Past Year Paper, Maths(Set - 1), 2014, Class 11, Mathematics | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


 
 
 
 
 
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
+
+