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CBSE XI | Mathematics
Sample Paper – 4
CBSE Board
Class XI Mathematics
Sample Paper – 4
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. Identify the function which the given graph represents.
2. If 4x + i(3x – y) = 3 + i(– 6), where x and y are real numbers, then find x and y.
3. Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.
OR
Find x and y if (x + 3, 5) = (6, 2x + y)
4. Write the negation of statement : “Australia is a continent.”
Page 2
CBSE XI | Mathematics
Sample Paper – 4
CBSE Board
Class XI Mathematics
Sample Paper – 4
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. Identify the function which the given graph represents.
2. If 4x + i(3x – y) = 3 + i(– 6), where x and y are real numbers, then find x and y.
3. Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.
OR
Find x and y if (x + 3, 5) = (6, 2x + y)
4. Write the negation of statement : “Australia is a continent.”
CBSE XI | Mathematics
Sample Paper – 4
SECTION – B
5. If f : R?R is defined by f(x) = x/(x
2
-1), find f(f(2)).
OR
If f(x) = 3x
4
– 5x
2
+ 9 find f(x – 1).
6. Solve : cos 3? + 8cos
3
? = 0
7. Show that the roots of equation (a
2
+b
2
)x
2
-2b(a+c) x+(b
2
+c
2
)=0 are real and equal if a,b,c
are in GP.
8. Draw the graph of the function |x + 2| - 1.
9. Find the co-ordinates of the foci of the ellipse
22
xy
1
25 9
??
OR
If the latus rectum of an ellipse is equal to half of minor axis, find its eccentricity.
10. In a survey of 600 students in a school, 150 students drink tea and 225 drink coffee,
and 100 drink both tea and coffee. Find how many students drink neither tea nor
coffee?
OR
In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many
can speak both Hindi and English?
11. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ? A , a divides b}
(i) Write in the roster form
(ii) Find the domain of R
(iii) Find the range of R
12. f(x) = -1 if x < 0
= 1 if x > 0
Draw the graph of the above function
SECTION – C
13. Represent the complex number z = 1 + i 3 in the polar form.
OR
Solve the following
2
18
25
1
i
i
??
?
??
??
Page 3
CBSE XI | Mathematics
Sample Paper – 4
CBSE Board
Class XI Mathematics
Sample Paper – 4
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. Identify the function which the given graph represents.
2. If 4x + i(3x – y) = 3 + i(– 6), where x and y are real numbers, then find x and y.
3. Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.
OR
Find x and y if (x + 3, 5) = (6, 2x + y)
4. Write the negation of statement : “Australia is a continent.”
CBSE XI | Mathematics
Sample Paper – 4
SECTION – B
5. If f : R?R is defined by f(x) = x/(x
2
-1), find f(f(2)).
OR
If f(x) = 3x
4
– 5x
2
+ 9 find f(x – 1).
6. Solve : cos 3? + 8cos
3
? = 0
7. Show that the roots of equation (a
2
+b
2
)x
2
-2b(a+c) x+(b
2
+c
2
)=0 are real and equal if a,b,c
are in GP.
8. Draw the graph of the function |x + 2| - 1.
9. Find the co-ordinates of the foci of the ellipse
22
xy
1
25 9
??
OR
If the latus rectum of an ellipse is equal to half of minor axis, find its eccentricity.
10. In a survey of 600 students in a school, 150 students drink tea and 225 drink coffee,
and 100 drink both tea and coffee. Find how many students drink neither tea nor
coffee?
OR
In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many
can speak both Hindi and English?
11. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ? A , a divides b}
(i) Write in the roster form
(ii) Find the domain of R
(iii) Find the range of R
12. f(x) = -1 if x < 0
= 1 if x > 0
Draw the graph of the above function
SECTION – C
13. Represent the complex number z = 1 + i 3 in the polar form.
OR
Solve the following
2
18
25
1
i
i
??
?
??
??
CBSE XI | Mathematics
Sample Paper – 4
14. Find n given that,
n - 1
P3 :
n
P4 = 1 : 9
15. Solve the given equation 2cos
2
x + 3sin x = 0
16. Prove that
cos4x cos3x cos2x
cot3x
sin4x sin3x sin2x
??
?
??
17. The income of a person is Rs. 3, 00, 000, in the first year and he receives an increment
of Rs. 10, 000 to his income per year for the next 19 years. Find the total amount, he
received in 20 years.
18. Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.
OR
Find the sum of the n terms of the series 5 + 11 + 19 + 29 + ...
19. Find the equation of a circle which passes through the points (2, -2), and (3, 4) and
whose centre lies on the line x + y = 2.
20. Solve 5 x² + x + 5 = 0.
21. Find the r
th
term from the end in the expansion of (x + a)
n
.
OR
Find the coefficient of x
6
y
3
in the expansion of (x + 2y)
9
.
22. Prove by induction that the sum, S = n
3
+ 3n
2
+ 5n + 3, is divisible by 3 for all n ? N.
23. Prove that
9 3 5
2cos cos cos cos 0
13 13 13 13
? ? ? ?
? ? ?
SECTION – D
24. Find the solution region for the following system of inequations:
x + 2y ? 10, x + y ? 1, x - y ? 0, x ? 0, y ? 0
Page 4
CBSE XI | Mathematics
Sample Paper – 4
CBSE Board
Class XI Mathematics
Sample Paper – 4
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. Identify the function which the given graph represents.
2. If 4x + i(3x – y) = 3 + i(– 6), where x and y are real numbers, then find x and y.
3. Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.
OR
Find x and y if (x + 3, 5) = (6, 2x + y)
4. Write the negation of statement : “Australia is a continent.”
CBSE XI | Mathematics
Sample Paper – 4
SECTION – B
5. If f : R?R is defined by f(x) = x/(x
2
-1), find f(f(2)).
OR
If f(x) = 3x
4
– 5x
2
+ 9 find f(x – 1).
6. Solve : cos 3? + 8cos
3
? = 0
7. Show that the roots of equation (a
2
+b
2
)x
2
-2b(a+c) x+(b
2
+c
2
)=0 are real and equal if a,b,c
are in GP.
8. Draw the graph of the function |x + 2| - 1.
9. Find the co-ordinates of the foci of the ellipse
22
xy
1
25 9
??
OR
If the latus rectum of an ellipse is equal to half of minor axis, find its eccentricity.
10. In a survey of 600 students in a school, 150 students drink tea and 225 drink coffee,
and 100 drink both tea and coffee. Find how many students drink neither tea nor
coffee?
OR
In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many
can speak both Hindi and English?
11. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ? A , a divides b}
(i) Write in the roster form
(ii) Find the domain of R
(iii) Find the range of R
12. f(x) = -1 if x < 0
= 1 if x > 0
Draw the graph of the above function
SECTION – C
13. Represent the complex number z = 1 + i 3 in the polar form.
OR
Solve the following
2
18
25
1
i
i
??
?
??
??
CBSE XI | Mathematics
Sample Paper – 4
14. Find n given that,
n - 1
P3 :
n
P4 = 1 : 9
15. Solve the given equation 2cos
2
x + 3sin x = 0
16. Prove that
cos4x cos3x cos2x
cot3x
sin4x sin3x sin2x
??
?
??
17. The income of a person is Rs. 3, 00, 000, in the first year and he receives an increment
of Rs. 10, 000 to his income per year for the next 19 years. Find the total amount, he
received in 20 years.
18. Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.
OR
Find the sum of the n terms of the series 5 + 11 + 19 + 29 + ...
19. Find the equation of a circle which passes through the points (2, -2), and (3, 4) and
whose centre lies on the line x + y = 2.
20. Solve 5 x² + x + 5 = 0.
21. Find the r
th
term from the end in the expansion of (x + a)
n
.
OR
Find the coefficient of x
6
y
3
in the expansion of (x + 2y)
9
.
22. Prove by induction that the sum, S = n
3
+ 3n
2
+ 5n + 3, is divisible by 3 for all n ? N.
23. Prove that
9 3 5
2cos cos cos cos 0
13 13 13 13
? ? ? ?
? ? ?
SECTION – D
24. Find the solution region for the following system of inequations:
x + 2y ? 10, x + y ? 1, x - y ? 0, x ? 0, y ? 0
CBSE XI | Mathematics
Sample Paper – 4
25. Find the mean deviation about the mean for the following continuous frequency
distribution, using the short cut method for finding mean.
Marks Obtained Number of Students
0 – 10 12
10 – 20 18
20 – 30 27
30 – 40 20
40 - 50 17
50 - 60 6
OR
The scores of 48 children in an intelligence test are shown in the following frequency
table.
Calculate the variance
2
? and find out the percentage of children whose scores lie
between x and x ? ? ? ?
Score Frequency
71 4
76 3
79 4
83 5
86 6
89 5
92 4
97 4
101 3
103 3
107 3
110 2
114 2
26. Find the equations of the lines through the point (3, 2) which are at an angle of 45°
with the line x - 2y = 3.
OR
The mid points of the sides of a triangle are (2, 1), (-5, 7) and (-5, -5). Find the
equations of the sides of the triangle.
27. Find the derivative using the first principle of f(x), where f(x) is given by
1
f(x) x
x
??
Page 5
CBSE XI | Mathematics
Sample Paper – 4
CBSE Board
Class XI Mathematics
Sample Paper – 4
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. Identify the function which the given graph represents.
2. If 4x + i(3x – y) = 3 + i(– 6), where x and y are real numbers, then find x and y.
3. Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.
OR
Find x and y if (x + 3, 5) = (6, 2x + y)
4. Write the negation of statement : “Australia is a continent.”
CBSE XI | Mathematics
Sample Paper – 4
SECTION – B
5. If f : R?R is defined by f(x) = x/(x
2
-1), find f(f(2)).
OR
If f(x) = 3x
4
– 5x
2
+ 9 find f(x – 1).
6. Solve : cos 3? + 8cos
3
? = 0
7. Show that the roots of equation (a
2
+b
2
)x
2
-2b(a+c) x+(b
2
+c
2
)=0 are real and equal if a,b,c
are in GP.
8. Draw the graph of the function |x + 2| - 1.
9. Find the co-ordinates of the foci of the ellipse
22
xy
1
25 9
??
OR
If the latus rectum of an ellipse is equal to half of minor axis, find its eccentricity.
10. In a survey of 600 students in a school, 150 students drink tea and 225 drink coffee,
and 100 drink both tea and coffee. Find how many students drink neither tea nor
coffee?
OR
In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many
can speak both Hindi and English?
11. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ? A , a divides b}
(i) Write in the roster form
(ii) Find the domain of R
(iii) Find the range of R
12. f(x) = -1 if x < 0
= 1 if x > 0
Draw the graph of the above function
SECTION – C
13. Represent the complex number z = 1 + i 3 in the polar form.
OR
Solve the following
2
18
25
1
i
i
??
?
??
??
CBSE XI | Mathematics
Sample Paper – 4
14. Find n given that,
n - 1
P3 :
n
P4 = 1 : 9
15. Solve the given equation 2cos
2
x + 3sin x = 0
16. Prove that
cos4x cos3x cos2x
cot3x
sin4x sin3x sin2x
??
?
??
17. The income of a person is Rs. 3, 00, 000, in the first year and he receives an increment
of Rs. 10, 000 to his income per year for the next 19 years. Find the total amount, he
received in 20 years.
18. Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.
OR
Find the sum of the n terms of the series 5 + 11 + 19 + 29 + ...
19. Find the equation of a circle which passes through the points (2, -2), and (3, 4) and
whose centre lies on the line x + y = 2.
20. Solve 5 x² + x + 5 = 0.
21. Find the r
th
term from the end in the expansion of (x + a)
n
.
OR
Find the coefficient of x
6
y
3
in the expansion of (x + 2y)
9
.
22. Prove by induction that the sum, S = n
3
+ 3n
2
+ 5n + 3, is divisible by 3 for all n ? N.
23. Prove that
9 3 5
2cos cos cos cos 0
13 13 13 13
? ? ? ?
? ? ?
SECTION – D
24. Find the solution region for the following system of inequations:
x + 2y ? 10, x + y ? 1, x - y ? 0, x ? 0, y ? 0
CBSE XI | Mathematics
Sample Paper – 4
25. Find the mean deviation about the mean for the following continuous frequency
distribution, using the short cut method for finding mean.
Marks Obtained Number of Students
0 – 10 12
10 – 20 18
20 – 30 27
30 – 40 20
40 - 50 17
50 - 60 6
OR
The scores of 48 children in an intelligence test are shown in the following frequency
table.
Calculate the variance
2
? and find out the percentage of children whose scores lie
between x and x ? ? ? ?
Score Frequency
71 4
76 3
79 4
83 5
86 6
89 5
92 4
97 4
101 3
103 3
107 3
110 2
114 2
26. Find the equations of the lines through the point (3, 2) which are at an angle of 45°
with the line x - 2y = 3.
OR
The mid points of the sides of a triangle are (2, 1), (-5, 7) and (-5, -5). Find the
equations of the sides of the triangle.
27. Find the derivative using the first principle of f(x), where f(x) is given by
1
f(x) x
x
??
CBSE XI | Mathematics
Sample Paper – 4
28. For all n = 1, prove using Principle of Mathematical Induction
1 1 1 1 n
1.2 2.3 3.4 n(n 1) n 1
? ? ? ? ? ?
??
29. One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally
likely, calculate the probability that the card will be
(i) A diamond
(ii) An ace
(iii) A black card
(iv) Not a diamond
(v) Not a black card
(vi) Not an ace
OR
A committee of two persons is to be selected from two men and two women.
What is the probability that the committee will have (a) no man (b) one man (c) two
men?
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FAQs on Sample Question Paper 4 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce
| 1. What are the important topics to study for the Class 11 Math exam? |  |
Ans. The important topics to study for the Class 11 Math exam include Sets, Relations and Functions, Trigonometric Functions, Algebra, Coordinate Geometry, Calculus, Statistics, and Probability.
| 2. How should I prepare for the Class 11 Math exam? | |
Ans. To prepare for the Class 11 Math exam, it is important to understand the concepts thoroughly. Practice solving different types of problems from each chapter, refer to textbooks and study materials, create a study schedule, and solve previous year question papers to get an idea of the exam pattern.
| 3. Is it necessary to solve additional practice questions apart from the textbook exercises? | |
Ans. Yes, solving additional practice questions apart from the textbook exercises is highly recommended. It helps in strengthening your understanding of the concepts, improves problem-solving skills, and prepares you for a variety of questions that may appear in the exam.
| 4. Are there any online resources available for Class 11 Math exam preparation? | |
Ans. Yes, there are several online resources available for Class 11 Math exam preparation. Websites like Khan Academy, BYJU'S, and Vedantu offer video lessons, practice questions, and mock tests to help students prepare for their exams effectively.
| 5. What should I do if I am struggling with a particular topic in Math? | |
Ans. If you are struggling with a particular topic in Math, it is important to seek help. You can approach your teacher or classmates for clarification, join online forums or study groups to discuss the topic, refer to additional study materials or online tutorials, and practice more problems related to that topic to improve your understanding.
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Dec 18, 2024 Last updated |
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