Class 11 Mathematics: CBSE Sample Question Paper - 1 (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. cos 15° - sin 15° = ? [1]
1 2 ( - 1 ) 2 v 2 v 1 2 v ( + 1 ) 2 v 2 v a) {b, c} b) {c}
c) {a, b} d) {a, b, c}
2. Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is [1]
a) b)
c) d)
3. The probability that a leap year will have 53 Fridays or 53 Saturdays is [1]
2 7 3 7 1 7 4 7 a) b) 2
c) 0 d) -1
4.  is equal to
[1]
( - x ) l i m x ? 8 + x + 1 x 2 - - - - - - - - v 1 2 a) x + y = 1 b) x – y = 5
c) x + y = 5 d) x – y = 1
5. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is [1]
a)
2
n
-1
b)
2
n
 - 2
6. The number of subsets of a set containing n elements is [1]
Page 1 of 18
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. cos 15° - sin 15° = ? [1]
1 2 ( - 1 ) 2 v 2 v 1 2 v ( + 1 ) 2 v 2 v a) {b, c} b) {c}
c) {a, b} d) {a, b, c}
2. Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is [1]
a) b)
c) d)
3. The probability that a leap year will have 53 Fridays or 53 Saturdays is [1]
2 7 3 7 1 7 4 7 a) b) 2
c) 0 d) -1
4.  is equal to
[1]
( - x ) l i m x ? 8 + x + 1 x 2 - - - - - - - - v 1 2 a) x + y = 1 b) x – y = 5
c) x + y = 5 d) x – y = 1
5. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is [1]
a)
2
n
-1
b)
2
n
 - 2
6. The number of subsets of a set containing n elements is [1]
Page 1 of 18
c)
2
n d) n
a)
|z
2
| = |z|
2 b)
|z
2
| < |z|
2
c)
|z
2
|  |z|
2 d)
|z
2
| > |z|
2
7. If z is a complex number, then [1]
= a) R - [0, 4] b) (0, 4)
c) d) R - (0, 4)
8. The domain of definition of f(x) =  is [1] 4 x - x 2 - - - - - - v [ 0 , 4 ] a) 3  x  91 b) 3  x  5
c) 5  x  91 d) 8  x  22
9. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm
longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for
the shortest board if the third piece is to be at least 5 cm longer than the second?
[1]
= = = = = = = = a) both are equal b) cos 24°
c) sin 24° d) cannot be compared
10. Which is greater, sin 24° or cos 24° ? [1]
a) 6 b) 7
c) 8 d) 5
11. The number of proper subsets of the set {1, 2, 3} is : [1]
a) b)
c) d) -1
12. The sum of the infinite geometric series  ?
[1]
( + - + … 8 ) = - 5 4 5 1 6 5 6 4 - 1 4 5 8 1 4 a) b) 2n
c)
2
n-1 d)
2
n
13.  = ?
[1]
{ + 2 + c 1 c 0 C 2 C 1 3 + … + n · } C 3 C 2 C n C n - 1 n ( n + 1 ) 1 2 a) x  (– 13, 7] b) x  (– 10, 7]
c) x  (– , – 13]  [8, ) d) x  (– , – 13]  [7, )
14. If |x + 3|  10 , then [1] = ? ? ? 8 ? 8 ? 8 ? 8 a) A and the complement of B are always non-
disjoint
b) none of these
c) A and B are always disjoint d) B is always a subset of A
15. Let A and B be two non- empty subsets of a set X such that A is not a subset of B, then [1]
a) 7.7 cm b) 8.8 cm
c) 9.1 cm d) 6.6 cm
16. In a circle of radius 14 cm an arc subtends an angle of 36° at the centre. The length of the arc is [1]
Page 2 of 18
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. cos 15° - sin 15° = ? [1]
1 2 ( - 1 ) 2 v 2 v 1 2 v ( + 1 ) 2 v 2 v a) {b, c} b) {c}
c) {a, b} d) {a, b, c}
2. Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is [1]
a) b)
c) d)
3. The probability that a leap year will have 53 Fridays or 53 Saturdays is [1]
2 7 3 7 1 7 4 7 a) b) 2
c) 0 d) -1
4.  is equal to
[1]
( - x ) l i m x ? 8 + x + 1 x 2 - - - - - - - - v 1 2 a) x + y = 1 b) x – y = 5
c) x + y = 5 d) x – y = 1
5. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is [1]
a)
2
n
-1
b)
2
n
 - 2
6. The number of subsets of a set containing n elements is [1]
Page 1 of 18
c)
2
n d) n
a)
|z
2
| = |z|
2 b)
|z
2
| < |z|
2
c)
|z
2
|  |z|
2 d)
|z
2
| > |z|
2
7. If z is a complex number, then [1]
= a) R - [0, 4] b) (0, 4)
c) d) R - (0, 4)
8. The domain of definition of f(x) =  is [1] 4 x - x 2 - - - - - - v [ 0 , 4 ] a) 3  x  91 b) 3  x  5
c) 5  x  91 d) 8  x  22
9. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm
longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for
the shortest board if the third piece is to be at least 5 cm longer than the second?
[1]
= = = = = = = = a) both are equal b) cos 24°
c) sin 24° d) cannot be compared
10. Which is greater, sin 24° or cos 24° ? [1]
a) 6 b) 7
c) 8 d) 5
11. The number of proper subsets of the set {1, 2, 3} is : [1]
a) b)
c) d) -1
12. The sum of the infinite geometric series  ?
[1]
( + - + … 8 ) = - 5 4 5 1 6 5 6 4 - 1 4 5 8 1 4 a) b) 2n
c)
2
n-1 d)
2
n
13.  = ?
[1]
{ + 2 + c 1 c 0 C 2 C 1 3 + … + n · } C 3 C 2 C n C n - 1 n ( n + 1 ) 1 2 a) x  (– 13, 7] b) x  (– 10, 7]
c) x  (– , – 13]  [8, ) d) x  (– , – 13]  [7, )
14. If |x + 3|  10 , then [1] = ? ? ? 8 ? 8 ? 8 ? 8 a) A and the complement of B are always non-
disjoint
b) none of these
c) A and B are always disjoint d) B is always a subset of A
15. Let A and B be two non- empty subsets of a set X such that A is not a subset of B, then [1]
a) 7.7 cm b) 8.8 cm
c) 9.1 cm d) 6.6 cm
16. In a circle of radius 14 cm an arc subtends an angle of 36° at the centre. The length of the arc is [1]
Page 2 of 18
Section B
Section C
a) None of these b) 1
c) 100 d) 0
17. If x + iy = (1 + i) (1 + 2i) (1 + 3i), then x
2
 + y
2
 =
[1]
a) 240 b) 3125
c) 216 d) 600
18. A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The
total number of ways this can be done is 
[Hint: 5 digit numbers can be formed using digits 0, 1, 2, 4, 5 or by using digits 1, 2, 3, 4, 5 since sum of digits
in these cases is divisible by 3.]
[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 proper measure of dispersion about the mean of a set of observations i.e. standard deviation
is expressed as positive square root of the variance. 
Reason (R): The units of individual observations x
i
 and the unit of their mean are different that of variance.
Since, variance involves sum of squares of (x - ).
[1]
x ¯ 21. Draw the graph of the step function f(x) = [x]. [2]
OR
Find the domain of the real function: f(x) = 
2 x - 3 + x - 2 x 2 22. Differentiate: (3x-5)(4x
2 
- 3 + e
x
).
[2]
23. Find the equation of the circle, the coordinates of the end points of one of whose diameters are A (5, -3) and B
(2, -4)
[2]
OR
Find the equation of the parabola whose: focus is (0, 0) and the directrix is 2x - y - 1 = 0.
24. Write A = in set - builder form.
[2]
{ 1 , , , , , , } 1 4 1 9 1 1 6 1 2 5 1 3 6 1 4 9 25. Find the angle between the lines whose slopes are  and . [2] 3 – v 1 3 v 26. For any sets A, B and C, prove that: [3] A × ( B n C ) = ( A × B ) n ( A × C ) 27. Solve the inequation . [3] ? 4 2 x + 4 x - 3 28. Find the foot of perpendicular from the point (2, 3, -8) to the line . Also, find the perpendicular
distance from the given point to the line.
[3]
OR
Find the distance between the point (-1, -5, -10) and the point of intersection of the line and the
= = 4 - x 2 y 6 1 - z 3 = = x - 2 3 y + 1 4 z - 2 1 2 Page 3 of 18
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. cos 15° - sin 15° = ? [1]
1 2 ( - 1 ) 2 v 2 v 1 2 v ( + 1 ) 2 v 2 v a) {b, c} b) {c}
c) {a, b} d) {a, b, c}
2. Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is [1]
a) b)
c) d)
3. The probability that a leap year will have 53 Fridays or 53 Saturdays is [1]
2 7 3 7 1 7 4 7 a) b) 2
c) 0 d) -1
4.  is equal to
[1]
( - x ) l i m x ? 8 + x + 1 x 2 - - - - - - - - v 1 2 a) x + y = 1 b) x – y = 5
c) x + y = 5 d) x – y = 1
5. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is [1]
a)
2
n
-1
b)
2
n
 - 2
6. The number of subsets of a set containing n elements is [1]
Page 1 of 18
c)
2
n d) n
a)
|z
2
| = |z|
2 b)
|z
2
| < |z|
2
c)
|z
2
|  |z|
2 d)
|z
2
| > |z|
2
7. If z is a complex number, then [1]
= a) R - [0, 4] b) (0, 4)
c) d) R - (0, 4)
8. The domain of definition of f(x) =  is [1] 4 x - x 2 - - - - - - v [ 0 , 4 ] a) 3  x  91 b) 3  x  5
c) 5  x  91 d) 8  x  22
9. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm
longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for
the shortest board if the third piece is to be at least 5 cm longer than the second?
[1]
= = = = = = = = a) both are equal b) cos 24°
c) sin 24° d) cannot be compared
10. Which is greater, sin 24° or cos 24° ? [1]
a) 6 b) 7
c) 8 d) 5
11. The number of proper subsets of the set {1, 2, 3} is : [1]
a) b)
c) d) -1
12. The sum of the infinite geometric series  ?
[1]
( + - + … 8 ) = - 5 4 5 1 6 5 6 4 - 1 4 5 8 1 4 a) b) 2n
c)
2
n-1 d)
2
n
13.  = ?
[1]
{ + 2 + c 1 c 0 C 2 C 1 3 + … + n · } C 3 C 2 C n C n - 1 n ( n + 1 ) 1 2 a) x  (– 13, 7] b) x  (– 10, 7]
c) x  (– , – 13]  [8, ) d) x  (– , – 13]  [7, )
14. If |x + 3|  10 , then [1] = ? ? ? 8 ? 8 ? 8 ? 8 a) A and the complement of B are always non-
disjoint
b) none of these
c) A and B are always disjoint d) B is always a subset of A
15. Let A and B be two non- empty subsets of a set X such that A is not a subset of B, then [1]
a) 7.7 cm b) 8.8 cm
c) 9.1 cm d) 6.6 cm
16. In a circle of radius 14 cm an arc subtends an angle of 36° at the centre. The length of the arc is [1]
Page 2 of 18
Section B
Section C
a) None of these b) 1
c) 100 d) 0
17. If x + iy = (1 + i) (1 + 2i) (1 + 3i), then x
2
 + y
2
 =
[1]
a) 240 b) 3125
c) 216 d) 600
18. A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The
total number of ways this can be done is 
[Hint: 5 digit numbers can be formed using digits 0, 1, 2, 4, 5 or by using digits 1, 2, 3, 4, 5 since sum of digits
in these cases is divisible by 3.]
[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 proper measure of dispersion about the mean of a set of observations i.e. standard deviation
is expressed as positive square root of the variance. 
Reason (R): The units of individual observations x
i
 and the unit of their mean are different that of variance.
Since, variance involves sum of squares of (x - ).
[1]
x ¯ 21. Draw the graph of the step function f(x) = [x]. [2]
OR
Find the domain of the real function: f(x) = 
2 x - 3 + x - 2 x 2 22. Differentiate: (3x-5)(4x
2 
- 3 + e
x
).
[2]
23. Find the equation of the circle, the coordinates of the end points of one of whose diameters are A (5, -3) and B
(2, -4)
[2]
OR
Find the equation of the parabola whose: focus is (0, 0) and the directrix is 2x - y - 1 = 0.
24. Write A = in set - builder form.
[2]
{ 1 , , , , , , } 1 4 1 9 1 1 6 1 2 5 1 3 6 1 4 9 25. Find the angle between the lines whose slopes are  and . [2] 3 – v 1 3 v 26. For any sets A, B and C, prove that: [3] A × ( B n C ) = ( A × B ) n ( A × C ) 27. Solve the inequation . [3] ? 4 2 x + 4 x - 3 28. Find the foot of perpendicular from the point (2, 3, -8) to the line . Also, find the perpendicular
distance from the given point to the line.
[3]
OR
Find the distance between the point (-1, -5, -10) and the point of intersection of the line and the
= = 4 - x 2 y 6 1 - z 3 = = x - 2 3 y + 1 4 z - 2 1 2 Page 3 of 18
Section D
Section E
plane x - y + z = 5.
29. Find the expansion of (3x
2
 - 2ax + 3a
2
)
3 
using binomial theorem.
[3]
OR
If a and b are distinct integers, prove that a - b is a factor of a
n
 - b
n
, whenever n is a positive integer.
30. Express the complex number  in the form of a + ib.
[3]
OR
Find the square root of 
( - 2 - i ) 1 3 3 - 2 + 2 i 3 – v 31. For all sets A, B and C 
Is (A – B)  (C – B) = (A  C) – B? 
Justify your answer.
[3]
n n 32. A number is chosen from the numbers 1 to 100. Find the probability of its being divisible by 4 or 6. [5]
33. i. Find the derivative of 
ii. Let  find quadratic equation whose roots are  and 
[5]
OR
Show that  .
. s i n x + c o s x s i n x - c o s x f ( x ) = { , - 1 , x 2 2 x + 3 , 0 < x < 2 2 = x < 3 f ( x ) l i m x ? 2 - f ( x ) . l i m x ? 2 + ( - x ) l i m x ? 8 + x + 1 x 2 - - - - - - - - v ? ( - x ) l i m x ? 8 + 1 x 2 - - - - - v 34. Find the three numbers in GP, whose sum is 52 and sum of whose product in pairs is 624. [5]
35. Prove that [5]
OR
Prove that: cos 10° cos 30° cos 50° cos 70° = .
c o s 2 x · c o s - c o s 3 x · c o s = s i n 5 x · s i n x 2 9 x 2 5 x 2 3 1 6 36. Read the text carefully and answer the questions:
A farmer wishes to install 2 handpumps in his field for watering. 
The farmer moves in the field while watering in such a way that the sum of distances between the farmer and
each handpump is always 26m. Also, the distance between the hand pumps is 10 m. 
[4]
OR
Name the curve traced by farmer and hence find the foci of curve. (i)
Find the equation of curve traced by farmer. (ii)
Find the length of major axis, minor axis and eccentricity of curve along which farmer moves. (iii)
Find the length of latus rectum.
Page 4 of 18
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. cos 15° - sin 15° = ? [1]
1 2 ( - 1 ) 2 v 2 v 1 2 v ( + 1 ) 2 v 2 v a) {b, c} b) {c}
c) {a, b} d) {a, b, c}
2. Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is [1]
a) b)
c) d)
3. The probability that a leap year will have 53 Fridays or 53 Saturdays is [1]
2 7 3 7 1 7 4 7 a) b) 2
c) 0 d) -1
4.  is equal to
[1]
( - x ) l i m x ? 8 + x + 1 x 2 - - - - - - - - v 1 2 a) x + y = 1 b) x – y = 5
c) x + y = 5 d) x – y = 1
5. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is [1]
a)
2
n
-1
b)
2
n
 - 2
6. The number of subsets of a set containing n elements is [1]
Page 1 of 18
c)
2
n d) n
a)
|z
2
| = |z|
2 b)
|z
2
| < |z|
2
c)
|z
2
|  |z|
2 d)
|z
2
| > |z|
2
7. If z is a complex number, then [1]
= a) R - [0, 4] b) (0, 4)
c) d) R - (0, 4)
8. The domain of definition of f(x) =  is [1] 4 x - x 2 - - - - - - v [ 0 , 4 ] a) 3  x  91 b) 3  x  5
c) 5  x  91 d) 8  x  22
9. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm
longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for
the shortest board if the third piece is to be at least 5 cm longer than the second?
[1]
= = = = = = = = a) both are equal b) cos 24°
c) sin 24° d) cannot be compared
10. Which is greater, sin 24° or cos 24° ? [1]
a) 6 b) 7
c) 8 d) 5
11. The number of proper subsets of the set {1, 2, 3} is : [1]
a) b)
c) d) -1
12. The sum of the infinite geometric series  ?
[1]
( + - + … 8 ) = - 5 4 5 1 6 5 6 4 - 1 4 5 8 1 4 a) b) 2n
c)
2
n-1 d)
2
n
13.  = ?
[1]
{ + 2 + c 1 c 0 C 2 C 1 3 + … + n · } C 3 C 2 C n C n - 1 n ( n + 1 ) 1 2 a) x  (– 13, 7] b) x  (– 10, 7]
c) x  (– , – 13]  [8, ) d) x  (– , – 13]  [7, )
14. If |x + 3|  10 , then [1] = ? ? ? 8 ? 8 ? 8 ? 8 a) A and the complement of B are always non-
disjoint
b) none of these
c) A and B are always disjoint d) B is always a subset of A
15. Let A and B be two non- empty subsets of a set X such that A is not a subset of B, then [1]
a) 7.7 cm b) 8.8 cm
c) 9.1 cm d) 6.6 cm
16. In a circle of radius 14 cm an arc subtends an angle of 36° at the centre. The length of the arc is [1]
Page 2 of 18
Section B
Section C
a) None of these b) 1
c) 100 d) 0
17. If x + iy = (1 + i) (1 + 2i) (1 + 3i), then x
2
 + y
2
 =
[1]
a) 240 b) 3125
c) 216 d) 600
18. A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The
total number of ways this can be done is 
[Hint: 5 digit numbers can be formed using digits 0, 1, 2, 4, 5 or by using digits 1, 2, 3, 4, 5 since sum of digits
in these cases is divisible by 3.]
[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 proper measure of dispersion about the mean of a set of observations i.e. standard deviation
is expressed as positive square root of the variance. 
Reason (R): The units of individual observations x
i
 and the unit of their mean are different that of variance.
Since, variance involves sum of squares of (x - ).
[1]
x ¯ 21. Draw the graph of the step function f(x) = [x]. [2]
OR
Find the domain of the real function: f(x) = 
2 x - 3 + x - 2 x 2 22. Differentiate: (3x-5)(4x
2 
- 3 + e
x
).
[2]
23. Find the equation of the circle, the coordinates of the end points of one of whose diameters are A (5, -3) and B
(2, -4)
[2]
OR
Find the equation of the parabola whose: focus is (0, 0) and the directrix is 2x - y - 1 = 0.
24. Write A = in set - builder form.
[2]
{ 1 , , , , , , } 1 4 1 9 1 1 6 1 2 5 1 3 6 1 4 9 25. Find the angle between the lines whose slopes are  and . [2] 3 – v 1 3 v 26. For any sets A, B and C, prove that: [3] A × ( B n C ) = ( A × B ) n ( A × C ) 27. Solve the inequation . [3] ? 4 2 x + 4 x - 3 28. Find the foot of perpendicular from the point (2, 3, -8) to the line . Also, find the perpendicular
distance from the given point to the line.
[3]
OR
Find the distance between the point (-1, -5, -10) and the point of intersection of the line and the
= = 4 - x 2 y 6 1 - z 3 = = x - 2 3 y + 1 4 z - 2 1 2 Page 3 of 18
Section D
Section E
plane x - y + z = 5.
29. Find the expansion of (3x
2
 - 2ax + 3a
2
)
3 
using binomial theorem.
[3]
OR
If a and b are distinct integers, prove that a - b is a factor of a
n
 - b
n
, whenever n is a positive integer.
30. Express the complex number  in the form of a + ib.
[3]
OR
Find the square root of 
( - 2 - i ) 1 3 3 - 2 + 2 i 3 – v 31. For all sets A, B and C 
Is (A – B)  (C – B) = (A  C) – B? 
Justify your answer.
[3]
n n 32. A number is chosen from the numbers 1 to 100. Find the probability of its being divisible by 4 or 6. [5]
33. i. Find the derivative of 
ii. Let  find quadratic equation whose roots are  and 
[5]
OR
Show that  .
. s i n x + c o s x s i n x - c o s x f ( x ) = { , - 1 , x 2 2 x + 3 , 0 < x < 2 2 = x < 3 f ( x ) l i m x ? 2 - f ( x ) . l i m x ? 2 + ( - x ) l i m x ? 8 + x + 1 x 2 - - - - - - - - v ? ( - x ) l i m x ? 8 + 1 x 2 - - - - - v 34. Find the three numbers in GP, whose sum is 52 and sum of whose product in pairs is 624. [5]
35. Prove that [5]
OR
Prove that: cos 10° cos 30° cos 50° cos 70° = .
c o s 2 x · c o s - c o s 3 x · c o s = s i n 5 x · s i n x 2 9 x 2 5 x 2 3 1 6 36. Read the text carefully and answer the questions:
A farmer wishes to install 2 handpumps in his field for watering. 
The farmer moves in the field while watering in such a way that the sum of distances between the farmer and
each handpump is always 26m. Also, the distance between the hand pumps is 10 m. 
[4]
OR
Name the curve traced by farmer and hence find the foci of curve. (i)
Find the equation of curve traced by farmer. (ii)
Find the length of major axis, minor axis and eccentricity of curve along which farmer moves. (iii)
Find the length of latus rectum.
Page 4 of 18
37. Read the text carefully and answer the questions:
For a group of 200 candidates, the mean and the standard deviation of scores were found to be 40 and 15 ,
respectively. Later on it was discovered that the scores of 43 and 35 were misread as 34 and 53, respectively.
Student Eng Hindi S.St Science Maths
Ramu 39 59 84 80 41
Rajitha 79 92 68 38 75
Komala 41 60 38 71 82
Patil 77 77 87 75 42
Pursi 72 65 69 83 67
Gayathri 46 96 53 71 39
[4]
OR
Find the correct variance. (i)
What is the formula of variance. (ii)
Find the correct mean. (iii)
Find the sum of correct scores.
38. Read the text carefully and answer the questions:
A state cricket authority has to choose a team of 11 members, to do it so the authority asks 2 coaches of a
government academy to select the team members that have experience as well as the best performers in last 15
matches. They can make up a team of 11 cricketers amongst 15 possible candidates. In how many ways can the
final eleven be selected from 15 cricket players if: 
[4]
Two of them being leg spinners, in how many ways can be the final eleven be selected from 15 cricket
players if one and only one leg spinner must be included?
(i)
If there are 6 bowlers, 3 wicketkeepers, and 6 batsmen in all. In how many ways can be the final eleven be
selected from 15 cricket players if 4 bowlers, 2 wicketkeepers and 5 batsmen are included.
(ii)
Page 5 of 18