Class 11 Mathematics (Maths) Previous Year Paper - 3 | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


  
 
 
                
                
 
                                          Class: XI 
Mathematics(041) (Set A) 
 
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 Find the component statements of the following and check whether they are true or not. 
    “ All prime numbers are either even or odd’’ 
1 
2 
Find the multiplicative inverse of the complex number 32i ? . 
1 
3 
Reduce the equation v          in normal form. 
1 
 
4 
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 
5 Write the contrapositive of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
 
6 
If 
2
2
lim 80
2
nn
x
x
x
?
?
?
?
and , nN ? find n . 1 
 Section B 
 
7 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. 
 
4 
 
 
 
 
 
8 Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 8.             
 
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 
 
 
 
 
 
 
Page 2


  
 
 
                
                
 
                                          Class: XI 
Mathematics(041) (Set A) 
 
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 Find the component statements of the following and check whether they are true or not. 
    “ All prime numbers are either even or odd’’ 
1 
2 
Find the multiplicative inverse of the complex number 32i ? . 
1 
3 
Reduce the equation v          in normal form. 
1 
 
4 
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 
5 Write the contrapositive of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
 
6 
If 
2
2
lim 80
2
nn
x
x
x
?
?
?
?
and , nN ? find n . 1 
 Section B 
 
7 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. 
 
4 
 
 
 
 
 
8 Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 8.             
 
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 
 
 
 
 
 
 
XI A 2 of 3 
 
11 
 
Let 
? ? 1,2,3,4,5,6 A ? .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 
 
 
12 
 
How many four letter words can be formed using the letter of the word INEFFECTIVE. 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 length of axes; the coordinates of the vertices and the foci; the eccentricity and the length of 
latus rectum of the hyperbola         
 
    
 
    . 
4 
 
15 
Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0) to 
the line 
 
 
      
 
 
        is  
 
  
 
4 
 
16 
 
 
 
 
Prove the following by the principle of mathematical induction for all n  : 
 
   
 
 
   
        
 
            
 
 
      
 
4 
 
17 If       
 
       then show that 
 
 
 
 
 
    
 
  
 
   
4 
 
18 
 
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 
 
19 
 
Find the equation of line passing through the point of intersection of two lines  
                   and having x intercept equal to 3. 
4 
 
Section C 
 
20 Solve the following system of linear inequality graphically: 
                                
6 
 
21 
Find the sum of n term of the series: 
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
Show that   
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
 
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 
 
 
6 
Page 3


  
 
 
                
                
 
                                          Class: XI 
Mathematics(041) (Set A) 
 
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 Find the component statements of the following and check whether they are true or not. 
    “ All prime numbers are either even or odd’’ 
1 
2 
Find the multiplicative inverse of the complex number 32i ? . 
1 
3 
Reduce the equation v          in normal form. 
1 
 
4 
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 
5 Write the contrapositive of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
 
6 
If 
2
2
lim 80
2
nn
x
x
x
?
?
?
?
and , nN ? find n . 1 
 Section B 
 
7 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. 
 
4 
 
 
 
 
 
8 Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 8.             
 
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 
 
 
 
 
 
 
XI A 2 of 3 
 
11 
 
Let 
? ? 1,2,3,4,5,6 A ? .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 
 
 
12 
 
How many four letter words can be formed using the letter of the word INEFFECTIVE. 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 length of axes; the coordinates of the vertices and the foci; the eccentricity and the length of 
latus rectum of the hyperbola         
 
    
 
    . 
4 
 
15 
Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0) to 
the line 
 
 
      
 
 
        is  
 
  
 
4 
 
16 
 
 
 
 
Prove the following by the principle of mathematical induction for all n  : 
 
   
 
 
   
        
 
            
 
 
      
 
4 
 
17 If       
 
       then show that 
 
 
 
 
 
    
 
  
 
   
4 
 
18 
 
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 
 
19 
 
Find the equation of line passing through the point of intersection of two lines  
                   and having x intercept equal to 3. 
4 
 
Section C 
 
20 Solve the following system of linear inequality graphically: 
                                
6 
 
21 
Find the sum of n term of the series: 
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
Show that   
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
 
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 
 
 
6 
XI A 3 of 3 
 
 
 
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. 
 
 
23 (i) Differentiate the following w.r.t. x :    
         
         
 
(ii) Differentiate the following w.r.t. x :           v   
 
    
(iii)Differentiate the following w.r.t. x : 
 
  
      
    
 
6 
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 
 
      Prove that :                              
 
 
        
 
6 
26 (i) Differentiate             using first principle. 
(ii)  For the function    given by       
 
       prove that 
 
 
      
 
     
 
    
 
4+2 
 
 
Page 4


  
 
 
                
                
 
                                          Class: XI 
Mathematics(041) (Set A) 
 
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 Find the component statements of the following and check whether they are true or not. 
    “ All prime numbers are either even or odd’’ 
1 
2 
Find the multiplicative inverse of the complex number 32i ? . 
1 
3 
Reduce the equation v          in normal form. 
1 
 
4 
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 
5 Write the contrapositive of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
 
6 
If 
2
2
lim 80
2
nn
x
x
x
?
?
?
?
and , nN ? find n . 1 
 Section B 
 
7 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. 
 
4 
 
 
 
 
 
8 Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 8.             
 
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 
 
 
 
 
 
 
XI A 2 of 3 
 
11 
 
Let 
? ? 1,2,3,4,5,6 A ? .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 
 
 
12 
 
How many four letter words can be formed using the letter of the word INEFFECTIVE. 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 length of axes; the coordinates of the vertices and the foci; the eccentricity and the length of 
latus rectum of the hyperbola         
 
    
 
    . 
4 
 
15 
Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0) to 
the line 
 
 
      
 
 
        is  
 
  
 
4 
 
16 
 
 
 
 
Prove the following by the principle of mathematical induction for all n  : 
 
   
 
 
   
        
 
            
 
 
      
 
4 
 
17 If       
 
       then show that 
 
 
 
 
 
    
 
  
 
   
4 
 
18 
 
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 
 
19 
 
Find the equation of line passing through the point of intersection of two lines  
                   and having x intercept equal to 3. 
4 
 
Section C 
 
20 Solve the following system of linear inequality graphically: 
                                
6 
 
21 
Find the sum of n term of the series: 
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
Show that   
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
 
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 
 
 
6 
XI A 3 of 3 
 
 
 
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. 
 
 
23 (i) Differentiate the following w.r.t. x :    
         
         
 
(ii) Differentiate the following w.r.t. x :           v   
 
    
(iii)Differentiate the following w.r.t. x : 
 
  
      
    
 
6 
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 
 
      Prove that :                              
 
 
        
 
6 
26 (i) Differentiate             using first principle. 
(ii)  For the function    given by       
 
       prove that 
 
 
      
 
     
 
    
 
4+2 
 
 
 
Mathematics (Set A)  ANSWER KEY 
Date:                                            Class: XI 
Time: 3 hours                                                          M. M: 100  
 
Section A 
1 
Find the component statements of the following and check whether they are true or not. 
    “ All prime numbers are either even or odd’’ 
Ans.  p : All prime number are even        q:All prime number are odd.  False  
 
2 
Find the multiplicative inverse of the complex number 32i ? . 
Ans.
v    
 
 
 
3 
Reduce the equation v          normal form 
Ans.                      
 
4 
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) 
 
5 
Write the contrapositive of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
Ans“If you are true Indian then you are not taking part in the violent processions’’ 
 
 
6 
If 
2
2
lim 80
2
nn
x
x
x
?
?
?
?
and , nN ? find n . 
Ans. n = 5 
 
 Section B 
 
 
7 
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   (   )   ( )  ( )  (   ) 
              We get  39   (   )     (2+2 mark) 
OR 
Neither Tea nor Coffee  = 600-275 = 325   (2+2) 
 
8 
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(A B) = 3/36   …..(1) 
Using formula  we get P(A B)   5/9 …………….( ) 
 
 
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)(  )
   
 
 
 
 
 
Page 5


  
 
 
                
                
 
                                          Class: XI 
Mathematics(041) (Set A) 
 
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 Find the component statements of the following and check whether they are true or not. 
    “ All prime numbers are either even or odd’’ 
1 
2 
Find the multiplicative inverse of the complex number 32i ? . 
1 
3 
Reduce the equation v          in normal form. 
1 
 
4 
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 
5 Write the contrapositive of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
1 
 
6 
If 
2
2
lim 80
2
nn
x
x
x
?
?
?
?
and , nN ? find n . 1 
 Section B 
 
7 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. 
 
4 
 
 
 
 
 
8 Two dice are thrown once. Find the probability of getting an even number on the first die or a total of 8.             
 
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 
 
 
 
 
 
 
XI A 2 of 3 
 
11 
 
Let 
? ? 1,2,3,4,5,6 A ? .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 
 
 
12 
 
How many four letter words can be formed using the letter of the word INEFFECTIVE. 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 length of axes; the coordinates of the vertices and the foci; the eccentricity and the length of 
latus rectum of the hyperbola         
 
    
 
    . 
4 
 
15 
Prove that the lengths of the perpendiculars drawn from the points (v 
 
  
 
, 0) and ( v 
 
  
 
, 0) to 
the line 
 
 
      
 
 
        is  
 
  
 
4 
 
16 
 
 
 
 
Prove the following by the principle of mathematical induction for all n  : 
 
   
 
 
   
        
 
            
 
 
      
 
4 
 
17 If       
 
       then show that 
 
 
 
 
 
    
 
  
 
   
4 
 
18 
 
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 
 
19 
 
Find the equation of line passing through the point of intersection of two lines  
                   and having x intercept equal to 3. 
4 
 
Section C 
 
20 Solve the following system of linear inequality graphically: 
                                
6 
 
21 
Find the sum of n term of the series: 
 
     
 
 
     
 
 
      
 …………upto n terms 
OR 
Show that   
   
 
    
 
             
 
 
 
    
 
        
 
      
 
    
    
 
 
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 
 
 
6 
XI A 3 of 3 
 
 
 
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. 
 
 
23 (i) Differentiate the following w.r.t. x :    
         
         
 
(ii) Differentiate the following w.r.t. x :           v   
 
    
(iii)Differentiate the following w.r.t. x : 
 
  
      
    
 
6 
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 
 
      Prove that :                              
 
 
        
 
6 
26 (i) Differentiate             using first principle. 
(ii)  For the function    given by       
 
       prove that 
 
 
      
 
     
 
    
 
4+2 
 
 
 
Mathematics (Set A)  ANSWER KEY 
Date:                                            Class: XI 
Time: 3 hours                                                          M. M: 100  
 
Section A 
1 
Find the component statements of the following and check whether they are true or not. 
    “ All prime numbers are either even or odd’’ 
Ans.  p : All prime number are even        q:All prime number are odd.  False  
 
2 
Find the multiplicative inverse of the complex number 32i ? . 
Ans.
v    
 
 
 
3 
Reduce the equation v          normal form 
Ans.                      
 
4 
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) 
 
5 
Write the contrapositive of the following statement : 
“ If you are taking part in violent processions then you are not true Indian” 
Ans“If you are true Indian then you are not taking part in the violent processions’’ 
 
 
6 
If 
2
2
lim 80
2
nn
x
x
x
?
?
?
?
and , nN ? find n . 
Ans. n = 5 
 
 Section B 
 
 
7 
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   (   )   ( )  ( )  (   ) 
              We get  39   (   )     (2+2 mark) 
OR 
Neither Tea nor Coffee  = 600-275 = 325   (2+2) 
 
8 
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(A B) = 3/36   …..(1) 
Using formula  we get P(A B)   5/9 …………….( ) 
 
 
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 secx = 1/cosx 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 
 
Let 
? ? 1,2,3,4,5,6 A ? .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 = {1,2,3,4,5,6} 
        Range = {1,2,3,4,5,6}……………..(1+1) 
 
12 
 
How many four letter words can be formed using the letter of the word INEFFECTIVE. 
Ans. There are 11 letters in the given word  
  The four letter words may consist of  
(i) 3 alike and 1 distinct  
(ii) 2 alike letters of one kind and two of other kind 
(iii) 2 alike letters and 2 distinct  
(iv) All different letters      ………………………..(3) 
Required answer  = C (6,1)×4+18+540+840 =1422………………(1) 
 
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 –Sin2B=0……….(1) 
solving we get A=B or angle C =90 ……( ) 
 
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 length of axes; the coordinates of the vertices and the foci; the eccentricity and the length of 
latus rectum of the hyperbola       9 
 
    
 
    . 
Ans.Let (-g,-f) be the centre of the circle  
-2g-f-4 =0 …………………..            (.5)