Class 11 Mathematics: CBSE Sample Question Paper - 2 (2023-24) | Sample Papers for Class 11 Medical and Non-Medical - JEE PDF Download

 Page 1


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are
internal choices in some questions.
2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub
parts.
Section A
a) b)
c) d)
1. tan 150° = ? [1]
- 1 3 v 1 3 v - 3 – v 3 – v a) f (|x|) = f(x) b)
f(x
2
) = (f(x)]
2
c) None of these d) f (x + y) = f(x) f(y)
2. Let f(x) = (x - 1) Then, [1]
a) b)
c) d)
3. Two dice are thrown simultaneously. The probability of obtaining total score of seven is [1]
6 3 6 8 3 6 7 3 6 5 3 6 a) 1 b)
c) d) 0
4.  is equal to
[1]
l i m x ? 3 - + 1 0 x 2 v 1 9 v x - 3 6 1 9 v 3 1 9 v a) ab' = ba' b) aa' + bb' = 0
c) ab + a'b' = 0 d) ab' + ba' = 0
5. The two lines ax + by = c and a'x + b'y = c' are perpendicular if [1]
a) 14 b) 16
6. The number of non-empty subsets of the set {1, 2, 3, 4} is: [1]
Page 1 of 19
Page 2


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are
internal choices in some questions.
2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub
parts.
Section A
a) b)
c) d)
1. tan 150° = ? [1]
- 1 3 v 1 3 v - 3 – v 3 – v a) f (|x|) = f(x) b)
f(x
2
) = (f(x)]
2
c) None of these d) f (x + y) = f(x) f(y)
2. Let f(x) = (x - 1) Then, [1]
a) b)
c) d)
3. Two dice are thrown simultaneously. The probability of obtaining total score of seven is [1]
6 3 6 8 3 6 7 3 6 5 3 6 a) 1 b)
c) d) 0
4.  is equal to
[1]
l i m x ? 3 - + 1 0 x 2 v 1 9 v x - 3 6 1 9 v 3 1 9 v a) ab' = ba' b) aa' + bb' = 0
c) ab + a'b' = 0 d) ab' + ba' = 0
5. The two lines ax + by = c and a'x + b'y = c' are perpendicular if [1]
a) 14 b) 16
6. The number of non-empty subsets of the set {1, 2, 3, 4} is: [1]
Page 1 of 19
c) 17 d) 15
a) b) -1
c) d) 1
7. Mark the correct answer for = ?
[1]
( ) 1 - i 1 + i 2 1 2 v - 1 2 a) R b)
c) d)
8. The range of the function f(x) = |x - 1| is [1]
( - 8 , 0 ) ( 0 , 8 ) [ 0 , 8 ) a) {0, 2, 4} b) {1, 2, 3}
c) {0, 1, 2} d) {0, 1, 2, 3}
9. If x belongs to set of integers, A is the solution set of 2(x - 1) < 3x - 1 and B is the solution set of 4x - 3  8 + x,
find A  B
[1] = n a) b)
c) d)
10. At 3 : 40, the hour and minute hands of a clock are inclined at [1]
7 p c 1 8 2 p c 3 3 p c 1 8 1 3 p c 1 8 a) [4, 5) b) [4, 5]
c) (4, 5] d) (4, 5)
11. Let A = {x : x  R, x > 4} and B = {x  R : x < 5}. Then, A  B = [1] ? ? n a) b)
c) d)
12. If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is [1]
1 9 1 1 1 1 1 0 1 2 0 a) an irrational number b) a negative real number
c) a rational number d) a negative integer
13.  is [1] + ( + 1 ) 5 – v 4 ( - 1 ) 5 – v 4 a) b)
c) none of these d)
14. Solve the system of inequalities -2  6x - 1 < 2 [1] = - = x < 1 6 1 2 - < x < 1 6 3 2 - = x > 1 7 1 2 a) {4}  A b) None of these
c) B  A d) 4  A
15. If A = {1, 3, 5, B} and B = {2, 4}, then [1]
? ? ? a) can't lie between -1 and 1 b) can't be less than 1
c) can't be greater than 1 d) can't be equal to 1
16. The value of sec  can [1] ? a) -i b) i
17. Mark the correct answer for: i
326
 = ?
[1]
Page 2 of 19
Page 3


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are
internal choices in some questions.
2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub
parts.
Section A
a) b)
c) d)
1. tan 150° = ? [1]
- 1 3 v 1 3 v - 3 – v 3 – v a) f (|x|) = f(x) b)
f(x
2
) = (f(x)]
2
c) None of these d) f (x + y) = f(x) f(y)
2. Let f(x) = (x - 1) Then, [1]
a) b)
c) d)
3. Two dice are thrown simultaneously. The probability of obtaining total score of seven is [1]
6 3 6 8 3 6 7 3 6 5 3 6 a) 1 b)
c) d) 0
4.  is equal to
[1]
l i m x ? 3 - + 1 0 x 2 v 1 9 v x - 3 6 1 9 v 3 1 9 v a) ab' = ba' b) aa' + bb' = 0
c) ab + a'b' = 0 d) ab' + ba' = 0
5. The two lines ax + by = c and a'x + b'y = c' are perpendicular if [1]
a) 14 b) 16
6. The number of non-empty subsets of the set {1, 2, 3, 4} is: [1]
Page 1 of 19
c) 17 d) 15
a) b) -1
c) d) 1
7. Mark the correct answer for = ?
[1]
( ) 1 - i 1 + i 2 1 2 v - 1 2 a) R b)
c) d)
8. The range of the function f(x) = |x - 1| is [1]
( - 8 , 0 ) ( 0 , 8 ) [ 0 , 8 ) a) {0, 2, 4} b) {1, 2, 3}
c) {0, 1, 2} d) {0, 1, 2, 3}
9. If x belongs to set of integers, A is the solution set of 2(x - 1) < 3x - 1 and B is the solution set of 4x - 3  8 + x,
find A  B
[1] = n a) b)
c) d)
10. At 3 : 40, the hour and minute hands of a clock are inclined at [1]
7 p c 1 8 2 p c 3 3 p c 1 8 1 3 p c 1 8 a) [4, 5) b) [4, 5]
c) (4, 5] d) (4, 5)
11. Let A = {x : x  R, x > 4} and B = {x  R : x < 5}. Then, A  B = [1] ? ? n a) b)
c) d)
12. If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is [1]
1 9 1 1 1 1 1 0 1 2 0 a) an irrational number b) a negative real number
c) a rational number d) a negative integer
13.  is [1] + ( + 1 ) 5 – v 4 ( - 1 ) 5 – v 4 a) b)
c) none of these d)
14. Solve the system of inequalities -2  6x - 1 < 2 [1] = - = x < 1 6 1 2 - < x < 1 6 3 2 - = x > 1 7 1 2 a) {4}  A b) None of these
c) B  A d) 4  A
15. If A = {1, 3, 5, B} and B = {2, 4}, then [1]
? ? ? a) can't lie between -1 and 1 b) can't be less than 1
c) can't be greater than 1 d) can't be equal to 1
16. The value of sec  can [1] ? a) -i b) i
17. Mark the correct answer for: i
326
 = ?
[1]
Page 2 of 19
Section B
Section C
c) -1 d) 1
a) None of these b) 248
c) 992 d) 496
18. If 
n
C
18 
= 
n
C
12
, then 
32
C
n
 = ?
[1]
a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): The expansion of (1 + x)
n
 = . 
Reason (R): If x = -1, then the above expansion is zero.
[1]
+ x + … + n c 0 n c 1 n c 2 x 2 n c n x n a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3. 
Reason (R): The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
[1]
21. If A = (1, 2, 3), B = {4}, C = {5}, then verify that . [2]
OR
Let A = {-2, -1, 0, 1, 2} and f: A  be given by f(x) = x
2
 - 2x - 3 find pre image of 6. -3 and 5.
A × ( B - C ) = ( A × B ) - ( A × C ) ? Z 22. Evaluate: .
[2]
( ) l i m x ? 0 - e 3 x e 2 x x 23. Find the eccentricity of an ellipse whose latus rectum is one half of its major axis. [2]
OR
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum:
x
2
 = -16y
24. Write the set in roster form: C = {x : x is a two-digit number such that the sum of its digits is 9}. [2]
25. Find the angles between the pairs of straight lines x - 4y = 3 and 6x - y = 11. [2]
26. Let A = {1, 2} and B = {2, 4, 6}. Let f = {(x, y) : x  A, y  B and y > 2x +1}. Write f as a set of ordered pairs.
Show that f is a relation but not a function from A to B.
[3] ? ? 27. Solve systems of linear inequation: [3] = 3 = , x > 0 4 x + 1 6 x + 1 28. Find the equation of the set of points P, the sum of whose distances from A(4, 0, 0) and B(-4, 0, 0) is equal to 10. [3]
OR
Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled isosceles triangle.
29. Find a, b and n in the expansion of (a + b)
n
 if the first three terms of the expansion are 729, 7290 and 30375
respectively.
[3]
OR
Using g binomial theorem, expand  and hence find the value of { + } ( x + y ) 5 ( x - y ) 5 { ( + 1 + ( - 1 } 2 – v ) 5 2 – v ) 5 30. If (a + ib) , where c is real, prove that a
2
 + b
2
 = 1 and ..
[3]
OR
= c + i c - i = b a 2 c - 1 c 2 Page 3 of 19
Page 4


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are
internal choices in some questions.
2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub
parts.
Section A
a) b)
c) d)
1. tan 150° = ? [1]
- 1 3 v 1 3 v - 3 – v 3 – v a) f (|x|) = f(x) b)
f(x
2
) = (f(x)]
2
c) None of these d) f (x + y) = f(x) f(y)
2. Let f(x) = (x - 1) Then, [1]
a) b)
c) d)
3. Two dice are thrown simultaneously. The probability of obtaining total score of seven is [1]
6 3 6 8 3 6 7 3 6 5 3 6 a) 1 b)
c) d) 0
4.  is equal to
[1]
l i m x ? 3 - + 1 0 x 2 v 1 9 v x - 3 6 1 9 v 3 1 9 v a) ab' = ba' b) aa' + bb' = 0
c) ab + a'b' = 0 d) ab' + ba' = 0
5. The two lines ax + by = c and a'x + b'y = c' are perpendicular if [1]
a) 14 b) 16
6. The number of non-empty subsets of the set {1, 2, 3, 4} is: [1]
Page 1 of 19
c) 17 d) 15
a) b) -1
c) d) 1
7. Mark the correct answer for = ?
[1]
( ) 1 - i 1 + i 2 1 2 v - 1 2 a) R b)
c) d)
8. The range of the function f(x) = |x - 1| is [1]
( - 8 , 0 ) ( 0 , 8 ) [ 0 , 8 ) a) {0, 2, 4} b) {1, 2, 3}
c) {0, 1, 2} d) {0, 1, 2, 3}
9. If x belongs to set of integers, A is the solution set of 2(x - 1) < 3x - 1 and B is the solution set of 4x - 3  8 + x,
find A  B
[1] = n a) b)
c) d)
10. At 3 : 40, the hour and minute hands of a clock are inclined at [1]
7 p c 1 8 2 p c 3 3 p c 1 8 1 3 p c 1 8 a) [4, 5) b) [4, 5]
c) (4, 5] d) (4, 5)
11. Let A = {x : x  R, x > 4} and B = {x  R : x < 5}. Then, A  B = [1] ? ? n a) b)
c) d)
12. If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is [1]
1 9 1 1 1 1 1 0 1 2 0 a) an irrational number b) a negative real number
c) a rational number d) a negative integer
13.  is [1] + ( + 1 ) 5 – v 4 ( - 1 ) 5 – v 4 a) b)
c) none of these d)
14. Solve the system of inequalities -2  6x - 1 < 2 [1] = - = x < 1 6 1 2 - < x < 1 6 3 2 - = x > 1 7 1 2 a) {4}  A b) None of these
c) B  A d) 4  A
15. If A = {1, 3, 5, B} and B = {2, 4}, then [1]
? ? ? a) can't lie between -1 and 1 b) can't be less than 1
c) can't be greater than 1 d) can't be equal to 1
16. The value of sec  can [1] ? a) -i b) i
17. Mark the correct answer for: i
326
 = ?
[1]
Page 2 of 19
Section B
Section C
c) -1 d) 1
a) None of these b) 248
c) 992 d) 496
18. If 
n
C
18 
= 
n
C
12
, then 
32
C
n
 = ?
[1]
a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): The expansion of (1 + x)
n
 = . 
Reason (R): If x = -1, then the above expansion is zero.
[1]
+ x + … + n c 0 n c 1 n c 2 x 2 n c n x n a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3. 
Reason (R): The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
[1]
21. If A = (1, 2, 3), B = {4}, C = {5}, then verify that . [2]
OR
Let A = {-2, -1, 0, 1, 2} and f: A  be given by f(x) = x
2
 - 2x - 3 find pre image of 6. -3 and 5.
A × ( B - C ) = ( A × B ) - ( A × C ) ? Z 22. Evaluate: .
[2]
( ) l i m x ? 0 - e 3 x e 2 x x 23. Find the eccentricity of an ellipse whose latus rectum is one half of its major axis. [2]
OR
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum:
x
2
 = -16y
24. Write the set in roster form: C = {x : x is a two-digit number such that the sum of its digits is 9}. [2]
25. Find the angles between the pairs of straight lines x - 4y = 3 and 6x - y = 11. [2]
26. Let A = {1, 2} and B = {2, 4, 6}. Let f = {(x, y) : x  A, y  B and y > 2x +1}. Write f as a set of ordered pairs.
Show that f is a relation but not a function from A to B.
[3] ? ? 27. Solve systems of linear inequation: [3] = 3 = , x > 0 4 x + 1 6 x + 1 28. Find the equation of the set of points P, the sum of whose distances from A(4, 0, 0) and B(-4, 0, 0) is equal to 10. [3]
OR
Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled isosceles triangle.
29. Find a, b and n in the expansion of (a + b)
n
 if the first three terms of the expansion are 729, 7290 and 30375
respectively.
[3]
OR
Using g binomial theorem, expand  and hence find the value of { + } ( x + y ) 5 ( x - y ) 5 { ( + 1 + ( - 1 } 2 – v ) 5 2 – v ) 5 30. If (a + ib) , where c is real, prove that a
2
 + b
2
 = 1 and ..
[3]
OR
= c + i c - i = b a 2 c - 1 c 2 Page 3 of 19
Section D
Section E
Evaluate: . 5 + 1 2 i - - - - - - v 31. Using the properties of sets and their complements prove that (A  B) - C = (A - C)  (B - C) [3] ? ? 32. A fair coin is tossed four times, and a person win Rs. 1 for each head and lose Rs. 1.50 for each tail that turns up. 
Form the sample space calculate how many different amounts of money you can have after four tosses and the
probability of having each of these amounts.
[5]
33. Differentiate  from first principle. [5]
OR
Differentiate log sin x from first principles.
s i n x x 34. In an increasing GP, the sum of the first and last terms is 66, the product of the second and the last but one is 128
and the sum of the terms is 126. How many terms are there in this GP?
[5]
35. 0  x   and x lies in the IInd quadrant such that sin x = . Find the values of cos , sin and tan . [5]
OR
Prove that: sin 20
o
 sin 40
o
 sin 80
o
 = 
= = p 1 4 x 2 x 2 x 2 3 v 8 36. Read the text carefully and answer the questions:
Indian track and field athlete Neeraj Chopra, who competes in the Javelin throw, won a gold medal at Tokyo
Olympics. He is the first track and field athlete to win a gold medal for India at the Olympics. 
[4]
OR
Name the shape of path followed by a javelin. If equation of such a curve is given by x
2
 = -16y, then find
the coordinates of foci.
(i)
Find the equation of directrix and length of latus rectum of parabola x
2
 = -16y.
(ii)
Find the equation of parabola with Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis
and also find equation of directrix.
(iii)
Find the equation of the parabola with focus (2, 0) and directrix x = -2 and also length of latus rectum.
37. Read the text carefully and answer the questions:
Consider the data.
Class Frequency
0-10 6
10-20 7
[4]
Page 4 of 19
Page 5


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are
internal choices in some questions.
2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub
parts.
Section A
a) b)
c) d)
1. tan 150° = ? [1]
- 1 3 v 1 3 v - 3 – v 3 – v a) f (|x|) = f(x) b)
f(x
2
) = (f(x)]
2
c) None of these d) f (x + y) = f(x) f(y)
2. Let f(x) = (x - 1) Then, [1]
a) b)
c) d)
3. Two dice are thrown simultaneously. The probability of obtaining total score of seven is [1]
6 3 6 8 3 6 7 3 6 5 3 6 a) 1 b)
c) d) 0
4.  is equal to
[1]
l i m x ? 3 - + 1 0 x 2 v 1 9 v x - 3 6 1 9 v 3 1 9 v a) ab' = ba' b) aa' + bb' = 0
c) ab + a'b' = 0 d) ab' + ba' = 0
5. The two lines ax + by = c and a'x + b'y = c' are perpendicular if [1]
a) 14 b) 16
6. The number of non-empty subsets of the set {1, 2, 3, 4} is: [1]
Page 1 of 19
c) 17 d) 15
a) b) -1
c) d) 1
7. Mark the correct answer for = ?
[1]
( ) 1 - i 1 + i 2 1 2 v - 1 2 a) R b)
c) d)
8. The range of the function f(x) = |x - 1| is [1]
( - 8 , 0 ) ( 0 , 8 ) [ 0 , 8 ) a) {0, 2, 4} b) {1, 2, 3}
c) {0, 1, 2} d) {0, 1, 2, 3}
9. If x belongs to set of integers, A is the solution set of 2(x - 1) < 3x - 1 and B is the solution set of 4x - 3  8 + x,
find A  B
[1] = n a) b)
c) d)
10. At 3 : 40, the hour and minute hands of a clock are inclined at [1]
7 p c 1 8 2 p c 3 3 p c 1 8 1 3 p c 1 8 a) [4, 5) b) [4, 5]
c) (4, 5] d) (4, 5)
11. Let A = {x : x  R, x > 4} and B = {x  R : x < 5}. Then, A  B = [1] ? ? n a) b)
c) d)
12. If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is [1]
1 9 1 1 1 1 1 0 1 2 0 a) an irrational number b) a negative real number
c) a rational number d) a negative integer
13.  is [1] + ( + 1 ) 5 – v 4 ( - 1 ) 5 – v 4 a) b)
c) none of these d)
14. Solve the system of inequalities -2  6x - 1 < 2 [1] = - = x < 1 6 1 2 - < x < 1 6 3 2 - = x > 1 7 1 2 a) {4}  A b) None of these
c) B  A d) 4  A
15. If A = {1, 3, 5, B} and B = {2, 4}, then [1]
? ? ? a) can't lie between -1 and 1 b) can't be less than 1
c) can't be greater than 1 d) can't be equal to 1
16. The value of sec  can [1] ? a) -i b) i
17. Mark the correct answer for: i
326
 = ?
[1]
Page 2 of 19
Section B
Section C
c) -1 d) 1
a) None of these b) 248
c) 992 d) 496
18. If 
n
C
18 
= 
n
C
12
, then 
32
C
n
 = ?
[1]
a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): The expansion of (1 + x)
n
 = . 
Reason (R): If x = -1, then the above expansion is zero.
[1]
+ x + … + n c 0 n c 1 n c 2 x 2 n c n x n a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3. 
Reason (R): The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
[1]
21. If A = (1, 2, 3), B = {4}, C = {5}, then verify that . [2]
OR
Let A = {-2, -1, 0, 1, 2} and f: A  be given by f(x) = x
2
 - 2x - 3 find pre image of 6. -3 and 5.
A × ( B - C ) = ( A × B ) - ( A × C ) ? Z 22. Evaluate: .
[2]
( ) l i m x ? 0 - e 3 x e 2 x x 23. Find the eccentricity of an ellipse whose latus rectum is one half of its major axis. [2]
OR
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum:
x
2
 = -16y
24. Write the set in roster form: C = {x : x is a two-digit number such that the sum of its digits is 9}. [2]
25. Find the angles between the pairs of straight lines x - 4y = 3 and 6x - y = 11. [2]
26. Let A = {1, 2} and B = {2, 4, 6}. Let f = {(x, y) : x  A, y  B and y > 2x +1}. Write f as a set of ordered pairs.
Show that f is a relation but not a function from A to B.
[3] ? ? 27. Solve systems of linear inequation: [3] = 3 = , x > 0 4 x + 1 6 x + 1 28. Find the equation of the set of points P, the sum of whose distances from A(4, 0, 0) and B(-4, 0, 0) is equal to 10. [3]
OR
Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled isosceles triangle.
29. Find a, b and n in the expansion of (a + b)
n
 if the first three terms of the expansion are 729, 7290 and 30375
respectively.
[3]
OR
Using g binomial theorem, expand  and hence find the value of { + } ( x + y ) 5 ( x - y ) 5 { ( + 1 + ( - 1 } 2 – v ) 5 2 – v ) 5 30. If (a + ib) , where c is real, prove that a
2
 + b
2
 = 1 and ..
[3]
OR
= c + i c - i = b a 2 c - 1 c 2 Page 3 of 19
Section D
Section E
Evaluate: . 5 + 1 2 i - - - - - - v 31. Using the properties of sets and their complements prove that (A  B) - C = (A - C)  (B - C) [3] ? ? 32. A fair coin is tossed four times, and a person win Rs. 1 for each head and lose Rs. 1.50 for each tail that turns up. 
Form the sample space calculate how many different amounts of money you can have after four tosses and the
probability of having each of these amounts.
[5]
33. Differentiate  from first principle. [5]
OR
Differentiate log sin x from first principles.
s i n x x 34. In an increasing GP, the sum of the first and last terms is 66, the product of the second and the last but one is 128
and the sum of the terms is 126. How many terms are there in this GP?
[5]
35. 0  x   and x lies in the IInd quadrant such that sin x = . Find the values of cos , sin and tan . [5]
OR
Prove that: sin 20
o
 sin 40
o
 sin 80
o
 = 
= = p 1 4 x 2 x 2 x 2 3 v 8 36. Read the text carefully and answer the questions:
Indian track and field athlete Neeraj Chopra, who competes in the Javelin throw, won a gold medal at Tokyo
Olympics. He is the first track and field athlete to win a gold medal for India at the Olympics. 
[4]
OR
Name the shape of path followed by a javelin. If equation of such a curve is given by x
2
 = -16y, then find
the coordinates of foci.
(i)
Find the equation of directrix and length of latus rectum of parabola x
2
 = -16y.
(ii)
Find the equation of parabola with Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis
and also find equation of directrix.
(iii)
Find the equation of the parabola with focus (2, 0) and directrix x = -2 and also length of latus rectum.
37. Read the text carefully and answer the questions:
Consider the data.
Class Frequency
0-10 6
10-20 7
[4]
Page 4 of 19
20-30 15
30-40 16
40-50 4
50-60 2
OR
Find the mean deviation about median. (i)
Find the Median. (ii)
Write the formula to calculate the Mean deviation about median? (iii)
Write the formula to calculate median?
38. Read the text carefully and answer the questions:
During the math class, a teacher clears the concept of permutation and combination to the 11th standard students.
After the class was over she asks the students some questions, one of the question was: how many numbers
between 99 and 1000 (both excluding) can be formed such that: 
[4]
How many numbers between 99 and 1000 (both excluding) can be formed such that every digit is either 3
or 7.
(i)
How many numbers between 99 and 1000 (both excluding) can be formed such that without any
restriction?
(ii)
Page 5 of 19