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Page 1
CBSE XI | Mathematics
Sample Paper – 10 Solution
CBSE Board
Class XI Mathematics
Sample Paper – 10 Solution
SECTION – A
1.
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
2. If Mohan is not poor then he is not a poet.
3.
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
OR
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Page 2
CBSE XI | Mathematics
Sample Paper – 10 Solution
CBSE Board
Class XI Mathematics
Sample Paper – 10 Solution
SECTION – A
1.
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
2. If Mohan is not poor then he is not a poet.
3.
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
OR
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
CBSE XI | Mathematics
Sample Paper – 10 Solution
4. The total number of elementary events associated to the random experiment of thrown
a dice is 6
n
where n is the number of throws. Hence, the total number of elementary
events associated to the random experiment of throwing a three dice together is 6
3
=
216.
SECTION – B
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6
The number of subsets of A × B = 2
6
= 64
The number of relations from A into B = 64
6. f(x) = = sin [log (x +
2
x1 ? )]
f(-x) = sin [log (-x +
2
x1 ? )]
=
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
=
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
=
? ?
1
2
sin log x 1 x
?
??
??
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
= -f(x)
OR
f(x) =
1x
1x
?
?
? ? ?
1 tan
f tan
1 tan
??
??
??
? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
Page 3
CBSE XI | Mathematics
Sample Paper – 10 Solution
CBSE Board
Class XI Mathematics
Sample Paper – 10 Solution
SECTION – A
1.
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
2. If Mohan is not poor then he is not a poet.
3.
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
OR
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
CBSE XI | Mathematics
Sample Paper – 10 Solution
4. The total number of elementary events associated to the random experiment of thrown
a dice is 6
n
where n is the number of throws. Hence, the total number of elementary
events associated to the random experiment of throwing a three dice together is 6
3
=
216.
SECTION – B
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6
The number of subsets of A × B = 2
6
= 64
The number of relations from A into B = 64
6. f(x) = = sin [log (x +
2
x1 ? )]
f(-x) = sin [log (-x +
2
x1 ? )]
=
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
=
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
=
? ?
1
2
sin log x 1 x
?
??
??
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
= -f(x)
OR
f(x) =
1x
1x
?
?
? ? ?
1 tan
f tan
1 tan
??
??
??
? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
CBSE XI | Mathematics
Sample Paper – 10 Solution
7. Taking ? = x we get area of sector AOB =
2
1
rx
2
22
1
r x s
2
?
2 2 2
1
r x r x
2
? ? S = rx
1
x rad
2
?
OR
5 5 180
300
33
??
? ? ? ?
?
? 1
c
=
180
?
??
??
?
??
180
4 4 720 ? ? ? ? ? ?
?
8. i. A = {L, O, Y, A} and B = {A, L, O, Y}
Clearly A = B
ii. C = {x: x ?Z and x
2
= 36} = {6, -6}
So, C is a finite set.
9. In triangle ABC, if a = 3, b = 5 and c = 7
2 2 2
b c a 25 49 9 65 13
cosA
2bc 2 5 7 70 14
? ? ? ?
? ? ? ?
??
2 2 2
a b c 9 25 49 15 1
cosC
2ab 2 3 5 30 2
? ? ? ? ? ?
? ? ? ?
??
OR
? ? ? ?
22
22
2 2 2 2 2 2 2 2
22
2
CC
a b cos a b sin
22
C C C C C C
a cos sin b cos sin 2ab cos sin
2 2 2 2 2 2
a b 2abcosC
c
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
?
10. If a number n
2
is even then n is even.
Page 4
CBSE XI | Mathematics
Sample Paper – 10 Solution
CBSE Board
Class XI Mathematics
Sample Paper – 10 Solution
SECTION – A
1.
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
2. If Mohan is not poor then he is not a poet.
3.
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
OR
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
CBSE XI | Mathematics
Sample Paper – 10 Solution
4. The total number of elementary events associated to the random experiment of thrown
a dice is 6
n
where n is the number of throws. Hence, the total number of elementary
events associated to the random experiment of throwing a three dice together is 6
3
=
216.
SECTION – B
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6
The number of subsets of A × B = 2
6
= 64
The number of relations from A into B = 64
6. f(x) = = sin [log (x +
2
x1 ? )]
f(-x) = sin [log (-x +
2
x1 ? )]
=
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
=
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
=
? ?
1
2
sin log x 1 x
?
??
??
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
= -f(x)
OR
f(x) =
1x
1x
?
?
? ? ?
1 tan
f tan
1 tan
??
??
??
? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
CBSE XI | Mathematics
Sample Paper – 10 Solution
7. Taking ? = x we get area of sector AOB =
2
1
rx
2
22
1
r x s
2
?
2 2 2
1
r x r x
2
? ? S = rx
1
x rad
2
?
OR
5 5 180
300
33
??
? ? ? ?
?
? 1
c
=
180
?
??
??
?
??
180
4 4 720 ? ? ? ? ? ?
?
8. i. A = {L, O, Y, A} and B = {A, L, O, Y}
Clearly A = B
ii. C = {x: x ?Z and x
2
= 36} = {6, -6}
So, C is a finite set.
9. In triangle ABC, if a = 3, b = 5 and c = 7
2 2 2
b c a 25 49 9 65 13
cosA
2bc 2 5 7 70 14
? ? ? ?
? ? ? ?
??
2 2 2
a b c 9 25 49 15 1
cosC
2ab 2 3 5 30 2
? ? ? ? ? ?
? ? ? ?
??
OR
? ? ? ?
22
22
2 2 2 2 2 2 2 2
22
2
CC
a b cos a b sin
22
C C C C C C
a cos sin b cos sin 2ab cos sin
2 2 2 2 2 2
a b 2abcosC
c
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
?
10. If a number n
2
is even then n is even.
CBSE XI | Mathematics
Sample Paper – 10 Solution
11. f(x) is defined for all x satisfying
2
4 x 0 and x 1 0 ? ? ? ?
? ? ? ? x 4 0 and x 1 x 1 0 ? ? ? ? ?
x 4 and x 1 or x 1 ? ? ? ?
? ? ? ?
x , 1 1,4 ? ? ? ? ?
Domain f = ? ? ? ?
, 1 1,4 ? ? ? ?
12. x
2
+ y
2
– 4x + 6y = 12
x
2
– 4x + y
2
+ 6y = 12
x
2
– 4x + 4 + y
2
+ 6y + 9 = 12 + 4 + 9
(x – 2)
2
+ (y + 3)
2
= 25
(x – 2)
2
+ [y – (-3)
2
] = 5
2
Comparing with the equation
(x – a)
2
+ [y – b
2
] = r
2
Radius of the circle is 5 units and centre is (2, -3).
SECTION – C
13. Sin 75° = sin (45° + 30°)
= sin 45°cos 30° + cos 45° sin 30°
=
1 3 1 1
22
22
???
=
31
22
?
Cos 75° = cos (45° + 30°)
= cos 45° cos 30° – sin 45° sin 30°
=
1 3 1 1
22
22
? ? ?
=
31
22
?
tan 15° = tan (45° – 30°)
=
tan45 tan30
1 tan45 tan30
? ? ?
? ? ?
=
1
1
3
1
1
3
?
?
Page 5
CBSE XI | Mathematics
Sample Paper – 10 Solution
CBSE Board
Class XI Mathematics
Sample Paper – 10 Solution
SECTION – A
1.
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
2. If Mohan is not poor then he is not a poet.
3.
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
OR
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
CBSE XI | Mathematics
Sample Paper – 10 Solution
4. The total number of elementary events associated to the random experiment of thrown
a dice is 6
n
where n is the number of throws. Hence, the total number of elementary
events associated to the random experiment of throwing a three dice together is 6
3
=
216.
SECTION – B
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6
The number of subsets of A × B = 2
6
= 64
The number of relations from A into B = 64
6. f(x) = = sin [log (x +
2
x1 ? )]
f(-x) = sin [log (-x +
2
x1 ? )]
=
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
=
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
=
? ?
1
2
sin log x 1 x
?
??
??
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
=
? ?
2
sin log x 1 x
??
? ? ?
??
??
= -f(x)
OR
f(x) =
1x
1x
?
?
? ? ?
1 tan
f tan
1 tan
??
??
??
? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
CBSE XI | Mathematics
Sample Paper – 10 Solution
7. Taking ? = x we get area of sector AOB =
2
1
rx
2
22
1
r x s
2
?
2 2 2
1
r x r x
2
? ? S = rx
1
x rad
2
?
OR
5 5 180
300
33
??
? ? ? ?
?
? 1
c
=
180
?
??
??
?
??
180
4 4 720 ? ? ? ? ? ?
?
8. i. A = {L, O, Y, A} and B = {A, L, O, Y}
Clearly A = B
ii. C = {x: x ?Z and x
2
= 36} = {6, -6}
So, C is a finite set.
9. In triangle ABC, if a = 3, b = 5 and c = 7
2 2 2
b c a 25 49 9 65 13
cosA
2bc 2 5 7 70 14
? ? ? ?
? ? ? ?
??
2 2 2
a b c 9 25 49 15 1
cosC
2ab 2 3 5 30 2
? ? ? ? ? ?
? ? ? ?
??
OR
? ? ? ?
22
22
2 2 2 2 2 2 2 2
22
2
CC
a b cos a b sin
22
C C C C C C
a cos sin b cos sin 2ab cos sin
2 2 2 2 2 2
a b 2abcosC
c
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
?
10. If a number n
2
is even then n is even.
CBSE XI | Mathematics
Sample Paper – 10 Solution
11. f(x) is defined for all x satisfying
2
4 x 0 and x 1 0 ? ? ? ?
? ? ? ? x 4 0 and x 1 x 1 0 ? ? ? ? ?
x 4 and x 1 or x 1 ? ? ? ?
? ? ? ?
x , 1 1,4 ? ? ? ? ?
Domain f = ? ? ? ?
, 1 1,4 ? ? ? ?
12. x
2
+ y
2
– 4x + 6y = 12
x
2
– 4x + y
2
+ 6y = 12
x
2
– 4x + 4 + y
2
+ 6y + 9 = 12 + 4 + 9
(x – 2)
2
+ (y + 3)
2
= 25
(x – 2)
2
+ [y – (-3)
2
] = 5
2
Comparing with the equation
(x – a)
2
+ [y – b
2
] = r
2
Radius of the circle is 5 units and centre is (2, -3).
SECTION – C
13. Sin 75° = sin (45° + 30°)
= sin 45°cos 30° + cos 45° sin 30°
=
1 3 1 1
22
22
???
=
31
22
?
Cos 75° = cos (45° + 30°)
= cos 45° cos 30° – sin 45° sin 30°
=
1 3 1 1
22
22
? ? ?
=
31
22
?
tan 15° = tan (45° – 30°)
=
tan45 tan30
1 tan45 tan30
? ? ?
? ? ?
=
1
1
3
1
1
3
?
?
CBSE XI | Mathematics
Sample Paper – 10 Solution
=
31
31
?
?
=
3 1 3 1
3 1 3 1
??
?
??
=
3 2 3 1
31
??
?
=
4 2 3
2
?
= 23 ?
14.
? ?
1x
f x log
1x
? ??
?
??
?
??
? ? ? ?
1 a 1 b
f a f b log log
1 a 1 b
?? ? ? ? ?
? ? ?
? ? ? ?
??
? ? ? ?
1 a 1 b
log
1 a 1 b
?? ??
??
??
??
??
1 b a ab
log
1 b a ab
? ? ? ??
?
??
? ? ?
??
1 ab b a
log
1 ab b a
? ? ? ??
?
??
? ? ?
??
ba
1
1 ab
log
ba
1
1 ab
? ??
?
??
?
?
??
?
??
?
? ??
ab
f
1 ab
? ??
?
??
?
??
? ? ? ?
ab
f a f b f
1 ab
? ??
??
??
?
??
where
? ?
1x
f x log
1x
? ??
?
??
?
??
15. i. x 2x 1 ??
? ? ? ? f x x and g x 2x 1 ? ? ?
Let domain of f(x) = A and domain of g(x) = B
Thus, ? ? A 0, ?? and
1
B,
2
??
??
?
?
??
Domain of x 2x 1 ?? = A n B =
1
,
2
??
?
?
?
??
ii. ? ? log x 2 3 x ? ? ?
? ? ? ? ? ? f x log x 2 and g x 3 x ? ? ? ?
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FAQs on Sample Solution Paper 10 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce
| 1. What is the importance of studying mathematics in Class 11? |  |
Ans. Studying mathematics in Class 11 is important for several reasons. Firstly, it provides a strong foundation for higher-level mathematics courses in Class 12 and beyond. Secondly, mathematics develops critical thinking and problem-solving skills, which are valuable in various fields. Additionally, it enhances logical reasoning and analytical abilities. Lastly, mathematics is a subject that is used in everyday life, such as in calculating bills, managing finances, and making informed decisions.
| 2. How can I improve my performance in mathematics in Class 11? | |
Ans. Improving performance in mathematics requires consistent effort and practice. Here are some tips to help you improve:
- Regularly attend classes and pay attention to the concepts taught by the teacher.
- Practice solving a variety of problems from textbooks, reference books, and previous year question papers.
- Seek help from teachers or classmates when facing difficulties in understanding a particular topic.
- Create a study schedule and allocate specific time for mathematics practice.
- Work on developing a strong conceptual understanding rather than just memorizing formulas.
- Utilize online resources, educational apps, and interactive tools to reinforce learning.
| 3. What are the important topics to focus on for the Class 11 mathematics exam? | |
Ans. While preparing for the Class 11 mathematics exam, it is crucial to focus on the following important topics:
- Sets and Functions
- Trigonometry
- Algebra
- Coordinate Geometry
- Calculus (Limits and Derivatives)
- Statistics and Probability
- Mathematical Reasoning
- Relations and Functions
These topics form the core of the Class 11 mathematics syllabus and are likely to be extensively covered in the exam.
| 4. How can I manage time effectively during the Class 11 mathematics exam? | |
Ans. Managing time effectively during the Class 11 mathematics exam is essential to complete the paper within the given duration. Here are some time management tips:
- Familiarize yourself with the exam pattern and marking scheme beforehand.
- Read the question paper thoroughly and prioritize the questions based on difficulty level.
- Allocate time for each section or topic based on the number of marks assigned to it.
- Start with the easier questions to build confidence and save time for challenging ones.
- Avoid spending too much time on a single question; if stuck, move on and return to it later if time permits.
- Keep track of the time using a wristwatch or the clock in the examination hall.
- Reserve some time at the end for reviewing and correcting any errors.
| 5. Are there any additional resources available for Class 11 mathematics exam preparation? | |
Ans. Yes, there are several additional resources available for Class 11 mathematics exam preparation. Some of them include:
- Reference books and study guides specifically designed for Class 11 mathematics.
- Online platforms offering video tutorials, practice questions, and mock tests.
- Educational websites providing interactive lessons, quizzes, and solutions to textbook problems.
- Mobile applications with math-related exercises and explanations.
- Joining study groups or online forums where students can discuss and clarify doubts.
- Seeking guidance from experienced teachers or tutors who can provide personalized assistance.
These additional resources can supplement your regular textbook study and help you strengthen your understanding of the subject.
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Document Description: Sample Solution Paper 10 - Math, Class 11 for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation.
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