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CBSE XI | Mathematics
Sample Paper – 10
CBSE Board
Class XI Mathematics
Sample Paper – 10
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
xx
x0
32
lim
x
?
?
.
2. Write contrapositive of the statement: If Mohan is a poet then he is poor.
3. Write the value of
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
.
OR
Write the value of 25 9 ? ? ? .
4. What is the total number of elementary events associated to the random experiment of
throwing three dice together?
SECTION – B
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B.
6. If f(x) = sin [log (x +
2
x1 ? )] then show that f(-x) = -f(x).
OR
If f(x) =
1x
1x
?
?
show that f[f(tan ?)] = -cot?.
Page 2
CBSE XI | Mathematics
Sample Paper – 10
CBSE Board
Class XI Mathematics
Sample Paper – 10
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
xx
x0
32
lim
x
?
?
.
2. Write contrapositive of the statement: If Mohan is a poet then he is poor.
3. Write the value of
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
.
OR
Write the value of 25 9 ? ? ? .
4. What is the total number of elementary events associated to the random experiment of
throwing three dice together?
SECTION – B
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B.
6. If f(x) = sin [log (x +
2
x1 ? )] then show that f(-x) = -f(x).
OR
If f(x) =
1x
1x
?
?
show that f[f(tan ?)] = -cot?.
CBSE XI | Mathematics
Sample Paper – 10
7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that
the area of a sector AOB is equal to the square of the length of the arc AB, find the value
of x.
OR
Find the degree measure of
5
3
?
and 4p.
8. i. Is the following pair equal? Justify?
A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”}
ii. Is the set C = {x : x ?Z and x
2
= 36} finite or infinite?
9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC.
OR
In triangle ABC, ? ? ? ?
22
2 2 2
CC
a b cos a b sin c
22
? ? ? ? incomplete question
10. Write converse of the statement “If a number is even then n
2
is even.”
11. Find domain of the function f(x) =
2
1
4x
x1
??
?
12. Find the centre and radius of a circle : x
2
+ y
2
– 4x + 6y = 12
SECTION – C
13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°.
14. If f(x) = log
1x
1x
? ??
??
?
??
show that f(a) + f(b) =
ab
f
1 ab
? ??
??
?
??
15. Find the domain of
i. x 2x 1 ??
ii. ? ? log x 2 3 x ? ? ?
16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21.
Determine the first five terms of the G. P.
17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that
? ?
2 2 2 2
22
1 2 1 2 1 2
az bz bz az a b z z
??
? ? ? ? ? ?
??
??
Page 3
CBSE XI | Mathematics
Sample Paper – 10
CBSE Board
Class XI Mathematics
Sample Paper – 10
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
xx
x0
32
lim
x
?
?
.
2. Write contrapositive of the statement: If Mohan is a poet then he is poor.
3. Write the value of
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
.
OR
Write the value of 25 9 ? ? ? .
4. What is the total number of elementary events associated to the random experiment of
throwing three dice together?
SECTION – B
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B.
6. If f(x) = sin [log (x +
2
x1 ? )] then show that f(-x) = -f(x).
OR
If f(x) =
1x
1x
?
?
show that f[f(tan ?)] = -cot?.
CBSE XI | Mathematics
Sample Paper – 10
7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that
the area of a sector AOB is equal to the square of the length of the arc AB, find the value
of x.
OR
Find the degree measure of
5
3
?
and 4p.
8. i. Is the following pair equal? Justify?
A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”}
ii. Is the set C = {x : x ?Z and x
2
= 36} finite or infinite?
9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC.
OR
In triangle ABC, ? ? ? ?
22
2 2 2
CC
a b cos a b sin c
22
? ? ? ? incomplete question
10. Write converse of the statement “If a number is even then n
2
is even.”
11. Find domain of the function f(x) =
2
1
4x
x1
??
?
12. Find the centre and radius of a circle : x
2
+ y
2
– 4x + 6y = 12
SECTION – C
13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°.
14. If f(x) = log
1x
1x
? ??
??
?
??
show that f(a) + f(b) =
ab
f
1 ab
? ??
??
?
??
15. Find the domain of
i. x 2x 1 ??
ii. ? ? log x 2 3 x ? ? ?
16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21.
Determine the first five terms of the G. P.
17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that
? ?
2 2 2 2
22
1 2 1 2 1 2
az bz bz az a b z z
??
? ? ? ? ? ?
??
??
CBSE XI | Mathematics
Sample Paper – 10
18. When two dice are thrown. Calculate the probability of throwing a total of
i. A 7 or an 11
ii. A doublet or a total of 6.
19. Sum up 5 + 55 + 555 + … to n terms.
20. Find the value of
? ? ? ?
66
2 1 2 1 ? ? ? and show that the value of
? ?
6
21 ? lies between
197 and 198.
OR
A code word is consist of two distinct English alphabets followed by two distinct
numbers from 1 to 9. For example CA23 is a code word. How many such code words
are there? How many of them end with an even integer?
21. Find the equation of the line through the point (4, -5) and parallel to 3x + 4y + 5 = 0 and
perpendicular to 3x + 4y + 5 = 0.
OR
The length L (in cm) of a copper rod is a linear function of its Celsius temperature C. In
an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in
terms of C.
22. (i) Find the derivative of
1
f(x) , using first principle.
x
??
(ii) Evaluate:
x x x
2
x0
6 3 2 1
lim
x
?
? ? ?
OR
(i) Find the derivative of the given function using first principle:
f(x)=cos x -
16
? ??
??
??
(ii) Evaluate:
cos x
x
2
51
lim , x .
2
x
2
?
?
??
?
?
?
23. Find the equations of the lines through the point (3, 2) which are at an angle of 45° with
the line x - 2y = 3.
SECTION – D
24.
? ? ?
? ? ? ? ?
b c c a a b cosA cosB cosC
If in a ABC, ,then prove that: .
12 13 15 2 7 11
OR
If A = cos
2
? + sin
4
? prove that
3
A1
4
?? for all values of ?.
Page 4
CBSE XI | Mathematics
Sample Paper – 10
CBSE Board
Class XI Mathematics
Sample Paper – 10
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
xx
x0
32
lim
x
?
?
.
2. Write contrapositive of the statement: If Mohan is a poet then he is poor.
3. Write the value of
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
.
OR
Write the value of 25 9 ? ? ? .
4. What is the total number of elementary events associated to the random experiment of
throwing three dice together?
SECTION – B
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B.
6. If f(x) = sin [log (x +
2
x1 ? )] then show that f(-x) = -f(x).
OR
If f(x) =
1x
1x
?
?
show that f[f(tan ?)] = -cot?.
CBSE XI | Mathematics
Sample Paper – 10
7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that
the area of a sector AOB is equal to the square of the length of the arc AB, find the value
of x.
OR
Find the degree measure of
5
3
?
and 4p.
8. i. Is the following pair equal? Justify?
A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”}
ii. Is the set C = {x : x ?Z and x
2
= 36} finite or infinite?
9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC.
OR
In triangle ABC, ? ? ? ?
22
2 2 2
CC
a b cos a b sin c
22
? ? ? ? incomplete question
10. Write converse of the statement “If a number is even then n
2
is even.”
11. Find domain of the function f(x) =
2
1
4x
x1
??
?
12. Find the centre and radius of a circle : x
2
+ y
2
– 4x + 6y = 12
SECTION – C
13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°.
14. If f(x) = log
1x
1x
? ??
??
?
??
show that f(a) + f(b) =
ab
f
1 ab
? ??
??
?
??
15. Find the domain of
i. x 2x 1 ??
ii. ? ? log x 2 3 x ? ? ?
16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21.
Determine the first five terms of the G. P.
17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that
? ?
2 2 2 2
22
1 2 1 2 1 2
az bz bz az a b z z
??
? ? ? ? ? ?
??
??
CBSE XI | Mathematics
Sample Paper – 10
18. When two dice are thrown. Calculate the probability of throwing a total of
i. A 7 or an 11
ii. A doublet or a total of 6.
19. Sum up 5 + 55 + 555 + … to n terms.
20. Find the value of
? ? ? ?
66
2 1 2 1 ? ? ? and show that the value of
? ?
6
21 ? lies between
197 and 198.
OR
A code word is consist of two distinct English alphabets followed by two distinct
numbers from 1 to 9. For example CA23 is a code word. How many such code words
are there? How many of them end with an even integer?
21. Find the equation of the line through the point (4, -5) and parallel to 3x + 4y + 5 = 0 and
perpendicular to 3x + 4y + 5 = 0.
OR
The length L (in cm) of a copper rod is a linear function of its Celsius temperature C. In
an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in
terms of C.
22. (i) Find the derivative of
1
f(x) , using first principle.
x
??
(ii) Evaluate:
x x x
2
x0
6 3 2 1
lim
x
?
? ? ?
OR
(i) Find the derivative of the given function using first principle:
f(x)=cos x -
16
? ??
??
??
(ii) Evaluate:
cos x
x
2
51
lim , x .
2
x
2
?
?
??
?
?
?
23. Find the equations of the lines through the point (3, 2) which are at an angle of 45° with
the line x - 2y = 3.
SECTION – D
24.
? ? ?
? ? ? ? ?
b c c a a b cosA cosB cosC
If in a ABC, ,then prove that: .
12 13 15 2 7 11
OR
If A = cos
2
? + sin
4
? prove that
3
A1
4
?? for all values of ?.
CBSE XI | Mathematics
Sample Paper – 10
25. Given below is the frequency distribution of weekly study hours of a group of class 11
students. Find the mean, variance and standard deviation of the distribution using the
short cut method.
Classes Frequency
0 - 10 5
10 - 20 8
20 - 30 15
30 - 40 16
40 - 50 6
26. Prove that:
cos
2
x +
22
3
cos x cos x
3 3 2
?? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
27. Find the solution region for the following system of inequations:
x + 2y ? 10, x + y ? 1, x - y ? 0, x ? 0, y ? 0
OR
Solve the inequality given below and represent the solution on the number line.
? ?
1 3x 20 1
x6
2 5 3
? ??
??
??
??
28. The sum of the coefficients of the first three terms in the expansion of
m
2
3
x
x
??
?
??
??
is 559,
where x ? 0 and m being a natural number. Find the term of the expansion containing
x
3
.
29. Find the sum of the following series upto n terms:
3 3 3 3 3 3
1 1 2 1 2 3
...........
1 1 3 1 3 5
? ? ?
? ? ? ?
? ? ?
………..
OR
If S1, S2, S3 be the sum of n, 2n and 3n terms of a GP respectively.
Prove that S1 (S3 – S2) = (S2 – S1)
2
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FAQs on Sample Question Paper 10 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce
| 1. What are the topics covered in Class 11 Math? |  |
Ans. Class 11 Math covers various topics such as sets, relations, and functions, trigonometric functions, mathematical reasoning, statistics, probability, and more.
| 2. How can I prepare for the Class 11 Math exam effectively? | |
Ans. To prepare effectively for the Class 11 Math exam, you can start by understanding the syllabus thoroughly. Make a study plan, practice solving different types of problems, refer to textbooks and study materials, seek help from teachers or classmates if needed, and regularly revise the topics.
| 3. Are there any important formulas I should memorize for the Class 11 Math exam? | |
Ans. Yes, there are some important formulas that you should memorize for the Class 11 Math exam. These include trigonometric formulas, formulas related to sets and functions, formulas for statistics and probability, etc. It is recommended to make flashcards or summary sheets to help you memorize these formulas more easily.
| 4. Is it necessary to solve previous years' question papers for the Class 11 Math exam? | |
Ans. Solving previous years' question papers is highly recommended for the Class 11 Math exam. It helps you become familiar with the exam pattern, understand the question types, and identify important topics. By solving these papers, you can also assess your preparation level and work on your weak areas.
| 5. Are there any online resources or video tutorials available for Class 11 Math exam preparation? | |
Ans. Yes, there are several online resources and video tutorials available for Class 11 Math exam preparation. You can find educational websites, YouTube channels, and online learning platforms that offer comprehensive study materials, video lectures, practice questions, and mock tests. These resources can supplement your classroom learning and provide additional guidance for exam preparation.
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Dec 22, 2024 Last updated |
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