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Page 1
CBSE XI | Mathematics
Sample Paper – 6
w
CBSE Board
Class XI Mathematics
Sample Paper – 6
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 the derivative of cos[sin v x].
2. Write negation of : “Either he is bald or he is tall.”
3. Express
6
i ?
in the form of b or bi where b is a real number.
OR
Find modulus of sin ? – i cos ?.
4. Two coins tossed simultaneously, find the probability that getting two heads.
SECTION – B
5. A and B are sub-sets of U where U is universal set containing 700 elements. n(A) = 200,
n(B) = 300 and n (A n B) = 100. Find n(A’ n B’).
6. If the function f : N ? N is defined by f(x) = vx then find
? ?
? ? ? ?
f 25
f 16 f 1 ?
.
OR
If f(x) = x
2
– 1 and g(x) = vx find f ° g(x) =?
Page 2
CBSE XI | Mathematics
Sample Paper – 6
w
CBSE Board
Class XI Mathematics
Sample Paper – 6
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 the derivative of cos[sin v x].
2. Write negation of : “Either he is bald or he is tall.”
3. Express
6
i ?
in the form of b or bi where b is a real number.
OR
Find modulus of sin ? – i cos ?.
4. Two coins tossed simultaneously, find the probability that getting two heads.
SECTION – B
5. A and B are sub-sets of U where U is universal set containing 700 elements. n(A) = 200,
n(B) = 300 and n (A n B) = 100. Find n(A’ n B’).
6. If the function f : N ? N is defined by f(x) = vx then find
? ?
? ? ? ?
f 25
f 16 f 1 ?
.
OR
If f(x) = x
2
– 1 and g(x) = vx find f ° g(x) =?
CBSE XI | Mathematics
Sample Paper – 6
7. Find the range of the function f(x) = |x – 3|
OR
Let a and B be two sets such that : n(A) = 50, n(A ? B) = 60 and n(A n B) = 10.
Find n(B) and n(A – B).
8. Let A = {6, 8} and B = {3, 5}. Write A × B and A × A.
9.
cos A sin A 1
Prove that:
1 tan A 1 cot A cosA sin A
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
OR
Prove that tan
4
? + tan
2
? = sec
4
? - sec
2
?
10. By giving an example, show that the following statement is false.
“If n is an odd integer, then n is prime.”
11. If a, b, c are in GP then prove that log a
n
, log b
n
and log c
n
are in AP.
12. The focal distance of a point on the parabola y
2
= 12x is 4. Find the abscissa of this point.
SECTION – C
13. If tan (pcos ?) = cot (psin ?) prove that
1
cos
4
22
? ??
? ? ? ?
??
??
.
14. Let a relation R1 on the set of R of all real numbers be defined as (a, b) ? R1 ?
1 + ab > 0 for all a, b ?R. Show that (a, a) ? R1 for all a ? R and (a, b) ? R1 ?
(b, a) ? R1 for all a, b ?R.
15. Prove that
4
2 3 4 1
cos cos cos cos
9 9 9 9 2
? ? ? ?
? .
16. If x = a + b, y =ab ? ? ? , z = ab ? ? ? where , ?? are complex cube root of unity. Show
that xyz = a
3
+ b
3
.
17. A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random from
the bag, find the probability that they are not of the same colour.
18. The sums of first p, q, r terms of an AP are a, b, c respectively. Prove that
? ? ? ? ? ?
a b c
q r r p p q 0
p q r
? ? ? ? ? ?
Page 3
CBSE XI | Mathematics
Sample Paper – 6
w
CBSE Board
Class XI Mathematics
Sample Paper – 6
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 the derivative of cos[sin v x].
2. Write negation of : “Either he is bald or he is tall.”
3. Express
6
i ?
in the form of b or bi where b is a real number.
OR
Find modulus of sin ? – i cos ?.
4. Two coins tossed simultaneously, find the probability that getting two heads.
SECTION – B
5. A and B are sub-sets of U where U is universal set containing 700 elements. n(A) = 200,
n(B) = 300 and n (A n B) = 100. Find n(A’ n B’).
6. If the function f : N ? N is defined by f(x) = vx then find
? ?
? ? ? ?
f 25
f 16 f 1 ?
.
OR
If f(x) = x
2
– 1 and g(x) = vx find f ° g(x) =?
CBSE XI | Mathematics
Sample Paper – 6
7. Find the range of the function f(x) = |x – 3|
OR
Let a and B be two sets such that : n(A) = 50, n(A ? B) = 60 and n(A n B) = 10.
Find n(B) and n(A – B).
8. Let A = {6, 8} and B = {3, 5}. Write A × B and A × A.
9.
cos A sin A 1
Prove that:
1 tan A 1 cot A cosA sin A
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
OR
Prove that tan
4
? + tan
2
? = sec
4
? - sec
2
?
10. By giving an example, show that the following statement is false.
“If n is an odd integer, then n is prime.”
11. If a, b, c are in GP then prove that log a
n
, log b
n
and log c
n
are in AP.
12. The focal distance of a point on the parabola y
2
= 12x is 4. Find the abscissa of this point.
SECTION – C
13. If tan (pcos ?) = cot (psin ?) prove that
1
cos
4
22
? ??
? ? ? ?
??
??
.
14. Let a relation R1 on the set of R of all real numbers be defined as (a, b) ? R1 ?
1 + ab > 0 for all a, b ?R. Show that (a, a) ? R1 for all a ? R and (a, b) ? R1 ?
(b, a) ? R1 for all a, b ?R.
15. Prove that
4
2 3 4 1
cos cos cos cos
9 9 9 9 2
? ? ? ?
? .
16. If x = a + b, y =ab ? ? ? , z = ab ? ? ? where , ?? are complex cube root of unity. Show
that xyz = a
3
+ b
3
.
17. A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random from
the bag, find the probability that they are not of the same colour.
18. The sums of first p, q, r terms of an AP are a, b, c respectively. Prove that
? ? ? ? ? ?
a b c
q r r p p q 0
p q r
? ? ? ? ? ?
CBSE XI | Mathematics
Sample Paper – 6
19. How many different numbers can be formed with the digits 1, 3, 5, 7, 9 when takes all
at a time, and what is their sum?
OR
A student is to answer 10 out of 13 questions in an examination such that he must
choose at least 4 from the first five questions. Find the number of choices available to
him.
20. Find all the points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y =
10.
OR
Find the equation of the internal bisector of angle BAC of the triangle ABC whose
vertices A, B, C are (5, 2), (2, 3) and (6, 5) respectively.
21. If in a ?ABC,
? ?
? ?
sin A B
sin A
sinC sin B C
?
?
?
prove that a
2
, b
2
, c
2
are in AP.
OR
Prove that
cos5x cos4x
cos2x cosx
1 2cos3x
?
? ? ?
?
22. Find the value of k, if
4 3 3
22
x 1 x k
x 1 x k
lim lim
x 1 x k
??
??
?
??
23. Using binomial theorem, prove that 6
n
– 5n always leaves the remainder 1 when
divided by 25.
SECTION – D
24. Prove that
1. tan3A tan2AtanA = tan3A – tan2A – tanA
2. cotAcot2A – cot2Acot3A – cot3AcotA = 1
OR
If A = cos
2
? + sin
4
? prove that
3
A1
4
?? for all values of ?.
25. Find the mean deviation about the median for the following data:
x 10 15 20 25 30 35 40 45
f 7 3 8 5 6 8 4 9
Page 4
CBSE XI | Mathematics
Sample Paper – 6
w
CBSE Board
Class XI Mathematics
Sample Paper – 6
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 the derivative of cos[sin v x].
2. Write negation of : “Either he is bald or he is tall.”
3. Express
6
i ?
in the form of b or bi where b is a real number.
OR
Find modulus of sin ? – i cos ?.
4. Two coins tossed simultaneously, find the probability that getting two heads.
SECTION – B
5. A and B are sub-sets of U where U is universal set containing 700 elements. n(A) = 200,
n(B) = 300 and n (A n B) = 100. Find n(A’ n B’).
6. If the function f : N ? N is defined by f(x) = vx then find
? ?
? ? ? ?
f 25
f 16 f 1 ?
.
OR
If f(x) = x
2
– 1 and g(x) = vx find f ° g(x) =?
CBSE XI | Mathematics
Sample Paper – 6
7. Find the range of the function f(x) = |x – 3|
OR
Let a and B be two sets such that : n(A) = 50, n(A ? B) = 60 and n(A n B) = 10.
Find n(B) and n(A – B).
8. Let A = {6, 8} and B = {3, 5}. Write A × B and A × A.
9.
cos A sin A 1
Prove that:
1 tan A 1 cot A cosA sin A
? ? ? ?
??
? ? ? ?
? ? ?
? ? ? ?
OR
Prove that tan
4
? + tan
2
? = sec
4
? - sec
2
?
10. By giving an example, show that the following statement is false.
“If n is an odd integer, then n is prime.”
11. If a, b, c are in GP then prove that log a
n
, log b
n
and log c
n
are in AP.
12. The focal distance of a point on the parabola y
2
= 12x is 4. Find the abscissa of this point.
SECTION – C
13. If tan (pcos ?) = cot (psin ?) prove that
1
cos
4
22
? ??
? ? ? ?
??
??
.
14. Let a relation R1 on the set of R of all real numbers be defined as (a, b) ? R1 ?
1 + ab > 0 for all a, b ?R. Show that (a, a) ? R1 for all a ? R and (a, b) ? R1 ?
(b, a) ? R1 for all a, b ?R.
15. Prove that
4
2 3 4 1
cos cos cos cos
9 9 9 9 2
? ? ? ?
? .
16. If x = a + b, y =ab ? ? ? , z = ab ? ? ? where , ?? are complex cube root of unity. Show
that xyz = a
3
+ b
3
.
17. A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random from
the bag, find the probability that they are not of the same colour.
18. The sums of first p, q, r terms of an AP are a, b, c respectively. Prove that
? ? ? ? ? ?
a b c
q r r p p q 0
p q r
? ? ? ? ? ?
CBSE XI | Mathematics
Sample Paper – 6
19. How many different numbers can be formed with the digits 1, 3, 5, 7, 9 when takes all
at a time, and what is their sum?
OR
A student is to answer 10 out of 13 questions in an examination such that he must
choose at least 4 from the first five questions. Find the number of choices available to
him.
20. Find all the points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y =
10.
OR
Find the equation of the internal bisector of angle BAC of the triangle ABC whose
vertices A, B, C are (5, 2), (2, 3) and (6, 5) respectively.
21. If in a ?ABC,
? ?
? ?
sin A B
sin A
sinC sin B C
?
?
?
prove that a
2
, b
2
, c
2
are in AP.
OR
Prove that
cos5x cos4x
cos2x cosx
1 2cos3x
?
? ? ?
?
22. Find the value of k, if
4 3 3
22
x 1 x k
x 1 x k
lim lim
x 1 x k
??
??
?
??
23. Using binomial theorem, prove that 6
n
– 5n always leaves the remainder 1 when
divided by 25.
SECTION – D
24. Prove that
1. tan3A tan2AtanA = tan3A – tan2A – tanA
2. cotAcot2A – cot2Acot3A – cot3AcotA = 1
OR
If A = cos
2
? + sin
4
? prove that
3
A1
4
?? for all values of ?.
25. Find the mean deviation about the median for the following data:
x 10 15 20 25 30 35 40 45
f 7 3 8 5 6 8 4 9
CBSE XI | Mathematics
Sample Paper – 6
26.
4 x x x
If x and tanx ,find sin , cos , tan .
2 3 2 2 2
?
? ? ? ? ?
27. Solve the following system of inequalities graphically:
3x + 2y ? 150; x + 4y ? 80; x ? 15; x ? 0; y ? 0
OR
How many litres of water will have to be added to 1125 litres of the 45% solution of
acid so that the resulting mixture will contain more than 25% but less than 30% acid
content?
28. If the coefficients of a
r – 1
, a
r
and a
r + 1
in the binomial expansion of (1 + a)
n
are in AP,
prove that n
2
– n(4r + 1) + 4r
2
– 2 = 0
29. Along a road lie an odd number of stones placed at intervals of 10 m. These stones have
to be assembled around the middle stone. A person can carry only one stone at a time.
A man carried the job with one of the end stones by carrying them in succession. In
carrying all the stones he covered a distance of 3 km. Find the number of stones.
OR
Find the sum of an infinitely decreasing GP, whose first term is equal to b +2 and the
common ratio to 2/c, where b is the least value of the product of the roots of the
equation (m
2
+ 1)x
2
– 3x + (m
2
+ 1)
2
= 0 and c is the greatest value of the sum of its
roots.
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FAQs on Sample Question Paper 6 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce
| 1. What are the important topics covered in the Class 11 Math exam? |  |
Ans. The important topics covered in the Class 11 Math exam include sets, relations, functions, trigonometry, sequences and series, limits and derivatives, mathematical reasoning, statistics, and probability.
| 2. How can I prepare effectively for the Class 11 Math exam? | |
Ans. To prepare effectively for the Class 11 Math exam, you can follow these tips:
- Understand the concepts and theories thoroughly.
- Practice solving a variety of problems from each topic.
- Create a study schedule and allocate specific time for each topic.
- Refer to textbooks, class notes, and online resources for additional practice materials.
- Seek help from your teacher or classmates if you have any doubts or difficulties.
- Take regular breaks during your study sessions to avoid burnout.
| 3. Are there any recommended reference books for Class 11 Math exam preparation? | |
Ans. Yes, there are several recommended reference books for Class 11 Math exam preparation. Some popular ones include:
- "Mathematics for Class 11" by R.D. Sharma
- "NCERT Exemplar Problems: Solutions Mathematics Class 11" by Disha Experts
- "Mathematics for Class 11 (Set of 2 Volumes)" by R.D. Sharma
- "NCERT Solutions Mathematics Class 11" by Disha Experts
| 4. How can I improve my problem-solving skills for the Class 11 Math exam? | |
Ans. To improve your problem-solving skills for the Class 11 Math exam, you can follow these strategies:
- Understand the problem statement thoroughly before attempting to solve it.
- Break down complex problems into smaller, manageable steps.
- Practice solving a variety of problems from different topics.
- Analyze your mistakes and learn from them.
- Seek help from your teacher or classmates if you're stuck on a problem.
- Try to solve problems using different methods and approaches to enhance your problem-solving abilities.
| 5. Are there any online resources or websites that can help in Class 11 Math exam preparation? | |
Ans. Yes, there are several online resources and websites that can help in Class 11 Math exam preparation. Some popular ones include:
- Khan Academy: Offers video lessons and practice exercises for various math topics.
- NCERT Solutions: Provides solutions to NCERT textbooks and exemplar problems.
- TopperLearning: Offers study materials, video lessons, and practice tests.
- Vedantu: Provides live online classes and doubt-solving sessions.
- ExamFear: Offers video lessons and practice questions for CBSE and other board exams.
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Dec 22, 2024 Last updated |
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