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Page 1
CBSE XI | Mathematics
Sample Paper – 8
CBSE Board
Class XI Mathematics
Sample Paper – 8
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
2
1
x
2
4x 1
lim
2x 1
?
?
?
.
2. Write the negation of the statement: The number 2 is greater than 7.
3. Find the value of
1
i
?
.
OR
Find modulus of 1 – 3i.
4. If variance of a distribution is 4 then find standard deviation of the distribution.
SECTION – B
5. If A = {a, b, c, d}, B = {f, b, d, g} and n(A ? B) = total number of elements = 8 then find
n(A’ ? B’).
6. Let f : R ? R be a function given by f(x) = x
2
+ 1, find : f
-1
(-5).
OR
If f(x) =
x1
x1
?
?
then show that f(1/x) = -f(x).
7. Find the radian measures corresponding to the 5° 37’ 30’’.
Page 2
CBSE XI | Mathematics
Sample Paper – 8
CBSE Board
Class XI Mathematics
Sample Paper – 8
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
2
1
x
2
4x 1
lim
2x 1
?
?
?
.
2. Write the negation of the statement: The number 2 is greater than 7.
3. Find the value of
1
i
?
.
OR
Find modulus of 1 – 3i.
4. If variance of a distribution is 4 then find standard deviation of the distribution.
SECTION – B
5. If A = {a, b, c, d}, B = {f, b, d, g} and n(A ? B) = total number of elements = 8 then find
n(A’ ? B’).
6. Let f : R ? R be a function given by f(x) = x
2
+ 1, find : f
-1
(-5).
OR
If f(x) =
x1
x1
?
?
then show that f(1/x) = -f(x).
7. Find the radian measures corresponding to the 5° 37’ 30’’.
CBSE XI | Mathematics
Sample Paper – 8
OR
Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring
15 °.
8. If A = {1, 4}, B = {2, 3, 6} and C = {2, 3, 7} verify that A × (B – C) = A × B – A × C
9. Solve sin
2
x + sin x – 2 = 0 where 0° < ? < 360°
OR
Prove that tan tan 2sec
4 2 4 2
? ? ? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
10. Given below are two statements :
p: 25 is a multiple of 5
q: 25 is a multiple of 8
Write the compound statement connecting these two statements with “OR” and check
its validity.
11. Find the domain for which the functions f(x) = 2x
2
– 1 and g(x) = 1 – 3x are equal.
12. In what ratio the line joining (-1, 1) and (5, 7) is divided by the line x + y = 4.
SECTION – C
13. Prove that
sec8 1 tan8
sec4 1 tan2
? ? ?
?
? ? ?
14. Which of the following relations are functions?
1. A is the capital of b where b ? B and B is the set of all countries, a ? A and A is
the set of capital cities of countries.
2. y < x + 3
3. y is a Maths pupil of x, where x represents any Maths teacher in a school.
4. y = 3x + 2
15. Let A be the set of first ten natural numbers and let R be a relation on A defined by
(x, y) ? R ? x + 2y = 10 i. e. R = {(x, y) : x ? A, y ? A and x + 2y = 10} Express R and R
-1
as sets of ordered pairs. Also determine domains of R and R
-1
and ranges of R and R
-1
.
16. If log10 2, log10 (2
x
– 1) and log10 (2
x
+ 3) are in A. P. then find the value of x.
17. If 1, ?, ?
2
are the cube roots of unity, prove that
(1 + ?)
3
– (1 + ?
2
)
3
= 0 and (x – y)(x ? – y)(x?
2
– y) = x
3
– y
3
Page 3
CBSE XI | Mathematics
Sample Paper – 8
CBSE Board
Class XI Mathematics
Sample Paper – 8
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
2
1
x
2
4x 1
lim
2x 1
?
?
?
.
2. Write the negation of the statement: The number 2 is greater than 7.
3. Find the value of
1
i
?
.
OR
Find modulus of 1 – 3i.
4. If variance of a distribution is 4 then find standard deviation of the distribution.
SECTION – B
5. If A = {a, b, c, d}, B = {f, b, d, g} and n(A ? B) = total number of elements = 8 then find
n(A’ ? B’).
6. Let f : R ? R be a function given by f(x) = x
2
+ 1, find : f
-1
(-5).
OR
If f(x) =
x1
x1
?
?
then show that f(1/x) = -f(x).
7. Find the radian measures corresponding to the 5° 37’ 30’’.
CBSE XI | Mathematics
Sample Paper – 8
OR
Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring
15 °.
8. If A = {1, 4}, B = {2, 3, 6} and C = {2, 3, 7} verify that A × (B – C) = A × B – A × C
9. Solve sin
2
x + sin x – 2 = 0 where 0° < ? < 360°
OR
Prove that tan tan 2sec
4 2 4 2
? ? ? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
10. Given below are two statements :
p: 25 is a multiple of 5
q: 25 is a multiple of 8
Write the compound statement connecting these two statements with “OR” and check
its validity.
11. Find the domain for which the functions f(x) = 2x
2
– 1 and g(x) = 1 – 3x are equal.
12. In what ratio the line joining (-1, 1) and (5, 7) is divided by the line x + y = 4.
SECTION – C
13. Prove that
sec8 1 tan8
sec4 1 tan2
? ? ?
?
? ? ?
14. Which of the following relations are functions?
1. A is the capital of b where b ? B and B is the set of all countries, a ? A and A is
the set of capital cities of countries.
2. y < x + 3
3. y is a Maths pupil of x, where x represents any Maths teacher in a school.
4. y = 3x + 2
15. Let A be the set of first ten natural numbers and let R be a relation on A defined by
(x, y) ? R ? x + 2y = 10 i. e. R = {(x, y) : x ? A, y ? A and x + 2y = 10} Express R and R
-1
as sets of ordered pairs. Also determine domains of R and R
-1
and ranges of R and R
-1
.
16. If log10 2, log10 (2
x
– 1) and log10 (2
x
+ 3) are in A. P. then find the value of x.
17. If 1, ?, ?
2
are the cube roots of unity, prove that
(1 + ?)
3
– (1 + ?
2
)
3
= 0 and (x – y)(x ? – y)(x?
2
– y) = x
3
– y
3
CBSE XI | Mathematics
Sample Paper – 8
18. An integer is chosen at random from the first two hundred positive integers. What is
the probability that the integer chosen is divisible by 6 or 8?
19. Evaluate 0.2345
20. Determine the number of natural numbers smaller than 10
4
, in the decimal notation of
which all the digits are distinct.
OR
Find the sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at
a time.
21. Find the equation of the locus of all points such that the difference of their distances
from (4, 0) and (-4, 0) is always equal to 2.
OR
Find the lengths of the transverse and conjugate axes, co-ordinates of the foci, vertices
and eccentricity for the hyperbola 9x
2
– 16y
2
= 144
22. Evaluate the derivative of the following function at indicated points :
1 sinx
1 cosx
?
?
at x
2
?
?
OR
If y =
23
x x x
1 ....
1! 2! 3!
? ? ? ? show that
dy
y
dx
?
23. Find the vertex, focus and directrix of the parabola 4y
2
+ 12x – 12y + 39 = 0.
SECTION – D
24. Prove that sin10°sin30°sin50°sin70° = 1/16
OR
Prove that cosA cos(60° – A) cos(60° + A) =
1
cos3A
4
25. For a group of 200 candidates the mean and S. D. were found to be 40 and 15
respectively. Later on it was found that the score 43 was misread as 34. Find the correct
mean and correct S. D.
26. If
3
tan tan
4 2 4 2
? ? ? ? ? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
prove that
3
2
3sin sin
sin
1 3sin
? ? ?
??
??
Page 4
CBSE XI | Mathematics
Sample Paper – 8
CBSE Board
Class XI Mathematics
Sample Paper – 8
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
2
1
x
2
4x 1
lim
2x 1
?
?
?
.
2. Write the negation of the statement: The number 2 is greater than 7.
3. Find the value of
1
i
?
.
OR
Find modulus of 1 – 3i.
4. If variance of a distribution is 4 then find standard deviation of the distribution.
SECTION – B
5. If A = {a, b, c, d}, B = {f, b, d, g} and n(A ? B) = total number of elements = 8 then find
n(A’ ? B’).
6. Let f : R ? R be a function given by f(x) = x
2
+ 1, find : f
-1
(-5).
OR
If f(x) =
x1
x1
?
?
then show that f(1/x) = -f(x).
7. Find the radian measures corresponding to the 5° 37’ 30’’.
CBSE XI | Mathematics
Sample Paper – 8
OR
Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring
15 °.
8. If A = {1, 4}, B = {2, 3, 6} and C = {2, 3, 7} verify that A × (B – C) = A × B – A × C
9. Solve sin
2
x + sin x – 2 = 0 where 0° < ? < 360°
OR
Prove that tan tan 2sec
4 2 4 2
? ? ? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
10. Given below are two statements :
p: 25 is a multiple of 5
q: 25 is a multiple of 8
Write the compound statement connecting these two statements with “OR” and check
its validity.
11. Find the domain for which the functions f(x) = 2x
2
– 1 and g(x) = 1 – 3x are equal.
12. In what ratio the line joining (-1, 1) and (5, 7) is divided by the line x + y = 4.
SECTION – C
13. Prove that
sec8 1 tan8
sec4 1 tan2
? ? ?
?
? ? ?
14. Which of the following relations are functions?
1. A is the capital of b where b ? B and B is the set of all countries, a ? A and A is
the set of capital cities of countries.
2. y < x + 3
3. y is a Maths pupil of x, where x represents any Maths teacher in a school.
4. y = 3x + 2
15. Let A be the set of first ten natural numbers and let R be a relation on A defined by
(x, y) ? R ? x + 2y = 10 i. e. R = {(x, y) : x ? A, y ? A and x + 2y = 10} Express R and R
-1
as sets of ordered pairs. Also determine domains of R and R
-1
and ranges of R and R
-1
.
16. If log10 2, log10 (2
x
– 1) and log10 (2
x
+ 3) are in A. P. then find the value of x.
17. If 1, ?, ?
2
are the cube roots of unity, prove that
(1 + ?)
3
– (1 + ?
2
)
3
= 0 and (x – y)(x ? – y)(x?
2
– y) = x
3
– y
3
CBSE XI | Mathematics
Sample Paper – 8
18. An integer is chosen at random from the first two hundred positive integers. What is
the probability that the integer chosen is divisible by 6 or 8?
19. Evaluate 0.2345
20. Determine the number of natural numbers smaller than 10
4
, in the decimal notation of
which all the digits are distinct.
OR
Find the sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at
a time.
21. Find the equation of the locus of all points such that the difference of their distances
from (4, 0) and (-4, 0) is always equal to 2.
OR
Find the lengths of the transverse and conjugate axes, co-ordinates of the foci, vertices
and eccentricity for the hyperbola 9x
2
– 16y
2
= 144
22. Evaluate the derivative of the following function at indicated points :
1 sinx
1 cosx
?
?
at x
2
?
?
OR
If y =
23
x x x
1 ....
1! 2! 3!
? ? ? ? show that
dy
y
dx
?
23. Find the vertex, focus and directrix of the parabola 4y
2
+ 12x – 12y + 39 = 0.
SECTION – D
24. Prove that sin10°sin30°sin50°sin70° = 1/16
OR
Prove that cosA cos(60° – A) cos(60° + A) =
1
cos3A
4
25. For a group of 200 candidates the mean and S. D. were found to be 40 and 15
respectively. Later on it was found that the score 43 was misread as 34. Find the correct
mean and correct S. D.
26. If
3
tan tan
4 2 4 2
? ? ? ? ? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
prove that
3
2
3sin sin
sin
1 3sin
? ? ?
??
??
CBSE XI | Mathematics
Sample Paper – 8
27. Solve the following system of inequalities graphically:
x + 2y ? 10; x + y ? 1; x - y ? 0; x ? 0; y ? 0
OR
For the purpose of an experiment an acid solution between 4% and 6% is required.
640 liters of 8% acid solution and a 2% acid solution are available in a laboratory. How
many liters of the 2% solution needs to be added to the 8% solution?
28. Show by mathematical induction that the sum to n terms of the series
? ?
? ?
2 2 2 2 2 2
2
n
2
1 2 2 3 2 4 5 2 6 ....is
n n 1
, when n is even
2
S
n n 1
, when n is odd
2
? ? ? ? ? ? ? ? ?
?
?
?
?
?
?
? ?
?
?
29. A student wants to buy a computer for Rs. 12,000. He has saved up to Rs. 6000 which he
pays as cash. He is to pay the balance in annual installments of Rs. 500 plus an interest
of 12% on the unpaid amount. How much will the computer cost him?
OR
Find the value of
2 2 2
2 2 2
1 2 2 3 3 4 ....uptill the nth term
1 2 2 3 3 4 ....uptill the nth term
? ? ? ? ? ?
? ? ? ? ? ?
.
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FAQs on Sample Question Paper 8 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce
| 1. What topics are covered in the Math exam for Class 11? |  |
Ans. The Math exam for Class 11 covers topics such as algebra, trigonometry, calculus, geometry, and statistics.
| 2. How can I prepare effectively for the Math exam in Class 11? | |
Ans. To prepare effectively for the Math exam in Class 11, it is important to start early, create a study schedule, understand the concepts thoroughly, practice solving a variety of problems, seek help from teachers or classmates when needed, and revise regularly.
| 3. Are there any important formulas that I need to remember for the Math exam in Class 11? | |
Ans. Yes, there are several important formulas that you need to remember for the Math exam in Class 11. Some of these include the quadratic formula, Pythagorean theorem, trigonometric identities, and differentiation rules. Make sure to review your textbook and class notes to identify the key formulas.
| 4. What is the marking scheme for the Math exam in Class 11? | |
Ans. The marking scheme for the Math exam in Class 11 may vary depending on the specific educational board or institution. Generally, it includes a combination of multiple-choice questions, short answer questions, and longer problem-solving questions. It is important to understand the weightage of each section and allocate your time accordingly during the exam.
| 5. Are there any recommended resources or study materials to help with the Math exam in Class 11? | |
Ans. Yes, there are several recommended resources and study materials that can help with the Math exam in Class 11. These may include textbooks prescribed by the educational board, reference books with additional practice problems, online tutorials or videos, and previous years' question papers. It is important to choose resources that align with the curriculum and provide clear explanations and practice opportunities.
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Dec 22, 2024 Last updated |
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