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SESSION ENDING Examination (2013-2014) 
Class XI (Mathematics) 
 
Time: 3 Hrs.           M.M =100   
General Instructions : 
a) All the questions are compulsory. 
b) The Question Paper  consists of  26 Questions divided into three sections A, B and C 
c) Section-A comprises of 6 questions of one mark each. 
d) Section-B consists of 13 questions of four marks each. 
e) Section-C comprises of 7 questions of Six marks each. 
f) There is no overall choice. However, an internal choice has been provided in 4 questions of 
four marks each and 2 questions of six marks each. You have to attempt only one of the 
alternatives in all such questions. 
g) The use of calculator is not permitted. 
 
SECTION – A 
1. ( 1, 2) (3,1) If x y + - = Find, the value of x and y. 
2. Express in the form of a ib + 
3 (7 7) (7 7) i i i + + +
 
3. Equation of a line is3 4 10 0 x y - + = . Find the slope of a line parallel to this line. 
4. Write the negation of the statement. 
Every natural number is greater than 0. 
5. Write the contrapositive of the statement 
If a triangle is equilateral, it is isosceles. 
6. Given below are two Paris of statements. Combine these two statements using “if and  only if” 
P   :    If a rectangle is a square, then all its four sides are equal. 
Q   :    if all the four sides of a rectangle are equal, then rectangle is a square. 
SECTION B 
7. { } { } { } 1,2,3, 4,5,6,7,8,9 , 2, 4,6,8 2,3,5,7 If U A and = = 
' '
'
( )
( )
( ) ( )
find i B A
ii B A
iii A B
- n
?
 
8. Find the domain and range of the real function F defined by ( ) ( ) ( 1) f x f x x = = - 
9. Prove that 
9 5
2 3 sin 5 sin
2 2 2
X X x
COS XCOS COS XCOS x - = 
OR 
Page 2


 
 
 
 
 
SESSION ENDING Examination (2013-2014) 
Class XI (Mathematics) 
 
Time: 3 Hrs.           M.M =100   
General Instructions : 
a) All the questions are compulsory. 
b) The Question Paper  consists of  26 Questions divided into three sections A, B and C 
c) Section-A comprises of 6 questions of one mark each. 
d) Section-B consists of 13 questions of four marks each. 
e) Section-C comprises of 7 questions of Six marks each. 
f) There is no overall choice. However, an internal choice has been provided in 4 questions of 
four marks each and 2 questions of six marks each. You have to attempt only one of the 
alternatives in all such questions. 
g) The use of calculator is not permitted. 
 
SECTION – A 
1. ( 1, 2) (3,1) If x y + - = Find, the value of x and y. 
2. Express in the form of a ib + 
3 (7 7) (7 7) i i i + + +
 
3. Equation of a line is3 4 10 0 x y - + = . Find the slope of a line parallel to this line. 
4. Write the negation of the statement. 
Every natural number is greater than 0. 
5. Write the contrapositive of the statement 
If a triangle is equilateral, it is isosceles. 
6. Given below are two Paris of statements. Combine these two statements using “if and  only if” 
P   :    If a rectangle is a square, then all its four sides are equal. 
Q   :    if all the four sides of a rectangle are equal, then rectangle is a square. 
SECTION B 
7. { } { } { } 1,2,3, 4,5,6,7,8,9 , 2, 4,6,8 2,3,5,7 If U A and = = 
' '
'
( )
( )
( ) ( )
find i B A
ii B A
iii A B
- n
?
 
8. Find the domain and range of the real function F defined by ( ) ( ) ( 1) f x f x x = = - 
9. Prove that 
9 5
2 3 sin 5 sin
2 2 2
X X x
COS XCOS COS XCOS x - = 
OR 
 
 
 
 
In a 
ABC ?
  prove that 
2
(cos cos ) 2 ( ) sin
2
A
a C b c + = + B 
10. Find the general solutions of the equation  sin sin 3 sin 5 0. × + × + × = 
11. Prove by using the principle of mathematical inducing all  . n N ? 
 
1 1 1 1
..........
3.5 5.7 7.9 (2 1)(2 3) 3(2 3)
n
n n n
+ + + =
+ + +
 
OR 
Prove by using the principle of mathematical induction for all n N ?   41 14
n n
- is a multiple 
of 27. 
12. In an examination, a question paper consists of 12 questions divided into two parts i.e. Part I 
and Part II containing 5 and 7 questions, respectively. A student required to attempt 8 
questions in all, selecting at least 3 from each part.  In how many ways can a student select 
the question? 
OR 
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not 
come together. 
13. The sum of first three term of a G.P is 16 and the sum of next three terms is 128.  Determine 
the first term, common ratio and the sum to n terms of the GP. 
14. In what ratio,  the line joining (-1,1) and (5,7) is divided by the line 4? x y + = 
15. Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through 
the point (2, 3). 
OR 
Find the equation of the hyperbola whose foci are (0, 12) ± and the length of the Latus rectum 
is 36. 
16. If A and B are the points (3, 4, 5) and (-1, 3, -7) respectively find the equation of the set of 
points P such  that
2 2 2
PA PB k + =  where k is a constant. 
17. calculate the mean deviation about median for the following date- 
Class    Frequency 
0-10      6 
10-20      7 
20-30     15 
30-40     16 
40-50      4 
50-60      2 
Page 3


 
 
 
 
 
SESSION ENDING Examination (2013-2014) 
Class XI (Mathematics) 
 
Time: 3 Hrs.           M.M =100   
General Instructions : 
a) All the questions are compulsory. 
b) The Question Paper  consists of  26 Questions divided into three sections A, B and C 
c) Section-A comprises of 6 questions of one mark each. 
d) Section-B consists of 13 questions of four marks each. 
e) Section-C comprises of 7 questions of Six marks each. 
f) There is no overall choice. However, an internal choice has been provided in 4 questions of 
four marks each and 2 questions of six marks each. You have to attempt only one of the 
alternatives in all such questions. 
g) The use of calculator is not permitted. 
 
SECTION – A 
1. ( 1, 2) (3,1) If x y + - = Find, the value of x and y. 
2. Express in the form of a ib + 
3 (7 7) (7 7) i i i + + +
 
3. Equation of a line is3 4 10 0 x y - + = . Find the slope of a line parallel to this line. 
4. Write the negation of the statement. 
Every natural number is greater than 0. 
5. Write the contrapositive of the statement 
If a triangle is equilateral, it is isosceles. 
6. Given below are two Paris of statements. Combine these two statements using “if and  only if” 
P   :    If a rectangle is a square, then all its four sides are equal. 
Q   :    if all the four sides of a rectangle are equal, then rectangle is a square. 
SECTION B 
7. { } { } { } 1,2,3, 4,5,6,7,8,9 , 2, 4,6,8 2,3,5,7 If U A and = = 
' '
'
( )
( )
( ) ( )
find i B A
ii B A
iii A B
- n
?
 
8. Find the domain and range of the real function F defined by ( ) ( ) ( 1) f x f x x = = - 
9. Prove that 
9 5
2 3 sin 5 sin
2 2 2
X X x
COS XCOS COS XCOS x - = 
OR 
 
 
 
 
In a 
ABC ?
  prove that 
2
(cos cos ) 2 ( ) sin
2
A
a C b c + = + B 
10. Find the general solutions of the equation  sin sin 3 sin 5 0. × + × + × = 
11. Prove by using the principle of mathematical inducing all  . n N ? 
 
1 1 1 1
..........
3.5 5.7 7.9 (2 1)(2 3) 3(2 3)
n
n n n
+ + + =
+ + +
 
OR 
Prove by using the principle of mathematical induction for all n N ?   41 14
n n
- is a multiple 
of 27. 
12. In an examination, a question paper consists of 12 questions divided into two parts i.e. Part I 
and Part II containing 5 and 7 questions, respectively. A student required to attempt 8 
questions in all, selecting at least 3 from each part.  In how many ways can a student select 
the question? 
OR 
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not 
come together. 
13. The sum of first three term of a G.P is 16 and the sum of next three terms is 128.  Determine 
the first term, common ratio and the sum to n terms of the GP. 
14. In what ratio,  the line joining (-1,1) and (5,7) is divided by the line 4? x y + = 
15. Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through 
the point (2, 3). 
OR 
Find the equation of the hyperbola whose foci are (0, 12) ± and the length of the Latus rectum 
is 36. 
16. If A and B are the points (3, 4, 5) and (-1, 3, -7) respectively find the equation of the set of 
points P such  that
2 2 2
PA PB k + =  where k is a constant. 
17. calculate the mean deviation about median for the following date- 
Class    Frequency 
0-10      6 
10-20      7 
20-30     15 
30-40     16 
40-50      4 
50-60      2 
 
 
 
 
18. One card is drawn from a well shuffled deck of 52 cards.  If each outcome is equally likely, 
calculate the probability that the card will be 
a) a diamond 
b) not an ace 
c) a black card 
What is the importance of Sports in life? Write any two. 
19. Out of 100 students, two section of 40 and 60 are formed.   If you and your friend, are among 
100 students, what is the probability that 
a) You both enter the same 
b) You both enter different sections? 
Write any two qualities of a good friend. 
SECTION C 
20. In a survey, it is found that 105 people take X brand pan-masala, 130 take Y brand pan-
masala and 145 take Z brand pan-masala.  If 70 people take X brand as well as Y brand, 75 
take Y brand as well as Z brand, 60 take X brand as well as Z brand and 40 take all the three.  
Find how many take Z brand pan-masala only? 
Pan masala is dangerous for health.  Mention two ways to spread awareness about ill-effects 
of taking Pan-masala. 
21. 
3 3
tan , ,
4 2
If x x
p
p = < <
Find the value of  sin , cos tan
2 2 2
x x x
and 
22. Convert the complex number
1
cos sin
3 3
i
Z
i
p p
- =
+
In the polar form. 
23. Solve graphically: 
2 3
2 6
, 0
x y
x y
x y
+ = - + =
=
 
24. Find a, b and n in the expansion of ( )
n
a b + if the first three terms of expansion are 729, 7290 
and 30375 respectively. 
OR 
The coefficients of the ( 1)
th
r - , ( 1)
th th
r and r + tern in the equation of ( 1)
n
x + are  in the  
ratio 1:3:5, find n and r. 
25. Show that
2 2 2
2 2 2
1 2 2 3 .......................... ( 1)
1 2 2 3 .......................... ( 1)
n n
n n
× + × + + +
× + × + + +
3 5 n = + 
OR 
Page 4


 
 
 
 
 
SESSION ENDING Examination (2013-2014) 
Class XI (Mathematics) 
 
Time: 3 Hrs.           M.M =100   
General Instructions : 
a) All the questions are compulsory. 
b) The Question Paper  consists of  26 Questions divided into three sections A, B and C 
c) Section-A comprises of 6 questions of one mark each. 
d) Section-B consists of 13 questions of four marks each. 
e) Section-C comprises of 7 questions of Six marks each. 
f) There is no overall choice. However, an internal choice has been provided in 4 questions of 
four marks each and 2 questions of six marks each. You have to attempt only one of the 
alternatives in all such questions. 
g) The use of calculator is not permitted. 
 
SECTION – A 
1. ( 1, 2) (3,1) If x y + - = Find, the value of x and y. 
2. Express in the form of a ib + 
3 (7 7) (7 7) i i i + + +
 
3. Equation of a line is3 4 10 0 x y - + = . Find the slope of a line parallel to this line. 
4. Write the negation of the statement. 
Every natural number is greater than 0. 
5. Write the contrapositive of the statement 
If a triangle is equilateral, it is isosceles. 
6. Given below are two Paris of statements. Combine these two statements using “if and  only if” 
P   :    If a rectangle is a square, then all its four sides are equal. 
Q   :    if all the four sides of a rectangle are equal, then rectangle is a square. 
SECTION B 
7. { } { } { } 1,2,3, 4,5,6,7,8,9 , 2, 4,6,8 2,3,5,7 If U A and = = 
' '
'
( )
( )
( ) ( )
find i B A
ii B A
iii A B
- n
?
 
8. Find the domain and range of the real function F defined by ( ) ( ) ( 1) f x f x x = = - 
9. Prove that 
9 5
2 3 sin 5 sin
2 2 2
X X x
COS XCOS COS XCOS x - = 
OR 
 
 
 
 
In a 
ABC ?
  prove that 
2
(cos cos ) 2 ( ) sin
2
A
a C b c + = + B 
10. Find the general solutions of the equation  sin sin 3 sin 5 0. × + × + × = 
11. Prove by using the principle of mathematical inducing all  . n N ? 
 
1 1 1 1
..........
3.5 5.7 7.9 (2 1)(2 3) 3(2 3)
n
n n n
+ + + =
+ + +
 
OR 
Prove by using the principle of mathematical induction for all n N ?   41 14
n n
- is a multiple 
of 27. 
12. In an examination, a question paper consists of 12 questions divided into two parts i.e. Part I 
and Part II containing 5 and 7 questions, respectively. A student required to attempt 8 
questions in all, selecting at least 3 from each part.  In how many ways can a student select 
the question? 
OR 
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not 
come together. 
13. The sum of first three term of a G.P is 16 and the sum of next three terms is 128.  Determine 
the first term, common ratio and the sum to n terms of the GP. 
14. In what ratio,  the line joining (-1,1) and (5,7) is divided by the line 4? x y + = 
15. Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through 
the point (2, 3). 
OR 
Find the equation of the hyperbola whose foci are (0, 12) ± and the length of the Latus rectum 
is 36. 
16. If A and B are the points (3, 4, 5) and (-1, 3, -7) respectively find the equation of the set of 
points P such  that
2 2 2
PA PB k + =  where k is a constant. 
17. calculate the mean deviation about median for the following date- 
Class    Frequency 
0-10      6 
10-20      7 
20-30     15 
30-40     16 
40-50      4 
50-60      2 
 
 
 
 
18. One card is drawn from a well shuffled deck of 52 cards.  If each outcome is equally likely, 
calculate the probability that the card will be 
a) a diamond 
b) not an ace 
c) a black card 
What is the importance of Sports in life? Write any two. 
19. Out of 100 students, two section of 40 and 60 are formed.   If you and your friend, are among 
100 students, what is the probability that 
a) You both enter the same 
b) You both enter different sections? 
Write any two qualities of a good friend. 
SECTION C 
20. In a survey, it is found that 105 people take X brand pan-masala, 130 take Y brand pan-
masala and 145 take Z brand pan-masala.  If 70 people take X brand as well as Y brand, 75 
take Y brand as well as Z brand, 60 take X brand as well as Z brand and 40 take all the three.  
Find how many take Z brand pan-masala only? 
Pan masala is dangerous for health.  Mention two ways to spread awareness about ill-effects 
of taking Pan-masala. 
21. 
3 3
tan , ,
4 2
If x x
p
p = < <
Find the value of  sin , cos tan
2 2 2
x x x
and 
22. Convert the complex number
1
cos sin
3 3
i
Z
i
p p
- =
+
In the polar form. 
23. Solve graphically: 
2 3
2 6
, 0
x y
x y
x y
+ = - + =
=
 
24. Find a, b and n in the expansion of ( )
n
a b + if the first three terms of expansion are 729, 7290 
and 30375 respectively. 
OR 
The coefficients of the ( 1)
th
r - , ( 1)
th th
r and r + tern in the equation of ( 1)
n
x + are  in the  
ratio 1:3:5, find n and r. 
25. Show that
2 2 2
2 2 2
1 2 2 3 .......................... ( 1)
1 2 2 3 .......................... ( 1)
n n
n n
× + × + + +
× + × + + +
3 5 n = + 
OR 
 
 
 
 
If A and G be A.M. and G.M. respectively between two positive numbers. Prove that the 
numbers are ( )( ) A G A G + - 
26. (a)
0
lim (cos cot )
x
Evaluate ec x x
?
- 
(b) Find the derivative at the function
4 5sin
3 7
x x
x
+
+
 
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FAQs on Past Year Paper, Maths(Set - 1), 2014, Class 11, Mathematics - Mathematics (Maths) Class 11 - Commerce

1. What are the important topics to study in Mathematics for Class 11?
Ans. Some important topics to study in Mathematics for Class 11 are sets, relations and functions, trigonometry, sequences and series, coordinate geometry, and statistics.
2. How can I improve my problem-solving skills in Mathematics?
Ans. To improve problem-solving skills in Mathematics, it is important to practice regularly. Solve a variety of problems from different topics, understand the concepts and formulas, and try to solve the problems using different approaches. Additionally, seeking help from teachers or joining a study group can also be beneficial.
3. How can I score well in the Mathematics exam for Class 11?
Ans. To score well in the Mathematics exam for Class 11, it is important to have a clear understanding of the concepts and formulas. Practice solving different types of problems and previous year question papers. Manage your time effectively during the exam and attempt all questions with accuracy. Also, seek guidance from your teacher to understand the marking scheme and important topics.
4. What are the common mistakes students make in Mathematics exams?
Ans. Some common mistakes students make in Mathematics exams include not reading the question carefully, not understanding the problem-solving approach, incorrect usage of formulas, calculation errors, and not showing proper steps in the solution. It is important to be attentive, practice regularly, and double-check the answers before submitting the paper to avoid such mistakes.
5. How can I overcome my fear of Mathematics?
Ans. To overcome the fear of Mathematics, it is important to approach the subject with a positive mindset. Start by understanding the basics and gradually build up your knowledge. Practice regularly, seek help from teachers or classmates when needed, and focus on understanding the concepts rather than just memorizing formulas. Breaking down complex problems into smaller steps can also help in building confidence.
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