce the equation v          in normal form 
Ans.                      
 
4 
Write the converse of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
Ans. “ If you are not true Indian then you are taking part in violent processions” 
 
5 
Find the component statements of the following and check whether they are true or not. 
“A rectangle is a quadrilateral or a 5 sided polygon’’ 
Ans. p: A rectangle is a quadrilateral 
    q: A rectangle is a 5 sided polygon   true 
 
 
6 
 Evaluate : 
0
1 3 1 3
lim
x
xx
x
?
? ? ?
 
Ans. 3
 
 
 Section B 
 
 
7 
Two dice are thrown once. Find the probability of getting an even number on the first 
die or a total of 8. 
Ans. Let A  denotes getting an even number on the first die  and B denotes a total of 8 
 P(A) = 18/36    
P(B) = 5/36  P(AnB) = 3/36   …..(1) 
Using formula  we get P(A?B)   5/9…………….( ) 
 
 
8 
Let A {1,2,3,4,6} .Let R be a relation on A defined by      
? ? ? ?
, : , , is exactly divisible by a b a b A b a ? 
             (i) Write R in Roster form (ii) Find the domain of R 
(iii) Find the range of R . 
 Ans. For roster form   (2 marks) 
        Domain = {1,2,3,4,6} 
        Range = {1,2,3,4,6}……………..(1+1) 
 
9 
Find n ,if the ratio of  fifth term from the beginning to the fifth term from the end in the 
expansion of    (v 
 
  
 
v 
 
)
 
  is v    
 
Page 5


  
 
 
                  
                   - 
 
                                        Class: XI 
Mathematics(041) (Set –B) 
 
Time: 3 hrs                                                                        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 Three vertices of a parallelogram ABCD are
? ? 3, 1,2 A ? , 
? ? 1,2, 4 B ? and 
? ? 1,1,2 C ? . Find the 
coordinates of the fourth vertex. 
1 
  2 
Find the multiplicative inverse of the complex numberv     
1 
3 
Reduce the equation v          in normal form. 
1 
  4 Write the converse of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
  5 Find the component statements of the following and check whether they are true or not. 
“A rectangle is a quadrilateral or a 5 sided polygon’’ 1 
 
6 
 Evaluate : 
0
1 3 1 3
lim
x
xx
x
?
? ? ?
 1 
 Section B 
 
7 
 
 
Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 
8. 
4 
  8 Let A ={1,2,3,4,6}.Let R be a relation on A defined by      
? ? ? ?
, : , , is exactly divisible by a b a b A b a ? 
                (i) Write R in Roster form (ii) Find the domain of R 
(iii) Find the range of R . 
4 
  9 Find n ,if the ratio of  fifth term from the beginning to the fifth term from the end in the expansion of    
 v 
 
  
 
v 
 
 
 
  is v    
4 
 
10 Evaluate:    
? ? ? ?
0
sec sec
lim
y
x y x y x x
y
?
? ? ?
 
OR 
Evaluate:       
     
         
 
4 
11 
 
A survey shows that 63% of the American like cheese where 76% like apples. If x% of the Americans 
like both cheese and apples, find the value of x. 
OR 
In a survey of 600 students in a school, 150 students were found to be drinking Tea  and 225 drinking 
4 
XI B 2 of 3 
 
coffee,100 were drinking both Tea and coffee. Find how many students were drinking neither Tea nor 
Coffee. 
12 
 
Find the ratio in which the join of A (1,2,3) and B(-3,4,-5)  is divided by the     plane 
Also ,find the coordinates of the point of division. 
4 
 
 
13 
 Prove that  
tan tan
44
cosec 2
tan tan
44
AA
AA
??
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
. 
OR 
In any triangle ABC , If  a cos A = b cos B,  Show that the triangle is either isosceles or right angled. 
 
4 
14 
Find the equation of the circle which passes through the points (1,3) and (2,-1), and has its centre on 
the line 2x+ y -4 =0. 
OR 
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the 
eccentricity and the length of the latus rectum of the ellipse: 400 25 16
2 2
? ? y x . 
4 
 
15 Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0)   
to the line    
 
 
      
 
 
           is  
 
  
 
4 
 
16 Using the Principle of Mathematical Induction prove the following for all : N n ? 
   ? ?
2
2
1
1 2
1 ....
9
7
1
4
5
1
1
3
1 ? ? ?
?
?
?
?
? ?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? ?
?
?
?
?
?
? n
n
n
  
4 
 
17 How many four letter words can be formed using the letter of the word INEFFECTIVE. 4 
 
18 If       
 
       then show that    
 
 
 
 
 
    
 
  
 
   
4 
19 Find the equation of line passing through the point of intersection of two lines 
                and having y intercept equal to 4. 
4 
 
Section C  
 
20 Prove that :                                  
 
 
        
6 
 
21 
Find the sum of n term of the series:
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
            
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
6 
22 Find the mean deviation about median of the following data: 
Height 
(in cm) 
95-105 105-115 115-125 125-135 135-145 145-155 
Number of 
boys 
9 13 25 30 13 10 
OR 
Given below the diameters of the circles (in mm) drawn in a design . 
Diameter 33-36 37-40 41-44 45-48 49-52 
Number of 
circles 
15 17 21 22 25 
Calculate the mean diameter of the circles and variance. 
6 
XI B 3 of 3 
 
 
23 (i) Differentiate             using first principle. 
(ii)  For the function    given by       
 
       prove that 
 
 
      
 
     
 
    
4+2 
 
24 
a) If 4 digit  numbers greater than 5000 are randomly formed from the digits 0,1,3,5,and 7  what 
is the probability of forming a number divisible by 5 when  
(i) the digits are repeated? 
      (ii) the repetition of digits is not allowed? 
b) The probability that a person will get an electric contract is 
 
 
 and the probability that he will 
not get a plumbing contract is 
 
 
.  If the probability of getting atleast one contract is 
 
 
  what is 
the probability that he will get both? 
 
4+2 
25       Solve the following system of linear inequality graphically: 
x + 2y = 6  ,  2x + y = 6  ,  x = 1  ,  y = 1 
 
6 
 26       Differentiate the following w.r.t. x  
(i) 
         
         
 
(ii) v     
 
      ) 
(iii)
 
   
      
    
 
 
2+2+
2 
 
 
Mathematics answer key(Set –B) 
Date:                                           Class: XI 
Time: 3 hours                                                              M. M: 100  
 
 
Section A 
1 
Three vertices of a parallelogram ABCD are
? ? 3, 1,2 A ? , 
? ? 1,2, 4 B ? and 
? ? 1,1,2 C ? . Find the 
coordinates of the fourth vertex. 
Ans. (1,-2,8) 
 
2 
Find the multiplicative inverse of the complex numberv     
Ans.
v    
 
 
 
3 
Reduce the equation v          in normal form 
Ans.                      
 
4 
Write the converse of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
Ans. “ If you are not true Indian then you are taking part in violent processions” 
 
5 
Find the component statements of the following and check whether they are true or not. 
“A rectangle is a quadrilateral or a 5 sided polygon’’ 
Ans. p: A rectangle is a quadrilateral 
    q: A rectangle is a 5 sided polygon   true 
 
 
6 
 Evaluate : 
0
1 3 1 3
lim
x
xx
x
?
? ? ?
 
Ans. 3
 
 
 Section B 
 
 
7 
Two dice are thrown once. Find the probability of getting an even number on the first 
die or a total of 8. 
Ans. Let A  denotes getting an even number on the first die  and B denotes a total of 8 
 P(A) = 18/36    
P(B) = 5/36  P(AnB) = 3/36   …..(1) 
Using formula  we get P(A?B)   5/9…………….( ) 
 
 
8 
Let A {1,2,3,4,6} .Let R be a relation on A defined by      
? ? ? ?
, : , , is exactly divisible by a b a b A b a ? 
             (i) Write R in Roster form (ii) Find the domain of R 
(iii) Find the range of R . 
 Ans. For roster form   (2 marks) 
        Domain = {1,2,3,4,6} 
        Range = {1,2,3,4,6}……………..(1+1) 
 
9 
Find n ,if the ratio of  fifth term from the beginning to the fifth term from the end in the 
expansion of    (v 
 
  
 
v 
 
)
 
  is v    
 
Ans. 5
th
 term from end  =(n-3)th term from the beginning 
5th term from beginning = C(n,4)(  )
   
 
 
 
 
5th term from end =  (     )   (
 
 
)
   
 
    ………….(2) 
fifth term from the beginning to the fifth term from the end in the expansion of    
(v 
 
  
 
v 
 
)
 
  is v      so using the above two equations we have  n =10………..(2) 
 
10 
Evaluate:    
? ? ? ?
0
sec sec
lim
y
x y x y x x
y
?
? ? ?
 
OR 
Evaluate:     i 
   
     
(       )
 
Ans.    First use sec x = 1/cos x and then formula of cosA - cosB and using the concept 
of limits we get                  ……………..(2+2) 
OR 
Using the identity of       in the denominator we get the limit as ½.(2+2) 
 
11 
 
A survey shows  that 63% of the American like cheese where 76% like apples . If x% 
of the Americans like both cheese and apples, find the value of x. 
OR 
In a survey of 600 students in a school, 150 students were found to be drinking Tea  
and 225 drinking coffee,100 were drinking both Tea and coffee. Find how many 
students were drinking neither Tea nor Coffee. 
Ans.  Apply formula   ( ? )   ( )  ( )  ( n ) 
              We get  39   ( n )     (2+2 mark) 
OR 
Neither Tea nor Coffee  = 600-275 = 325   (2+2) 
 
12 
 
Find the ratio in which the join of A (1,2,3) and B(-3,4,-5)  is divided by the     plane 
Also ,find the coordinates of the point of division. 
 Ans.   Let the required ratio is k:1 
   Let the point be (a ,b ,0) 
Using section formula  k = 3/5  and the point is (-1/2,11/4,0) …………(1+3) 
 
13 
 Prove that  
tan tan
44
cosec 2
tan tan
44
AA
AA
??
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
. 
OR 
In any triangle ABC , If  acos A = bcos B,  Show that the triangle is either isosceles or 
right angled. 
Ans.   
      
      
 
      
      
      
      
 
      
      
=
     
 
 
     
  = cosec2A……..   (1.5+1.5+1) 
OR 
Using the sine formula a = ksinA ,b = ksinB we get equation as  
acos A = bcos B 
ksinAcos A =ksinBcos B …….. ( 1 ) 
multiply both side by ½ 
we get   sin2A – S i n 2 B =0 …… ….(1)