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CBSE XI | Mathematics 
Sample Paper – 3 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 3 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. In ?ABC, a = 18, b = 24 and c = 30 and m ?C = 90
o
, find sin A. 
 
2. If f(x) is a linear function of x. f: Z ?Z, f(x) = a x + b. Find a and b  
if { (1,3) , (-1, -7 ) , (2, 8) (-2 , -12 )} ?f. 
 
3. 
2
2
x4
Find the domain of the function f(x) =
x 8x 12
?
??
 
 
4. With p: It is cloudy and q: Sun is shining and the usual meanings of the symbols: ?, ?, 
?, ?, ?,  express the statement below symbolically.  
 ‘It is not true that it is cloudy if and only if the Sun is not shining.’ 
OR 
 Write negation of the : Every living person is not 150 years old. 
 
SECTION – B 
 
5. What are the real numbers 'x' and 'y', if (x - iy) (3 + 5i) is the conjugate of (-1 - 3i) 
OR 
Find modulus of (3 + 4i)(4 + i). 
 
 
 
 
Page 2


  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 3 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. In ?ABC, a = 18, b = 24 and c = 30 and m ?C = 90
o
, find sin A. 
 
2. If f(x) is a linear function of x. f: Z ?Z, f(x) = a x + b. Find a and b  
if { (1,3) , (-1, -7 ) , (2, 8) (-2 , -12 )} ?f. 
 
3. 
2
2
x4
Find the domain of the function f(x) =
x 8x 12
?
??
 
 
4. With p: It is cloudy and q: Sun is shining and the usual meanings of the symbols: ?, ?, 
?, ?, ?,  express the statement below symbolically.  
 ‘It is not true that it is cloudy if and only if the Sun is not shining.’ 
OR 
 Write negation of the : Every living person is not 150 years old. 
 
SECTION – B 
 
5. What are the real numbers 'x' and 'y', if (x - iy) (3 + 5i) is the conjugate of (-1 - 3i) 
OR 
Find modulus of (3 + 4i)(4 + i). 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
6.  A pendulum, 36 cm long, oscillates through an angle of 10 degrees. Find the length of 
the path described by its extremity. 
OR 
The area of sector is 5.024 cm
2
 and its angle is 36°. Find the radius. (p = 3.14) 
 
7. Find the sum of 19 terms of A.P. whose nth term is 2n+1. 
 
8. Find the LCM of 4!, 5! and 6! 
  
OR 
Express 
? ?
2
1
2i ?
 in the standard form of a + ib. 
 
9.  Find the total number of rectangles in the given figure 
 
     
     
     
     
  
10.  Find the sum of the given sequence uptill the n
th
 term:  
 1.2 + 2. 3 + 3. 4 +… 
 
11. In a group of 400 people, 250 can speak Hindi and 200 can speak English. Everyone can 
speak atleast one language. How many people can speak both Hindi and English? 
 
12. If Sn = 210, then find Sn
2
. 
SECTION – C 
 
13. An equilateral triangle is inscribed in the parabola y
2
 = 4ax, where one vertex of the 
triangle is at the vertex of the parabola. Find the length of the side of the triangle. 
 
14. Prove that: (cos3x – cosx) cosx + (sin3x + sinx) sinx = 0 
OR 
 Simplify the expression: sin7x + sinx + sin3x + sin5x  
 
15. If the sum of an infinite geometric series is 15 and the sum of the squares of these terms 
is 45, find the series. 
 
 
 
 
Page 3


  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 3 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. In ?ABC, a = 18, b = 24 and c = 30 and m ?C = 90
o
, find sin A. 
 
2. If f(x) is a linear function of x. f: Z ?Z, f(x) = a x + b. Find a and b  
if { (1,3) , (-1, -7 ) , (2, 8) (-2 , -12 )} ?f. 
 
3. 
2
2
x4
Find the domain of the function f(x) =
x 8x 12
?
??
 
 
4. With p: It is cloudy and q: Sun is shining and the usual meanings of the symbols: ?, ?, 
?, ?, ?,  express the statement below symbolically.  
 ‘It is not true that it is cloudy if and only if the Sun is not shining.’ 
OR 
 Write negation of the : Every living person is not 150 years old. 
 
SECTION – B 
 
5. What are the real numbers 'x' and 'y', if (x - iy) (3 + 5i) is the conjugate of (-1 - 3i) 
OR 
Find modulus of (3 + 4i)(4 + i). 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
6.  A pendulum, 36 cm long, oscillates through an angle of 10 degrees. Find the length of 
the path described by its extremity. 
OR 
The area of sector is 5.024 cm
2
 and its angle is 36°. Find the radius. (p = 3.14) 
 
7. Find the sum of 19 terms of A.P. whose nth term is 2n+1. 
 
8. Find the LCM of 4!, 5! and 6! 
  
OR 
Express 
? ?
2
1
2i ?
 in the standard form of a + ib. 
 
9.  Find the total number of rectangles in the given figure 
 
     
     
     
     
  
10.  Find the sum of the given sequence uptill the n
th
 term:  
 1.2 + 2. 3 + 3. 4 +… 
 
11. In a group of 400 people, 250 can speak Hindi and 200 can speak English. Everyone can 
speak atleast one language. How many people can speak both Hindi and English? 
 
12. If Sn = 210, then find Sn
2
. 
SECTION – C 
 
13. An equilateral triangle is inscribed in the parabola y
2
 = 4ax, where one vertex of the 
triangle is at the vertex of the parabola. Find the length of the side of the triangle. 
 
14. Prove that: (cos3x – cosx) cosx + (sin3x + sinx) sinx = 0 
OR 
 Simplify the expression: sin7x + sinx + sin3x + sin5x  
 
15. If the sum of an infinite geometric series is 15 and the sum of the squares of these terms 
is 45, find the series. 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
16. Let A = {a, b, c}, B = {c, d} and C = {d, e, f }. Find 
 (i) A × (B ? C)  (ii) (A × B) ? (A × C) 
 (iii) A × (B ? C)  (iv) (A × B) ? (A × C) 
 
17. 
2
2
x
If f :R R; f(x) .What  is the range of f?
x1
??
?
 
 
18. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how 
many of these 
(i) four cards are of the same suit 
 (ii) four cards belong to four different suits 
 (iii) are face cards 
 (iv) two are red cards and two are black cards 
 
 
19. Evaluate: (99)
5
 using the Binomial theorem 
OR 
      Find the ratio of the co-efficient of x
2
 and x
3
 in the binomial expansion (3 + ax)
9 
 
20. 
? ?
2
22
a-ib
If x  iy = ,find x y .
c-id
?? 
OR 
 
 Let z1  =  2 – i  and z2 =  -2  +  i  , then find 
 
? ?
12
1 1 2
zz 1
i Re                      (ii)Im
z z z
? ? ? ?
? ? ? ?
? ? ? ?
 
 
21. Find the roots of the equation
2
10
3 x 4x 0
7
? ? ? 
22.  Find the domain and range of the function :  ? ?
1
fx
2 sin3x
?
?
 
 
23. Plot the given linear in equations and shade the region which is common to the solution 
of all inequations x ? 0, y ?? 0, 5x + 3y ? 500; x ? 70 and   y  ?  125. 
 
 
 
 
 
 
Page 4


  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 3 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. In ?ABC, a = 18, b = 24 and c = 30 and m ?C = 90
o
, find sin A. 
 
2. If f(x) is a linear function of x. f: Z ?Z, f(x) = a x + b. Find a and b  
if { (1,3) , (-1, -7 ) , (2, 8) (-2 , -12 )} ?f. 
 
3. 
2
2
x4
Find the domain of the function f(x) =
x 8x 12
?
??
 
 
4. With p: It is cloudy and q: Sun is shining and the usual meanings of the symbols: ?, ?, 
?, ?, ?,  express the statement below symbolically.  
 ‘It is not true that it is cloudy if and only if the Sun is not shining.’ 
OR 
 Write negation of the : Every living person is not 150 years old. 
 
SECTION – B 
 
5. What are the real numbers 'x' and 'y', if (x - iy) (3 + 5i) is the conjugate of (-1 - 3i) 
OR 
Find modulus of (3 + 4i)(4 + i). 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
6.  A pendulum, 36 cm long, oscillates through an angle of 10 degrees. Find the length of 
the path described by its extremity. 
OR 
The area of sector is 5.024 cm
2
 and its angle is 36°. Find the radius. (p = 3.14) 
 
7. Find the sum of 19 terms of A.P. whose nth term is 2n+1. 
 
8. Find the LCM of 4!, 5! and 6! 
  
OR 
Express 
? ?
2
1
2i ?
 in the standard form of a + ib. 
 
9.  Find the total number of rectangles in the given figure 
 
     
     
     
     
  
10.  Find the sum of the given sequence uptill the n
th
 term:  
 1.2 + 2. 3 + 3. 4 +… 
 
11. In a group of 400 people, 250 can speak Hindi and 200 can speak English. Everyone can 
speak atleast one language. How many people can speak both Hindi and English? 
 
12. If Sn = 210, then find Sn
2
. 
SECTION – C 
 
13. An equilateral triangle is inscribed in the parabola y
2
 = 4ax, where one vertex of the 
triangle is at the vertex of the parabola. Find the length of the side of the triangle. 
 
14. Prove that: (cos3x – cosx) cosx + (sin3x + sinx) sinx = 0 
OR 
 Simplify the expression: sin7x + sinx + sin3x + sin5x  
 
15. If the sum of an infinite geometric series is 15 and the sum of the squares of these terms 
is 45, find the series. 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
16. Let A = {a, b, c}, B = {c, d} and C = {d, e, f }. Find 
 (i) A × (B ? C)  (ii) (A × B) ? (A × C) 
 (iii) A × (B ? C)  (iv) (A × B) ? (A × C) 
 
17. 
2
2
x
If f :R R; f(x) .What  is the range of f?
x1
??
?
 
 
18. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how 
many of these 
(i) four cards are of the same suit 
 (ii) four cards belong to four different suits 
 (iii) are face cards 
 (iv) two are red cards and two are black cards 
 
 
19. Evaluate: (99)
5
 using the Binomial theorem 
OR 
      Find the ratio of the co-efficient of x
2
 and x
3
 in the binomial expansion (3 + ax)
9 
 
20. 
? ?
2
22
a-ib
If x  iy = ,find x y .
c-id
?? 
OR 
 
 Let z1  =  2 – i  and z2 =  -2  +  i  , then find 
 
? ?
12
1 1 2
zz 1
i Re                      (ii)Im
z z z
? ? ? ?
? ? ? ?
? ? ? ?
 
 
21. Find the roots of the equation
2
10
3 x 4x 0
7
? ? ? 
22.  Find the domain and range of the function :  ? ?
1
fx
2 sin3x
?
?
 
 
23. Plot the given linear in equations and shade the region which is common to the solution 
of all inequations x ? 0, y ?? 0, 5x + 3y ? 500; x ? 70 and   y  ?  125. 
 
 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
SECTION – D 
 
24. The scores of two batsmen A and B, in ten innings during a certain season are given 
below, Find which batsman is more consistent in scoring. 
 
 
A B 
32 19 
28 31 
47 48 
63 53 
71 67 
39 90 
10 10 
60 62 
96 40 
14 80 
 
OR 
The mean and variance of 7 observations are 8 and 16 respectively. If 5 of the 
observations are 2, 4, 10, 12, 14, find the remaining two observations. 
 
25. From the digits 0, 1, 3, 5 and 7, how many 4 digit numbers greater than 5000 can be  
formed? What is the probability that the number formed is divisible by 5, if 
 (i) the digits are repeated  
 (ii) the digits are not repeated  
 
26. ? ? ? ?
3
1 x 2
If x Q  and  cosx = ,thenshow that sin .
3 2 3
 
OR 
If 
3
tan tan
4 2 4 2
? ? ? ? ? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
 prove that 
3
2
3sin sin
sin
1 3sin
? ? ?
??
??
 
 
27. (i) Find the derivative of the given function  using the first principle:  
       
? ??
?
??
??
f(x) = cos x
16
 
       (ii) Evaluate: 
cos x
x
2
51
lim , x .
2
x
2
?
?
??
?
?
?
    
 
Page 5


  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 3 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. In ?ABC, a = 18, b = 24 and c = 30 and m ?C = 90
o
, find sin A. 
 
2. If f(x) is a linear function of x. f: Z ?Z, f(x) = a x + b. Find a and b  
if { (1,3) , (-1, -7 ) , (2, 8) (-2 , -12 )} ?f. 
 
3. 
2
2
x4
Find the domain of the function f(x) =
x 8x 12
?
??
 
 
4. With p: It is cloudy and q: Sun is shining and the usual meanings of the symbols: ?, ?, 
?, ?, ?,  express the statement below symbolically.  
 ‘It is not true that it is cloudy if and only if the Sun is not shining.’ 
OR 
 Write negation of the : Every living person is not 150 years old. 
 
SECTION – B 
 
5. What are the real numbers 'x' and 'y', if (x - iy) (3 + 5i) is the conjugate of (-1 - 3i) 
OR 
Find modulus of (3 + 4i)(4 + i). 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
6.  A pendulum, 36 cm long, oscillates through an angle of 10 degrees. Find the length of 
the path described by its extremity. 
OR 
The area of sector is 5.024 cm
2
 and its angle is 36°. Find the radius. (p = 3.14) 
 
7. Find the sum of 19 terms of A.P. whose nth term is 2n+1. 
 
8. Find the LCM of 4!, 5! and 6! 
  
OR 
Express 
? ?
2
1
2i ?
 in the standard form of a + ib. 
 
9.  Find the total number of rectangles in the given figure 
 
     
     
     
     
  
10.  Find the sum of the given sequence uptill the n
th
 term:  
 1.2 + 2. 3 + 3. 4 +… 
 
11. In a group of 400 people, 250 can speak Hindi and 200 can speak English. Everyone can 
speak atleast one language. How many people can speak both Hindi and English? 
 
12. If Sn = 210, then find Sn
2
. 
SECTION – C 
 
13. An equilateral triangle is inscribed in the parabola y
2
 = 4ax, where one vertex of the 
triangle is at the vertex of the parabola. Find the length of the side of the triangle. 
 
14. Prove that: (cos3x – cosx) cosx + (sin3x + sinx) sinx = 0 
OR 
 Simplify the expression: sin7x + sinx + sin3x + sin5x  
 
15. If the sum of an infinite geometric series is 15 and the sum of the squares of these terms 
is 45, find the series. 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
16. Let A = {a, b, c}, B = {c, d} and C = {d, e, f }. Find 
 (i) A × (B ? C)  (ii) (A × B) ? (A × C) 
 (iii) A × (B ? C)  (iv) (A × B) ? (A × C) 
 
17. 
2
2
x
If f :R R; f(x) .What  is the range of f?
x1
??
?
 
 
18. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how 
many of these 
(i) four cards are of the same suit 
 (ii) four cards belong to four different suits 
 (iii) are face cards 
 (iv) two are red cards and two are black cards 
 
 
19. Evaluate: (99)
5
 using the Binomial theorem 
OR 
      Find the ratio of the co-efficient of x
2
 and x
3
 in the binomial expansion (3 + ax)
9 
 
20. 
? ?
2
22
a-ib
If x  iy = ,find x y .
c-id
?? 
OR 
 
 Let z1  =  2 – i  and z2 =  -2  +  i  , then find 
 
? ?
12
1 1 2
zz 1
i Re                      (ii)Im
z z z
? ? ? ?
? ? ? ?
? ? ? ?
 
 
21. Find the roots of the equation
2
10
3 x 4x 0
7
? ? ? 
22.  Find the domain and range of the function :  ? ?
1
fx
2 sin3x
?
?
 
 
23. Plot the given linear in equations and shade the region which is common to the solution 
of all inequations x ? 0, y ?? 0, 5x + 3y ? 500; x ? 70 and   y  ?  125. 
 
 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
SECTION – D 
 
24. The scores of two batsmen A and B, in ten innings during a certain season are given 
below, Find which batsman is more consistent in scoring. 
 
 
A B 
32 19 
28 31 
47 48 
63 53 
71 67 
39 90 
10 10 
60 62 
96 40 
14 80 
 
OR 
The mean and variance of 7 observations are 8 and 16 respectively. If 5 of the 
observations are 2, 4, 10, 12, 14, find the remaining two observations. 
 
25. From the digits 0, 1, 3, 5 and 7, how many 4 digit numbers greater than 5000 can be  
formed? What is the probability that the number formed is divisible by 5, if 
 (i) the digits are repeated  
 (ii) the digits are not repeated  
 
26. ? ? ? ?
3
1 x 2
If x Q  and  cosx = ,thenshow that sin .
3 2 3
 
OR 
If 
3
tan tan
4 2 4 2
? ? ? ? ? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
 prove that 
3
2
3sin sin
sin
1 3sin
? ? ?
??
??
 
 
27. (i) Find the derivative of the given function  using the first principle:  
       
? ??
?
??
??
f(x) = cos x
16
 
       (ii) Evaluate: 
cos x
x
2
51
lim , x .
2
x
2
?
?
??
?
?
?
    
 
  
 
CBSE XI | Mathematics 
Sample Paper – 3 
 
     
28. If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are 
concurrent, then find (i) the condition of concurrence of the three lines(ii) the point of 
concurrence. 
                                                            OR 
 A beam is supported at its ends by supports which are 14 cm apart. Since the load is 
concentrated at its centre, there is a deflection of 5 cm at the centre and the deflected 
beam is in the shape of a parabola. How far from the centre is the deflection of 2 cm? 
 
29. Prove by using the principle of mathematical induction that (x
2n 
– y
2n
) is divisible by     
(x + y). 
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FAQs on Sample Question Paper 3 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce

1. What is the syllabus for the Class 11 Math exam?
Ans. The syllabus for the Class 11 Math exam typically covers topics such as sets, relations and functions, trigonometric functions, algebra, coordinate geometry, calculus, mathematical reasoning, and statistics.
2. How can I prepare for the Class 11 Math exam effectively?
Ans. To prepare for the Class 11 Math exam effectively, it is important to understand the concepts thoroughly. Practice solving a variety of problems from each topic, refer to textbooks and study materials, and solve previous years' question papers. Additionally, regular revision and seeking help from teachers or tutors can also be beneficial.
3. Are there any important tips for solving mathematical problems quickly in the Class 11 Math exam?
Ans. Yes, there are a few tips to solve mathematical problems quickly in the Class 11 Math exam. Firstly, familiarize yourself with all the relevant formulas and theorems. Secondly, practice mental calculations and approximation techniques to speed up calculations. Lastly, develop a systematic approach to problem-solving by breaking down complex problems into smaller, manageable steps.
4. Is it necessary to solve sample question papers before the Class 11 Math exam?
Ans. Yes, solving sample question papers before the Class 11 Math exam is highly recommended. It helps in understanding the exam pattern, time management, and identifying areas of improvement. Solving sample papers also gives you an idea of the types of questions that can be expected in the exam and helps in building confidence.
5. How can I improve my problem-solving skills for the Class 11 Math exam?
Ans. Improving problem-solving skills for the Class 11 Math exam requires regular practice. Start by solving problems from textbooks, reference books, and online resources. Understand the underlying concepts and try to solve problems using different approaches. Additionally, discussing problems with peers or seeking guidance from teachers can enhance problem-solving abilities.
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