Past Year Paper, Maths(Set - 1), 2015, Class 11, Mathematics | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


 
 
 
 
SESSION ENDING Examination (2014-2015) 
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) Use of calculator, is not permitted. 
 
SECTION – A 
1. { } { } , , , , , , . . If X a b c d and Y f b d g find X Y = = - 
2. Solve   3 7 5 1. x x - > - 
3. Fine the centre and radius of the circle : 
2 2
( 5) ( 3) 36 x y + + - = 
4. Write the contrapositive of the statement 
“If x is a prime number, then x is odd.” 
5. Write the  negation of  the statement. 
“All triangles are not equilateral triangles”. 
6. Write the converse of  the statement 
If a rectangle ‘R’ is square, then R is a Rhombus.” 
       SECTION – B 
7. Define a relation R on the set N of natural numbers by R={(x,y);  y=x+5, x  is natural  number 
less than 4, x, y ? N } 
a) roster form and 
b) an arrow diagram. 
Write down the domain and range. 
8. Prove that 
2 2
2
sin 6 sin 4 sin 2 sin10
sin 2 2sin 4 sin 6 4cos sin 4
x x x x
Or
x x x x x
- =
+ + =
 
9. Find the general solution of the equation 
2
sec 2 1 tan 2 x x = - 
Page 2


 
 
 
 
SESSION ENDING Examination (2014-2015) 
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) Use of calculator, is not permitted. 
 
SECTION – A 
1. { } { } , , , , , , . . If X a b c d and Y f b d g find X Y = = - 
2. Solve   3 7 5 1. x x - > - 
3. Fine the centre and radius of the circle : 
2 2
( 5) ( 3) 36 x y + + - = 
4. Write the contrapositive of the statement 
“If x is a prime number, then x is odd.” 
5. Write the  negation of  the statement. 
“All triangles are not equilateral triangles”. 
6. Write the converse of  the statement 
If a rectangle ‘R’ is square, then R is a Rhombus.” 
       SECTION – B 
7. Define a relation R on the set N of natural numbers by R={(x,y);  y=x+5, x  is natural  number 
less than 4, x, y ? N } 
a) roster form and 
b) an arrow diagram. 
Write down the domain and range. 
8. Prove that 
2 2
2
sin 6 sin 4 sin 2 sin10
sin 2 2sin 4 sin 6 4cos sin 4
x x x x
Or
x x x x x
- =
+ + =
 
9. Find the general solution of the equation 
2
sec 2 1 tan 2 x x = - 
 
 
 
 
10. Prove by using Principal of Mathematical Induction for all n N ? 
2 3 1
1.2 2.2 3.2 ......................... .2 ( 1)2 2
n n
n n
+
+ + + + = - + 
OR 
Prove by using Principle of Mathematical induction for all
2 2
3 8 9
n
n N n
+
? - - is divisible by 8. 
11. In how many ways can a student choose a  program of  5 courses. If 9 courses are available 
and 2 specific courses are compulsory for every student? 
OR 
If the different permutations of  all the letters of word; EXAMINATION’ are listed as in a 
dictionary, how many words are there in this list before the first word starting with E? 
12. If the first and the 
th
n terms of a G.P. are  ‘a’ and  ‘b’ ,  respectively, and if P is the product of 
the first n terms, prove that 
2
( )
n
p ab = 
13. Find the equation of the line passing through the mid-point of (-2, 4), (-4, 6) and 
perpendicular to the line through the point (2, 5) and (-3, 6). 
14. Find the coordinates of the focus, axis of the parabola, the equation of the directrix   and the 
length of the latus rectum of the parabola whose equation is 
2
6 x y = 
15. Using section formula, prove that the three points (-4, 6, 10), (2, 4, 6 ) and (14, 0, -2 ) 
 are collinear. 
16. Find the mean and the variance for the following distribution: 
Xi 6 10 14 18 24 28 30 
fi 2 4 7 12 8 4 3 
OR 
Find the mean deviation about median for the following date: 
i
x 15 21 27 30 35 
i
f 3 5 6 7 8 
17. A and B are two  events such that p(A)=0.54, P(B)=0.69 and ( ) 0.35 P A B n = 
Find (i) ( ) ( ) ( ' ') ( ) ( ') ( ) ( ') P A B ii P A B iii P A B iv P B A ? n n n 
18. Three letters are dictated to three persons and an envelope is addressed to each of them, the 
letters are interested into the envelope at random so that each envelope contains exactly one 
letter. Find the probability that at least one letter is in its proper envelope. 
19. Let A, B and C be the sets such that . A B A C and A B A C ? = ? n = n show that B=C. 
SECTION –C 
20. There are 200 individual with a skin disorder, 120 had been exposed to the chemical 
2
C .  
Find the number of individuals exposed to – 
a) Chemical 
1
C
 but not chemical 
2
C
 
Page 3


 
 
 
 
SESSION ENDING Examination (2014-2015) 
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) Use of calculator, is not permitted. 
 
SECTION – A 
1. { } { } , , , , , , . . If X a b c d and Y f b d g find X Y = = - 
2. Solve   3 7 5 1. x x - > - 
3. Fine the centre and radius of the circle : 
2 2
( 5) ( 3) 36 x y + + - = 
4. Write the contrapositive of the statement 
“If x is a prime number, then x is odd.” 
5. Write the  negation of  the statement. 
“All triangles are not equilateral triangles”. 
6. Write the converse of  the statement 
If a rectangle ‘R’ is square, then R is a Rhombus.” 
       SECTION – B 
7. Define a relation R on the set N of natural numbers by R={(x,y);  y=x+5, x  is natural  number 
less than 4, x, y ? N } 
a) roster form and 
b) an arrow diagram. 
Write down the domain and range. 
8. Prove that 
2 2
2
sin 6 sin 4 sin 2 sin10
sin 2 2sin 4 sin 6 4cos sin 4
x x x x
Or
x x x x x
- =
+ + =
 
9. Find the general solution of the equation 
2
sec 2 1 tan 2 x x = - 
 
 
 
 
10. Prove by using Principal of Mathematical Induction for all n N ? 
2 3 1
1.2 2.2 3.2 ......................... .2 ( 1)2 2
n n
n n
+
+ + + + = - + 
OR 
Prove by using Principle of Mathematical induction for all
2 2
3 8 9
n
n N n
+
? - - is divisible by 8. 
11. In how many ways can a student choose a  program of  5 courses. If 9 courses are available 
and 2 specific courses are compulsory for every student? 
OR 
If the different permutations of  all the letters of word; EXAMINATION’ are listed as in a 
dictionary, how many words are there in this list before the first word starting with E? 
12. If the first and the 
th
n terms of a G.P. are  ‘a’ and  ‘b’ ,  respectively, and if P is the product of 
the first n terms, prove that 
2
( )
n
p ab = 
13. Find the equation of the line passing through the mid-point of (-2, 4), (-4, 6) and 
perpendicular to the line through the point (2, 5) and (-3, 6). 
14. Find the coordinates of the focus, axis of the parabola, the equation of the directrix   and the 
length of the latus rectum of the parabola whose equation is 
2
6 x y = 
15. Using section formula, prove that the three points (-4, 6, 10), (2, 4, 6 ) and (14, 0, -2 ) 
 are collinear. 
16. Find the mean and the variance for the following distribution: 
Xi 6 10 14 18 24 28 30 
fi 2 4 7 12 8 4 3 
OR 
Find the mean deviation about median for the following date: 
i
x 15 21 27 30 35 
i
f 3 5 6 7 8 
17. A and B are two  events such that p(A)=0.54, P(B)=0.69 and ( ) 0.35 P A B n = 
Find (i) ( ) ( ) ( ' ') ( ) ( ') ( ) ( ') P A B ii P A B iii P A B iv P B A ? n n n 
18. Three letters are dictated to three persons and an envelope is addressed to each of them, the 
letters are interested into the envelope at random so that each envelope contains exactly one 
letter. Find the probability that at least one letter is in its proper envelope. 
19. Let A, B and C be the sets such that . A B A C and A B A C ? = ? n = n show that B=C. 
SECTION –C 
20. There are 200 individual with a skin disorder, 120 had been exposed to the chemical 
2
C .  
Find the number of individuals exposed to – 
a) Chemical 
1
C
 but not chemical 
2
C
 
 
 
 
 
b) Chemical 
2
C
 but not chemical 
1
C
 
c) Chemical 
1
C
 or chemical  
2
C
 
 
Exposure to UV rays result in skin disorders, what prevents harmful UV rays from sun to 
reach earth? 
21. Prove that in any triangle ( )cot ( )cot ( )cot 0
2 2 2
A B C
b c c a a b - + - + - = 
22. Find ? such that 
3 2 sin
1 2 sin
i
i
?
?
+
- is purely real. 
23. Solve the following system of inequalities graphically.
3 2 150, 4 80,
15, 0, 0
x y x y
x y x
+ = + =
= = =
 
24. Find n, if the ratio of the fifth them from the beginning to the fifth term from the end in the 
expansion of 
4
4
1
2
3
n
? ?
+
? ?
? ?
 is  6 :1 
Or 
The Coefficients’ of three consecutive terms in the expansion of (1 )
n
a + are in the ratio 1: 
7:,42. Find n. 
25. Find the sum of the following series upto n terms
3 3 3 3 3 3
1 1 2 1 2 3
1 1 3 1 3 5
+ + +
+ + + - - - - - - + + +
 
OR 
If p,  q, r are in G.P. and the equations, 
2 2
2 0 2 0 px qx r and dx ex f + + = + + = have a common 
root, then show that  , ,
d e f
p q r
 are in A.P. 
26.   
a) Evaluate 
0
sin
lim . . 0
sin
x
ax bx
a b a b
ax bx
?
+
+ ?
+
 
b) Fine the derivative of 
5
cos
sin
x x
x
-