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CBSE XI | Mathematics 
Sample Paper – 9 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 9 
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. Find 
x0
sinax
lim
bx
?
 
 
2. Is the given sentence statement? Justify. “There are 35 days in a month.” 
 
3. Write in the form of a + bi : 
1
i1 ?
 
OR 
Find modulus of 2i. 
 
4. If variance of 20 observations is 5. If each observation is multiplied by 2, then find 
variance of the new observations. 
 
                                                                     SECTION – B 
 
5. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} verify that A × C is a subset of 
B × D. 
  
6. Let f be defined by f(x) = x – 4 and g be defined by  
? ?
2
x 16
g x x 4
x4
x4
?
? ? ?
?
? ? ? ?
 
Find ? such that f(x) = g(x) for all x. 
Page 2


  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 9 
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. Find 
x0
sinax
lim
bx
?
 
 
2. Is the given sentence statement? Justify. “There are 35 days in a month.” 
 
3. Write in the form of a + bi : 
1
i1 ?
 
OR 
Find modulus of 2i. 
 
4. If variance of 20 observations is 5. If each observation is multiplied by 2, then find 
variance of the new observations. 
 
                                                                     SECTION – B 
 
5. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} verify that A × C is a subset of 
B × D. 
  
6. Let f be defined by f(x) = x – 4 and g be defined by  
? ?
2
x 16
g x x 4
x4
x4
?
? ? ?
?
? ? ? ?
 
Find ? such that f(x) = g(x) for all x. 
  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
OR 
Find domain and range of the function 
? ?
2
x9
fx
x3
?
?
?
 
7. Assuming that a person of normal sight can read print at such a distance that the letters 
subtend an angle of 5’ at this eye, find the height of the letters that he can read at a 
distance of 12 m. 
OR 
If the arcs of the same length in two circles subtend angles of 60° and 75° at their 
centres. Find the ratio of their radii. 
 
8. If n(U) = 600, n(A) = 460, n(B) = 390 and n(A n B) = 325 then find n(A ? B) and                         
n(A ? B)’ 
 
9. Prove that sin(? + 30°) = cos ? + sin (? – 30°) 
OR 
Prove that 
sin7A sin5A
tan A
cos5A cos7A
?
?
?
 
 
10. Find compound statements of the “It is raining and it is cold.” 
 
11. If f(x) = x
2
 find 
? ? ? ? f 1.1 f 1
1.1 1
?
?
 
 
12. Find the equation of line joining the points (-1, 3) and (4, -2). 
 
SECTION – C 
 
13. Prove that 
22
22
cos 33 cos 57
2
21 69
sin sin
22
? ? ?
??
??
?
 
 
 
14. If f is a real function defined by ? ?
x1
fx
x1
?
?
?
 then prove that ? ?
? ?
? ?
3f x 1
f 2x
f x 3
?
?
?
 
15. Let f : R ? R be given by f(x) = x
2
 + 3. Find 
i. {x : f(x) = 28} 
ii. The pre-image of 39 and 2 under f. 
 
16. A man accepts a position with an initial salary of Rs. 5200 per week. It is understood 
that he will receive an automatic increase of Rs. 320 in the very next and each month.  
i. find his salary for the tenth month  
ii. his total earning during the first year. 
Page 3


  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 9 
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. Find 
x0
sinax
lim
bx
?
 
 
2. Is the given sentence statement? Justify. “There are 35 days in a month.” 
 
3. Write in the form of a + bi : 
1
i1 ?
 
OR 
Find modulus of 2i. 
 
4. If variance of 20 observations is 5. If each observation is multiplied by 2, then find 
variance of the new observations. 
 
                                                                     SECTION – B 
 
5. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} verify that A × C is a subset of 
B × D. 
  
6. Let f be defined by f(x) = x – 4 and g be defined by  
? ?
2
x 16
g x x 4
x4
x4
?
? ? ?
?
? ? ? ?
 
Find ? such that f(x) = g(x) for all x. 
  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
OR 
Find domain and range of the function 
? ?
2
x9
fx
x3
?
?
?
 
7. Assuming that a person of normal sight can read print at such a distance that the letters 
subtend an angle of 5’ at this eye, find the height of the letters that he can read at a 
distance of 12 m. 
OR 
If the arcs of the same length in two circles subtend angles of 60° and 75° at their 
centres. Find the ratio of their radii. 
 
8. If n(U) = 600, n(A) = 460, n(B) = 390 and n(A n B) = 325 then find n(A ? B) and                         
n(A ? B)’ 
 
9. Prove that sin(? + 30°) = cos ? + sin (? – 30°) 
OR 
Prove that 
sin7A sin5A
tan A
cos5A cos7A
?
?
?
 
 
10. Find compound statements of the “It is raining and it is cold.” 
 
11. If f(x) = x
2
 find 
? ? ? ? f 1.1 f 1
1.1 1
?
?
 
 
12. Find the equation of line joining the points (-1, 3) and (4, -2). 
 
SECTION – C 
 
13. Prove that 
22
22
cos 33 cos 57
2
21 69
sin sin
22
? ? ?
??
??
?
 
 
 
14. If f is a real function defined by ? ?
x1
fx
x1
?
?
?
 then prove that ? ?
? ?
? ?
3f x 1
f 2x
f x 3
?
?
?
 
15. Let f : R ? R be given by f(x) = x
2
 + 3. Find 
i. {x : f(x) = 28} 
ii. The pre-image of 39 and 2 under f. 
 
16. A man accepts a position with an initial salary of Rs. 5200 per week. It is understood 
that he will receive an automatic increase of Rs. 320 in the very next and each month.  
i. find his salary for the tenth month  
ii. his total earning during the first year. 
  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
17. If (x + yi)
3
 = u + vi prove that 
? ?
22
uv
4 x y
xy
? ? ? 
 
18. Two cards are drawn from a pack of cards. What is the probability that either both are 
red or both are kings? 
 
19. Determine the number n in a geometric progression {an}, if a1 = 3, an = 96 and Sn = 189. 
 
20. Find n, if 
2n
1
C , 
2n
2
C and 
2n
3
C are in A. P. 
OR 
 Prove that the product of 2n consecutive negative integers is divisible by (2n)!. 
 
21. Find the equation of the straight line through the origin making angle of 60° with the 
straight line x + v3 y + 3v3 = 0 
OR 
         Find the equations of the lines, which cut off intercepts on the axes whose sum and 
product are 1 and -6 respectively. 
 
22. Differentiate x
-3/2
 with respect to x using first principle. 
OR 
 Differentiate 
2
x2
x3
?
?
 and find the value of derivative at x = 0. 
 
23. Find the equation of hyperbola whose foci are (8, 3) and (0, 3) and e = 4/3 
 
 
 
SECTION – D 
24. Prove that cot ? cot 2? + cot 2? cot 3? + 2 = cot ?(cot ? – cot 3?)  
 
OR 
 
Prove that 5cos ? + 3cos 
3
? ??
??
??
??
 + 3 lies between -4 and 10. 
 
25. Find the mean and variance of the following data  
 
Classes  0 - 30 30 - 60 60 – 90 90 - 120 120 - 150 150 - 180 180 - 210 
Frequency  2 3 5 10 3 5 2 
 
 
Page 4


  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 9 
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. Find 
x0
sinax
lim
bx
?
 
 
2. Is the given sentence statement? Justify. “There are 35 days in a month.” 
 
3. Write in the form of a + bi : 
1
i1 ?
 
OR 
Find modulus of 2i. 
 
4. If variance of 20 observations is 5. If each observation is multiplied by 2, then find 
variance of the new observations. 
 
                                                                     SECTION – B 
 
5. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} verify that A × C is a subset of 
B × D. 
  
6. Let f be defined by f(x) = x – 4 and g be defined by  
? ?
2
x 16
g x x 4
x4
x4
?
? ? ?
?
? ? ? ?
 
Find ? such that f(x) = g(x) for all x. 
  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
OR 
Find domain and range of the function 
? ?
2
x9
fx
x3
?
?
?
 
7. Assuming that a person of normal sight can read print at such a distance that the letters 
subtend an angle of 5’ at this eye, find the height of the letters that he can read at a 
distance of 12 m. 
OR 
If the arcs of the same length in two circles subtend angles of 60° and 75° at their 
centres. Find the ratio of their radii. 
 
8. If n(U) = 600, n(A) = 460, n(B) = 390 and n(A n B) = 325 then find n(A ? B) and                         
n(A ? B)’ 
 
9. Prove that sin(? + 30°) = cos ? + sin (? – 30°) 
OR 
Prove that 
sin7A sin5A
tan A
cos5A cos7A
?
?
?
 
 
10. Find compound statements of the “It is raining and it is cold.” 
 
11. If f(x) = x
2
 find 
? ? ? ? f 1.1 f 1
1.1 1
?
?
 
 
12. Find the equation of line joining the points (-1, 3) and (4, -2). 
 
SECTION – C 
 
13. Prove that 
22
22
cos 33 cos 57
2
21 69
sin sin
22
? ? ?
??
??
?
 
 
 
14. If f is a real function defined by ? ?
x1
fx
x1
?
?
?
 then prove that ? ?
? ?
? ?
3f x 1
f 2x
f x 3
?
?
?
 
15. Let f : R ? R be given by f(x) = x
2
 + 3. Find 
i. {x : f(x) = 28} 
ii. The pre-image of 39 and 2 under f. 
 
16. A man accepts a position with an initial salary of Rs. 5200 per week. It is understood 
that he will receive an automatic increase of Rs. 320 in the very next and each month.  
i. find his salary for the tenth month  
ii. his total earning during the first year. 
  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
17. If (x + yi)
3
 = u + vi prove that 
? ?
22
uv
4 x y
xy
? ? ? 
 
18. Two cards are drawn from a pack of cards. What is the probability that either both are 
red or both are kings? 
 
19. Determine the number n in a geometric progression {an}, if a1 = 3, an = 96 and Sn = 189. 
 
20. Find n, if 
2n
1
C , 
2n
2
C and 
2n
3
C are in A. P. 
OR 
 Prove that the product of 2n consecutive negative integers is divisible by (2n)!. 
 
21. Find the equation of the straight line through the origin making angle of 60° with the 
straight line x + v3 y + 3v3 = 0 
OR 
         Find the equations of the lines, which cut off intercepts on the axes whose sum and 
product are 1 and -6 respectively. 
 
22. Differentiate x
-3/2
 with respect to x using first principle. 
OR 
 Differentiate 
2
x2
x3
?
?
 and find the value of derivative at x = 0. 
 
23. Find the equation of hyperbola whose foci are (8, 3) and (0, 3) and e = 4/3 
 
 
 
SECTION – D 
24. Prove that cot ? cot 2? + cot 2? cot 3? + 2 = cot ?(cot ? – cot 3?)  
 
OR 
 
Prove that 5cos ? + 3cos 
3
? ??
??
??
??
 + 3 lies between -4 and 10. 
 
25. Find the mean and variance of the following data  
 
Classes  0 - 30 30 - 60 60 – 90 90 - 120 120 - 150 150 - 180 180 - 210 
Frequency  2 3 5 10 3 5 2 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 9 
 
     
26. If Find 
x x x
sin ,cos and tan
2 2 2
where tan x =
4
3
? , x is in quadrant II 
27. Plot the given linear inequations 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. 
 
 
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? 
 
28. Using principle of mathematical induction prove that 5
n
-5 is divisible by 4 for all n ?N.  
 Hence, prove that 2×7
n
+3×5
n
-5 is divisible by 24 for all n ?N. 
 
 
29. If a, b, and c are in A.P.; b, c, and d are in G.P. and 
1 1 1
, , and
c d e
 are in A.P., prove that a, c, 
and e are in G.P. 
OR 
 
 Show that:  
 
2 2 2
2 2 2
1 2 2 3 .. n (n 1) 3n 5
3n 1 1 2 2 3 .. n (n 1)
? ? ? ? ? ? ? ?
?
? ? ? ? ? ? ? ?
 
 
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FAQs on Sample Question Paper 9 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce

1. What are the topics covered in the Class 11 Math exam?
Ans. The Class 11 Math exam covers a wide range of topics, including algebra, trigonometry, coordinate geometry, calculus, 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 start early and create a study schedule. Practice solving a variety of problems from each topic, revise important formulas and concepts, and solve previous years' question papers.
3. What are some important tips to score well in the Class 11 Math exam?
Ans. Some important tips to score well in the Class 11 Math exam are: - Understand the concepts thoroughly and practice regularly. - Focus on solving problems from different sources to enhance problem-solving skills. - Manage time effectively during the exam and attempt all questions. - Revise regularly and solve previous years' question papers to understand the exam pattern.
4. Are there any online resources available to help with Class 11 Math preparation?
Ans. Yes, there are numerous online resources available to help with Class 11 Math preparation. These include websites, online tutorials, educational apps, and video lectures. These resources provide additional explanations, practice questions, and interactive learning tools to enhance understanding and retention of concepts.
5. How can I overcome Math anxiety and build confidence for the Class 11 Math exam?
Ans. Overcoming Math anxiety and building confidence for the Class 11 Math exam can be achieved through consistent practice and positive mindset. Break down complex problems into smaller steps, focus on understanding the concepts rather than rote memorization, seek help from teachers or peers when needed, and believe in your abilities to succeed. Additionally, adopting relaxation techniques such as deep breathing exercises before the exam can help reduce anxiety and improve performance.
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