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CBSE XI | Mathematics 
Sample Paper – 5 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 5 
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, if a = 2, b = 3 and sinA = 
2
3
, find m ? B. 
2. 
25
1
Find the value of 
i
??
??
??
 
OR 
Express the (1 + i)(1 + 2i) in the standard form of a + bi. 
 
3. Write the given statement in the form ‘If- then’, and state what are the component 
statements p and q.  
 If I have the money, i will buy an i-phone.  
 
4. The figure below gives a relation. Write it in the roster form. 
 
 
SECTION – B 
 
5. If P and Q are two sets such that P has 40 elements, P ? Q has 60 elements and P n Q has 
10 elements, how many elements does Q have? 
 
Page 2


  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 5 
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, if a = 2, b = 3 and sinA = 
2
3
, find m ? B. 
2. 
25
1
Find the value of 
i
??
??
??
 
OR 
Express the (1 + i)(1 + 2i) in the standard form of a + bi. 
 
3. Write the given statement in the form ‘If- then’, and state what are the component 
statements p and q.  
 If I have the money, i will buy an i-phone.  
 
4. The figure below gives a relation. Write it in the roster form. 
 
 
SECTION – B 
 
5. If P and Q are two sets such that P has 40 elements, P ? Q has 60 elements and P n Q has 
10 elements, how many elements does Q have? 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
6. Find the equation of the circle, the co-ordinates of the end points of whose diameter are 
(-1, 2) and (4, -3). 
 
7. What is the number of ways in which a set of 5 cards can be chosen out of a deck of 52 
cards, if each set of 5 cards has exactly one ace?  
OR 
   A die is thrown. Find the probability of getting  
1. a prime number  
2. a number more than 6 
 
8.  Prove that cos 5x = 16 cos
5
x – 20 cos
3
x + 5 cos x 
 
9.  In how many ways 6 different beads can be arranged on a thread to form a necklace? 
 
OR 
If 
1 1 x
9! 10! 11!
?? , find x. 
 
10.  Find an infinite GP whose first term is 1 and each term is the sum of all the terms which    
follow it. 
11. Find the values of' k' for which 
27
,k,
72
?? are in G.P. Find the common ratio/s of the G.P.  
OR 
Find the sum of 7 terms of the G.P. 3, 6, 12,… 
 
12. If 
(1 2) (1 2 3)
1 ...
23
? ? ?
? ? ? to n terms is S, then find S. 
 
SECTION – C 
 
13. 
?
?
?
1 + i 1 i
Evaluate:  
1 i 1 + i
 
OR 
 
    
22
If (a + ib) (c + id) (e + if) (g + ih) = A + iB,
then find the value of A B ?
 
 
14. Solve the given quadratic equation: ?
2
9x 12 x + 20 = 0 
 
15. Find the co-efficient of x
5
 in the expansion of the product (1 + 2x)
6
(1 - x)
7
 
 
Page 3


  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 5 
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, if a = 2, b = 3 and sinA = 
2
3
, find m ? B. 
2. 
25
1
Find the value of 
i
??
??
??
 
OR 
Express the (1 + i)(1 + 2i) in the standard form of a + bi. 
 
3. Write the given statement in the form ‘If- then’, and state what are the component 
statements p and q.  
 If I have the money, i will buy an i-phone.  
 
4. The figure below gives a relation. Write it in the roster form. 
 
 
SECTION – B 
 
5. If P and Q are two sets such that P has 40 elements, P ? Q has 60 elements and P n Q has 
10 elements, how many elements does Q have? 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
6. Find the equation of the circle, the co-ordinates of the end points of whose diameter are 
(-1, 2) and (4, -3). 
 
7. What is the number of ways in which a set of 5 cards can be chosen out of a deck of 52 
cards, if each set of 5 cards has exactly one ace?  
OR 
   A die is thrown. Find the probability of getting  
1. a prime number  
2. a number more than 6 
 
8.  Prove that cos 5x = 16 cos
5
x – 20 cos
3
x + 5 cos x 
 
9.  In how many ways 6 different beads can be arranged on a thread to form a necklace? 
 
OR 
If 
1 1 x
9! 10! 11!
?? , find x. 
 
10.  Find an infinite GP whose first term is 1 and each term is the sum of all the terms which    
follow it. 
11. Find the values of' k' for which 
27
,k,
72
?? are in G.P. Find the common ratio/s of the G.P.  
OR 
Find the sum of 7 terms of the G.P. 3, 6, 12,… 
 
12. If 
(1 2) (1 2 3)
1 ...
23
? ? ?
? ? ? to n terms is S, then find S. 
 
SECTION – C 
 
13. 
?
?
?
1 + i 1 i
Evaluate:  
1 i 1 + i
 
OR 
 
    
22
If (a + ib) (c + id) (e + if) (g + ih) = A + iB,
then find the value of A B ?
 
 
14. Solve the given quadratic equation: ?
2
9x 12 x + 20 = 0 
 
15. Find the co-efficient of x
5
 in the expansion of the product (1 + 2x)
6
(1 - x)
7
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
16. Show that: tan 3x tan 2x tan x = tan 3x – tan 2 x – tan x 
 
17. Prove that:  
sec8A 1 tan8A
sec4A 1 tan2A
?
?
?
 
OR 
 
 Prove that: a(sin B – sin C)+ b(sin C – sin A)+ c(sin A – sin B) = 0. 
 
18. Let A = {a, e, i, o, u} and B = {a, i, k, u}. Find A – B and B – A. Are the two sets A – B and B 
– A (i) equal (ii) mutually disjoint. Justify your answer.  
 
19.  Show that 2 2 2 2cos8 2cos , 0
8
?
? ? ? ? ? ? ? ? ? 
 
20. Draw the graph of f(x)
?? ?
?
?
?
?
?
?
3 x,x 1
1, x 1 and find the range of f .
2x, x 1
 
OR 
 
? ?
?
? ? ?
?
?
? ? ?
?
1, x 1
Draw the graph of f(x) x 1 x 1and find the range of f .
1, x 1
 
 
21. Let A = {a, b, c, d} and B = {p, q, r}. Write an example of onto and into function from A to   
   B. Does there exist a one-one function from A to B. Justify your answer. 
 
22. 
2 2 2
3
Prove that cos x cos (x ) cos (x )
3 3 2
??
? ? ? ? ? 
 
23. The mean of 8, 6, 7, 5, x and 4 is 7. Find (i) the value of x (ii) the mean if each 
observation was multiplied by 3 (iii) the mean deviation about the median for the 
original data 
 
SECTION – D 
 
24. When two dice are thrown simultaneously, find the probability that neither a doublet 
nor a total of 10 will appear. 
OR 
The probability that a student will receive A, B, C and D grade are 0.4, 0.35, 0.15 and 0.10 
respectively. Find the probability that a student will receive  
1. B or C grade 
2. At most C grade 
Page 4


  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 5 
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, if a = 2, b = 3 and sinA = 
2
3
, find m ? B. 
2. 
25
1
Find the value of 
i
??
??
??
 
OR 
Express the (1 + i)(1 + 2i) in the standard form of a + bi. 
 
3. Write the given statement in the form ‘If- then’, and state what are the component 
statements p and q.  
 If I have the money, i will buy an i-phone.  
 
4. The figure below gives a relation. Write it in the roster form. 
 
 
SECTION – B 
 
5. If P and Q are two sets such that P has 40 elements, P ? Q has 60 elements and P n Q has 
10 elements, how many elements does Q have? 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
6. Find the equation of the circle, the co-ordinates of the end points of whose diameter are 
(-1, 2) and (4, -3). 
 
7. What is the number of ways in which a set of 5 cards can be chosen out of a deck of 52 
cards, if each set of 5 cards has exactly one ace?  
OR 
   A die is thrown. Find the probability of getting  
1. a prime number  
2. a number more than 6 
 
8.  Prove that cos 5x = 16 cos
5
x – 20 cos
3
x + 5 cos x 
 
9.  In how many ways 6 different beads can be arranged on a thread to form a necklace? 
 
OR 
If 
1 1 x
9! 10! 11!
?? , find x. 
 
10.  Find an infinite GP whose first term is 1 and each term is the sum of all the terms which    
follow it. 
11. Find the values of' k' for which 
27
,k,
72
?? are in G.P. Find the common ratio/s of the G.P.  
OR 
Find the sum of 7 terms of the G.P. 3, 6, 12,… 
 
12. If 
(1 2) (1 2 3)
1 ...
23
? ? ?
? ? ? to n terms is S, then find S. 
 
SECTION – C 
 
13. 
?
?
?
1 + i 1 i
Evaluate:  
1 i 1 + i
 
OR 
 
    
22
If (a + ib) (c + id) (e + if) (g + ih) = A + iB,
then find the value of A B ?
 
 
14. Solve the given quadratic equation: ?
2
9x 12 x + 20 = 0 
 
15. Find the co-efficient of x
5
 in the expansion of the product (1 + 2x)
6
(1 - x)
7
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
16. Show that: tan 3x tan 2x tan x = tan 3x – tan 2 x – tan x 
 
17. Prove that:  
sec8A 1 tan8A
sec4A 1 tan2A
?
?
?
 
OR 
 
 Prove that: a(sin B – sin C)+ b(sin C – sin A)+ c(sin A – sin B) = 0. 
 
18. Let A = {a, e, i, o, u} and B = {a, i, k, u}. Find A – B and B – A. Are the two sets A – B and B 
– A (i) equal (ii) mutually disjoint. Justify your answer.  
 
19.  Show that 2 2 2 2cos8 2cos , 0
8
?
? ? ? ? ? ? ? ? ? 
 
20. Draw the graph of f(x)
?? ?
?
?
?
?
?
?
3 x,x 1
1, x 1 and find the range of f .
2x, x 1
 
OR 
 
? ?
?
? ? ?
?
?
? ? ?
?
1, x 1
Draw the graph of f(x) x 1 x 1and find the range of f .
1, x 1
 
 
21. Let A = {a, b, c, d} and B = {p, q, r}. Write an example of onto and into function from A to   
   B. Does there exist a one-one function from A to B. Justify your answer. 
 
22. 
2 2 2
3
Prove that cos x cos (x ) cos (x )
3 3 2
??
? ? ? ? ? 
 
23. The mean of 8, 6, 7, 5, x and 4 is 7. Find (i) the value of x (ii) the mean if each 
observation was multiplied by 3 (iii) the mean deviation about the median for the 
original data 
 
SECTION – D 
 
24. When two dice are thrown simultaneously, find the probability that neither a doublet 
nor a total of 10 will appear. 
OR 
The probability that a student will receive A, B, C and D grade are 0.4, 0.35, 0.15 and 0.10 
respectively. Find the probability that a student will receive  
1. B or C grade 
2. At most C grade 
  
 
CBSE XI | Mathematics 
Sample Paper – 5 
 
     
 
25. Using mathematical induction prove the following: 
  
1 1 1 1 n(n 3)
........
1.2.3 2.3.4 3.4.5 n(n 1)(n 2) 4(n 1)(n 2)
?
? ? ? ? ?
? ? ? ?
 
 
26. (i)A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are 
drawn from the box, what is the probability that 
 (a) all will be blue? (b) at least one will be green? 
 (ii) A die has two faces each with number ‘1’, three faces each with number ‘2’ and one 
face with number ‘3’. If die is rolled once, determine 
 (a)P(2) (b) P(1 or 3)             (c) P(not 3) 
 
 
27. Find the derivative of   
 
(i)sin(x + 1) by the abinitio method
x
(ii)
1 + tanx
 
OR 
 
 Evaluate the limits of the following two functions of x: 
 
2 3 2
x0
x0
x 2 1
(i)lim
x x x 3x 2x
sin4x
(ii)lim
sin2x
?
?
?? ?
?
??
? ? ? ??
  
 
28. Find the length of the perpendicular drawn from the points,  
2 2 2 2
xy
( a b ,0) and ( a b ,0) to the line cos sin 1
ab
? ? ? ? ? ? ? 
 Show that their product is b
2
.
 
 
 
29. Solve the inequalities and represent the solution graphically 
 
(3x+11)
5(2x 7) 3(2x + 3) 0; 2x + 19 6x + 47 and 7 11
2
? ? ? ? ? ? 
 
OR 
 
 How many litres of water will have to be added to 1125 litres of a 45% solution of acid 
so that the resulting mixture will contain more than 25% but less than 30% acid 
content? 
 
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FAQs on Sample Question Paper 5 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce

1. What are the important topics to study for the Math Class 11 exam?
Ans. The important topics to study for the Math Class 11 exam include Sets, Relations and Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics, and Probability.
2. How can I effectively prepare for the Math Class 11 exam?
Ans. To effectively prepare for the Math Class 11 exam, it is important to start early and create a study schedule. Understand the concepts thoroughly by referring to the textbook and class notes. Practice solving a variety of problems from different sources, including previous year's question papers and sample papers. Additionally, seek help from teachers or classmates for any doubts or difficult topics. Regularly revise the topics and solve mock tests to gauge your preparation level.
3. Are there any online resources available for Math Class 11 exam preparation?
Ans. Yes, there are several online resources available for Math Class 11 exam preparation. Some popular ones include educational websites, YouTube channels, online tutorials, and online test platforms. These resources provide video lessons, practice questions, mock tests, and solutions to help students understand and practice different topics effectively.
4. How can I manage my time effectively during the Math Class 11 exam?
Ans. To manage your time effectively during the Math Class 11 exam, it is important to practice solving questions within a given time limit. Allocate specific time slots for each section according to the marks weightage. Start with the easier questions to gain confidence and then move on to the more challenging ones. If you get stuck on a particular question, leave it and come back to it later. Use the last few minutes to review your answers and make sure you haven't made any silly mistakes.
5. What is the marking scheme for the Math Class 11 exam?
Ans. The marking scheme for the Math Class 11 exam may vary depending on the education board or institution. Generally, the exam consists of multiple-choice questions, short answer questions, and long answer questions. Each question carries a specific number of marks, which is mentioned in the question paper. It is important to read the instructions carefully and allocate your time accordingly to each question based on its marks weightage.
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